阅读说明：本技术 用于确定对估计的局部状态矢量的更新的估计器 (Estimator for determining an update to an estimated local state vector ) 是由 R·李 C·J·柳 于 2021-04-21 设计创作，主要内容包括：本申请涉及用于确定对估计的局部状态矢量的更新的估计器,并且公开了一种作为包括多个节点的通信网络的一部分的估计器。该估计器的中心化部分包括：一个或多个处理器,其与作为通信网络的一部分的多个节点无线地通信,其中该通信网络包括一对或多对协作节点；以及存储器,其耦合到一个或多个处理器,该存储器将数据存储成数据库和程序代码,该程序代码在由一个或多个处理器执行时使估计器的中心化部分确定局部更新和协作更新。协作更新应用于该对协作节点中的两个节点的相应估计的局部状态矢量。(The present application relates to an estimator for determining updates to an estimated local state vector, and discloses an estimator as part of a communication network comprising a plurality of nodes. The centralized portion of the estimator comprises: one or more processors that wirelessly communicate with a plurality of nodes that are part of a communication network, wherein the communication network includes one or more pairs of cooperating nodes; and a memory coupled to the one or more processors, the memory storing data as a database and program code, the program code when executed by the one or more processors, causing the centralized portion of the estimator to determine local updates and collaborative updates. The cooperation update is applied to the respective estimated local state vectors of both nodes of the pair of cooperating nodes.)

1. An estimator (140) as part of a communication network (10) comprising a plurality of nodes (18), wherein a centralized portion (100) of the estimator (140) comprises:

one or more processors (1032) in wireless communication with the plurality of nodes (18) that are part of the communication network (10), wherein the communication network (10) includes one or more pairs of cooperating nodes (18i, 18 j); and

a memory (1034) coupled to the one or more processors (1032), the memory (1034) storing data as a database (1044) and program code that, when executed by the one or more processors (1032), causes the centralized portion (100) of the estimator (140) to:

receiving, from each of the plurality of nodes (18) that are part of the communication network (10), a respective estimated local state vector, a respective estimated local measurement, a respective local residual, and a respective local measurement;

determining an overall error covariance matrix for the communication network (10) based on the respective estimated local state vector for each of the plurality of nodes (18) that are part of the communication network (10);

determining a respective local update (146) based on the total error covariance matrix and the local residuals for each of the plurality of nodes (18), wherein the respective local update (146) applies to the respective estimated local state vector for a particular node (18 i);

predicting an estimated cooperation measurement based on a cooperation measurement between a pair of cooperating nodes (18i, 18j) that are part of the communication network (10), wherein a cooperation residual is associated with the estimated cooperation measurement; and is

Determining a cooperation update (148) based on the estimated cooperation measure and the cooperation residual, wherein the cooperation update (148) is applied to the respective estimated local state vector of both nodes of the pair of cooperating nodes (18i, 18 j).

2. The estimator (140) according to claim 1, wherein the estimated cooperative measurement is based on a local state vector and a cooperative measurement vector for each node being part of the pair of cooperative nodes (18i, 18 j).

3. The estimator (140) according to claim 2, wherein the cooperation residual represents a difference between the cooperation measurement vector and the estimated cooperation measurement.

4. The estimator (140) of claim 1, wherein the one or more processors (1032) execute instructions to:

determining a cooperative measurement sensitivity matrix representing an amount of change experienced by the cooperative measurement result based on a corresponding change in a local state vector of a node (18i) with respect to which the cooperative measurement is made;

determining a composite covariance matrix that characterizes an uncertainty in the cooperative measurement when an effect of one or more states of a cooperative node (18j) of the pair of cooperative nodes (18i, 18j) is modeled as random noise; and is

Determining a cooperative error covariance matrix of the cooperative residuals based at least on the cooperative measurement sensitivity matrix and the composite covariance matrix.

5. The estimator (140) according to claim 4, wherein the one or more processors (1032) execute instructions to:

determining a cooperation gain matrix based on the cooperation error covariance matrix and the cooperation measurement sensitivity matrix of the cooperation residual; and is

Combining the cooperation gain matrix with the cooperation residual to create the cooperation update (148).

6. The estimator (140) according to claim 5, wherein the cooperation update (148) is a product of the cooperation gain matrix and the cooperation residual.

7. The estimator (140) according to claim 1, wherein the centralized portion (100) of the estimator (140) is comprised in one of the plurality of nodes (18) of the communication network (10).

8. The estimator (140) according to any one of claims 1-7, wherein the one or more processors (1032) execute instructions to:

determining a respective local measurement sensitivity matrix representing an amount of change experienced by a local measurement result for a particular node (18i) based on a change in a respective local state vector for the particular node (18 i);

determining a respective local measurement variance matrix representing an uncertainty in the local measurement for the particular node (18 i); and is

Determining a respective local residual covariance matrix for each of the plurality of nodes (18) that are part of the communication network (10) based on the total error covariance matrix and the respective local measurement variance matrix for the communication network (10).

9. The estimator (140) of claim 8, wherein the one or more processors (1032) execute instructions to:

determining a respective local gain matrix for the particular node (18i) based on the respective local residual covariance matrix for the particular node (18i), the total error covariance matrix for the communication network (10), and the respective local measurement sensitivity matrix for the particular node (18 i); and is

Combining the local residuals for the particular node (18i) with the respective local gain matrix to create the respective local update (146).

10. The estimator (140) according to claim 9, wherein the respective local update (146) is a product of the respective local residual corresponding to the particular node (18i) and the respective local gain matrix.

11. The estimator (140) according to claim 1, wherein the respective local residual for the particular node (18i) represents a difference between a local measurement vector for the particular node (18i) and the respective estimated local measurement.

12. The estimator (140) of claim 1, wherein the communication network (10) is part of a cooperative positioning, navigation, and timing system, PNT, system (26).

13. The estimator (140) according to claim 12, wherein the cooperative measurements between an individual node (18i) and a cooperative node (18j) comprise relative distance measurements between the individual node (18i) and the cooperative node (18j) in combination with relative line of sight (LOS) measurements between the individual node (18i) and the cooperative node (18 j).

14. The estimator (140) according to claim 13, wherein the relative distance measurement is represented by a first relative distance measured between the individual node (18i) and the cooperative node (18j) as measured by the individual node (18i) and a second relative distance measured between the individual node (18i) and the cooperative node (18j) as measured by the cooperative node (18 j).

15. The estimator (140) of claim 13, wherein the relative LOS measurement comprises:

a first relative LOS measurement represented by a first unit vector pointing from the individual node (18i) to the cooperative node (18j), wherein the first relative LOS measurement is measured by the individual node (18 i); and

a second relative LOS measurement represented by a second unit vector pointing from the cooperating node (18j) to the individual node (18i), wherein the second relative LOS measurement is measured by the cooperating node (18 j).

16. The estimator (140) according to claim 12, wherein the cooperative measurement comprises a first relative range measurement measured between an individual node (18i) and a cooperative node (18j) as measured with respect to the individual node (18i), and a second relative range measurement measured between the individual node (18i) and the cooperative node (18j) as measured with respect to the cooperative node (18 j).

Technical Field

The present disclosure relates to an estimator for a communication network. More particularly, the present disclosure relates to an estimator for determining updates for individual nodes based on local and collaborative measurements between other nodes that are part of a communication network.

Background

A collaborative positioning, navigation and timing (PNT) system includes a group of users interconnected by a wireless communications network. Each user may be a vehicle or may be an individual comprising a PNT device and a sensor, each user being referred to as a node. Each node that is part of the PNT system may be located in a different geographic area. Thus, some nodes may be located in locations where Global Navigation Satellite System (GNSS) based signals are widely available, while other nodes may receive very limited signals or no signals at all. For example, a group of tall buildings or tall buildings in an urban (referred to as an urban canyon) tend to block GNSS signals. In another example, some nodes may be located in areas with substantial radio frequency interference or congestion.

Some nodes may be equipped with only GNSS receivers and therefore, in some cases, may not be able to receive signals. However, other nodes may include combined GNSS and inertial measurement units. Some other nodes may include astronomical navigation systems or vision based navigation systems that can provide PNT solutions even when GNSS signals are not available. However, cooperative PNT systems help alleviate some of these problems by allowing nodes to utilize not only their own information, but also information available on the wireless network.

Disclosure of Invention

According to several aspects, an estimator as part of a communication network comprising a plurality of nodes is disclosed. The centralized portion of the estimator comprises: one or more processors in wireless communication with a plurality of nodes that are part of a communication network, wherein the communication network comprises one or more pairs of cooperating nodes; and a memory coupled to the one or more processors, the memory storing data as a database and program code that, when executed by the one or more processors, causes the centralized portion of the estimator to receive, from each of a plurality of nodes that are part of the communication network, a respective estimated local state vector, a respective estimated local measurement, a respective local residual, and a respective local measurement. A centralized portion of the estimator determines an overall error covariance matrix for the communication network based on the respective estimated local state vectors for each of a plurality of nodes that are part of the communication network. The centralized portion of the estimator determines a respective local update based on the total error covariance matrix and a local residual for each of the plurality of nodes. The respective local update is applied to the respective estimated local state vector for the particular node. The centralized portion of the estimator further predicts an estimated cooperative measurement based on a cooperative measurement between a pair of cooperating nodes that are part of the communication network, wherein a cooperative residual is associated with the estimated cooperative measurement. The centralized portion of the estimator further determines a cooperation update based on the estimated cooperation measurements and the cooperation residuals, wherein the cooperation update is applied to respective estimated local state vectors of two nodes of the pair of cooperating nodes.

In another aspect, a method for updating, by a centralized portion of an estimator, estimated local state vectors for a plurality of nodes that are part of a communication network is disclosed. The method includes receiving, by a centralized portion of an estimator, from each of a plurality of nodes that are part of a communication network, a respective estimated local state vector, a respective estimated local measurement, a respective local residual, and a respective local measurement. The method also includes determining, by the centralized portion of the estimator, an overall error covariance matrix for the communication network based on the respective estimated local state vector for each of the plurality of nodes that are part of the communication network. The method also includes determining, by the centralized portion of the estimator, a respective local measurement sensitivity matrix that represents an amount of change that the local measurement for the particular node experienced based on a change in the respective local state vector for the particular node. The method further includes determining, by the centralized portion of the estimator, a respective local measurement variance matrix that represents an uncertainty in the local measurement for the particular node. The method also includes determining, by the centralized portion of the estimator, a respective local residual covariance matrix for each of a plurality of nodes that are part of the communication network based on the total error covariance matrix and the respective local measurement variance matrix for the communication network. The method also includes determining, by the centralized portion of the estimator, a respective local gain matrix for the particular node based on the respective local residual covariance matrix for the particular node, the total error covariance matrix for the communication network, and the respective local measurement sensitivity matrix for the particular node. The method also includes combining, by the centralized portion of the estimator, the local residuals for the particular node with the respective local gain matrix to create respective local updates. The method also includes predicting, by the centralized portion of the estimator, an estimated cooperative measurement based on a cooperative measurement between a pair of cooperating nodes that are part of the communication network, wherein a cooperative residual is associated with the estimated cooperative measurement. The method also includes determining, by the centralized portion of the estimator, a cooperative measurement sensitivity matrix that represents an amount of change experienced by the cooperative measurement result based on a corresponding change in the respective local state vector for the particular node relative to which the cooperative measurement is being made. The method also includes determining, by the centralized portion of the estimator, a composite covariance matrix that characterizes an uncertainty in the cooperative measurements when an effect of one or more states of a cooperative node of the pair of cooperative nodes is modeled as random noise. The method includes determining, by a centralized portion of the estimator, a collaborative error covariance matrix of the collaborative residuals based at least on the collaborative measurement sensitivity matrix and the composite covariance matrix. The method also includes determining, by the centralized portion of the estimator, a cooperation gain matrix based on a cooperation error covariance matrix of the cooperation residuals and a cooperation measurement sensitivity matrix. Finally, the method includes combining, by the centralized portion of the estimator, the cooperation gain matrix with the cooperation residual to create a cooperation update.

The features, functions, and advantages that have been discussed can be achieved independently in various embodiments or may be combined in yet other embodiments further details of which can be seen with reference to the following description and drawings.

Drawings

The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way.

FIG. 1 is a schematic illustration of a disclosed communication network having a plurality of nodes in wireless communication with each other, according to an example embodiment;

FIG. 2 is a schematic diagram of a communication network according to a local and direct neighbor (LWIN) approach with estimated state vectors for updating individual nodes, according to an example embodiment;

FIG. 3 is a schematic diagram of individual nodes performing local measurement based and collaborative measurement based update of estimated state vectors according to an example embodiment based on the LWIN approach;

FIG. 4 illustrates a collaborative positioning, navigation and timing (PNT) system in accordance with an exemplary embodiment;

FIG. 5A illustrates one example of cooperative measurements between individual nodes and cooperative nodes including relative distance measurements combined with relative line of sight (LOS) measurements, according to an example implementation;

fig. 5B illustrates another example of cooperative measurement results between an individual node and a cooperative node including relative LOS direction measurement results according to an exemplary embodiment;

fig. 5C illustrates yet another example of cooperative measurement results between individual nodes and cooperative nodes including relative range measurement results according to an exemplary embodiment;

6A-6B illustrate a process flow diagram showing a method for determining updates for estimated state vectors for individual nodes based on the LWIN approach, according to an exemplary embodiment;

FIG. 7 is a schematic diagram of a communication network according to an Integrated Total Network Solutions (ITNS) approach for updating estimated state vectors, according to an exemplary embodiment;

FIG. 8 is a schematic diagram of a centralized portion of the estimator shown in FIG. 7 determining local and collaborative updates for each node that is part of a communication network in accordance with an exemplary embodiment;

9A-9B illustrate a process flow diagram showing a method for determining updates for estimated state vectors for individual nodes based on the ITNS pathway in accordance with an exemplary embodiment; and

FIG. 10 is a computing system for the disclosed estimator, according to an exemplary embodiment.

Detailed Description

The present disclosure relates to an estimator for determining corrections or updates to estimated local state vectors applied to individual nodes. The updating is based on the local measurements and the cooperative measurements between the individual nodes and the cooperative nodes. The present disclosure describes two different approaches for updating estimated local state vectors for individual nodes. In a first example, the individual node comprises its own estimator and the estimated local state vector is updated based on the local measurements and the cooperative measurements between the individual node and the cooperative nodes. This decentralized approach is called the local and direct neighbor (LWIN) approach. In a second approach, a portion of the local update for each node is performed locally, while the collaborative update for each pair of collaborative nodes is performed at the centralized (centralized) portion of the estimator. This is a more centralized approach and is therefore referred to as the Integrated Total Network Solution (ITNS) approach. Both approaches improve the accuracy of the estimated local state vector for each node, since the update is not only based on local measurements, but also on cooperative measurements between nodes.

The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses.

Referring to fig. 1, an exemplary communication network 10 having a plurality of nodes 18 is shown. The nodes 18 communicate wirelessly with each other over a network connection 20. Each node 18 that is part of the communication network 10 is configured to collect local measurements and cooperative measurements measured between two cooperating nodes 18. Some examples of local and collaborative measurements include, but are not limited to, time transfer and synchronization, three-dimensional images, range measurements between nodes 18, line of sight (LOS) measurements between nodes 18, angle of arrival (AOA) measurements between nodes 18, or direction of arrival (DOA) between nodes 18. Node 18 represents any device configured to estimate a local state vector, such as, for example, a machine, a vehicle, or an individual such as a soldier. For example, in one embodiment, nodes 18 may each represent a machine, where nodes 18 are located in a manufacturing facility. As explained below and shown in FIG. 4, in another embodiment, the nodes 18 each represent a user that is part of a collaborative positioning, navigation, and timing (PNT) network 26.

Referring to fig. 2 and 3, in one approach, the individual nodes 18i include an estimator 40, which estimator 40 determines updates to the estimated local state vectors. The update is determined based on the local measurement and the cooperative measurement measured between the individual node 18i and the cooperative node 18 j. This approach is referred to as the local and direct neighbor (LWIN) approach because all computations are performed locally at the individual nodes 18 i. Alternatively, in the embodiment as shown in fig. 7 and 8, the communication network 10 comprises a distributed approach. In particular, such an approach includes estimators 140 distributed throughout communication network 10. Specifically, a portion 98 of the estimator 140 is locally located at each node 18 that is part of the communication network 10 and determines some local updates. The centralized portion 100 of the estimator 140 determines a remaining portion of the local update for each node 18 that is part of the communication network 10 and determines a collaborative update based on collaborative measurements between two collaborative nodes 18. This approach is referred to as Integrated Total Network Solution (ITNS) because some of the calculations are performed at the centralized portion 100 of the estimator 140.

Returning to fig. 2, in the LWIN approach, each node 18 wirelessly communicates with at least one other neighboring node 18 that is part of the communication network 10. For purposes of this disclosure, a neighboring node 18 refers to a logical or topological relationship between two nodes 18. Further, although fig. 2 shows nodes 18i and 18j in electronic communication with each other, nodes 18k and 18n in electronic communication with each other, and nodes 18j and 18n in electronic communication with each other, it should be understood that each node 18 may communicate with all of the remaining nodes 18 that are part of communication network 10. In particular, if there are n nodes that are part of the communication network 10, each node 18 may wirelessly communicate with up to n-1 nodes.

Each node 18 includes a computing system 30, a measurement device 32, a transceiver 34, and an antenna 36, wherein the nodes 18 wirelessly communicate with each other through their respective antennas 36. The computing system 30 is in electronic communication with the measurement device 32, the transceiver 34, and the antenna 36. Measurement apparatus 32 represents any apparatus or combination of apparatuses configured to collect local and cooperative measurements for respective nodes 18. For example, in one embodiment, if the local measurement is a three-dimensional image, the measurement device 32 includes one or more cameras. In another embodiment, the measurement device 32 is a PNT system that determines the location of the respective node 18 in the Earth's reference frame. It should be understood that the PNT system is not limited to a particular type of system. For example, some nodes 18 that are part of the communication network 10 may include only Global Navigation Satellite System (GNSS) receivers as PNT systems. However, other nodes 18 may include GNSS receivers in combination with inertial measurement units as PNT systems. Alternatively, in another approach, some nodes 18 may include a vision-based navigation system or an astronomical navigation system as the PNT system.

Fig. 3 is a schematic diagram of a computing system 30 of the individual node 18i shown in fig. 2 that includes an estimator 40, the estimator 40 configured to determine a local update 46 based on local measurements collected from the measurement devices 32 (fig. 2) of the individual node 18 i. The local measurement results represent information based only on individual nodes 18 i. The estimator 40 is also configured to determine a cooperation update 48 (as shown in fig. 2) based on cooperation measurements between the individual nodes 18i and the cooperating nodes 18 j. The cooperative measurement result between the individual node 18i and the cooperative node 18j is measured with respect to the individual node 18 i.

The estimator 40 includes a local state propagation block 50, a local measurement block 52, and a local update block 54 for determining the local updates 46. The local state propagation block 50 determines a plurality of local state propagators (promoters). The plurality of local state propagators includes an estimated local state vector for the individual node 18i and a local error covariance matrix of the estimated local state vector. The local state propagation block 50 receives the local state vector x_i(k) Deterministic input vector u_i(k) And local measurement result vector z_i(k) As an input, where k denotes a specific point in time. Local state vector x_i(k) Deterministic input vector u_i(k) And local measurement result vector z_i(k) Based on measurements from individual nodes 18iThe local measurements collected by the device 32 (fig. 2).

The local state propagation block 50 includes a local state propagation block 60 and a local error covariance block 62. The local state propagation block 60 is based on the local state vector x according to equation 1_i(k) And a deterministic input vector u_i(k) Estimating the estimated local state vector for the individual node 18i, equation 1 is as follows:

whereinIs the estimated local state vector for the individual node 18i until the time point (k-1), and f_iRepresents a function that models the dynamic behavior of the communication network 10 (fig. 1) at the individual nodes 18 i.

Local error covariance block 62 determines local state vectors for estimationThe local error covariance matrix of (2). Local error covariance matrix characterization of estimated local state vectorsThe error of (2). Local error covariance matrix based on local measurements and estimated local state vectorsIs determined and expressed in equation 2:

P_i(k|k-1)＝Φ_i(k-1)P_i(k-1|k-1)Φ_i ^T(k-1)+Q_i(k) equation 2

Wherein P is_i(k | k-1) is a local error covariance matrix when the time based on the measurement results until the time point (k-1) is equal to (k-1), P_i(k-1| k-1) is based on the measurement results up to the time point (k-1)Covariance matrix, Φ, for individual nodes 18i when time equals k_iIs a state transition matrix, Φ, for the node 18i_i ^TRepresents a transposed state transition matrix, and Q_i(k) Is the process noise covariance matrix for node 18 i. It should be understood that the state transition matrix Φ_iSum process noise covariance matrix Q_i(k) Are all block diagonal matrices, which may result in a reduced computational effort.

The local measurement block 52 predicts estimated local measurements of the individual nodes 18iAnd local residual mu_i. In particular, the local measurement block 52 includes a local measurement prediction block 64 based on a deterministic input vector u according to equation 3_i(k) Local measurement result vector z_i(k) And local state vectors for individual nodes 18iTo predict estimated local measurements of individual nodes 18iThe equation 3 is as follows:

wherein g is_iA function is represented which represents a local measurement model at an individual node 18 i. Local residual mu_iLocal measurement results with estimation of individual nodes 18iAnd (4) associating. In particular, the local measurement block 52 includes a local residual block 66 that is based on a local measurement result vector z_i(k) And estimated local measurementsFor determining the difference betweenLocal residual mu at individual node 18i_iAnd is expressed as:

the local update block 54 includes a local measurement sensitivity block 68, a local residual covariance matrix block 70, and a local gain matrix block 72. The local update block 54 determines a local update 46, which local update 46 is applied to the local covariance matrix P for the individual node 18i_i(k-1| k-1) and estimated local state vectorSpecifically, the local measurement sensitivity block 68 first determines a local measurement sensitivity matrix H_zi(k) And a local measurement variance matrix R_zi(k) In that respect Local measurement sensitivity matrix H_zi(k) Representing local measurements based on local state vectors x_i(k) The amount of change experienced. Local measurement variance matrix R_zi(k) Represents the uncertainty in the local measurement, which uncertainty may also be referred to as error. Local measurement sensitivity matrix H_zi(k) Expressed in equation 5 as:

whereinRepresenting a local state vector x_i(k) Partial derivatives of (a). It should be appreciated that the local measurement sensitivity matrix H_zi(k) And a local measurement variance matrix R_zi(k) Both are block diagonal, which simplifies the computation. Local residual covariance matrix block 70 determines a local residual covariance matrixWhich represents μ for an individual node 18i_iUncertainty of (2). Local residualμ_iResidual covariance matrix ofBased on local error covariance matrix P_i(k | k-1) and the local measurement variance matrix R_zi(k) Is determined and expressed in equation 6 as:

whereinRepresenting a partial mapping matrix. The local gain matrix block 72 is based on a covariance matrixLocal error covariance matrix P_i(k | k-1) and local measurement sensitivity matrix H_zi(k) Determining a local gain matrix K_zi(k) Which is expressed in equation 7 as:

K_zi(k)＝P_i(k|k-1)H_zi ^T(k)B_μiequation 7

Wherein the covariance matrixInverse matrix P of_μi ^-1Is expressed as B_μi. Local gain matrix K_zi(k) And local residual mu_iTo create local updates 46. Specifically, the local update 46 is a local gain matrix K_zi(k) And local residual mu_iThe product of (a). The local update 46 is applied to the local state propagation block 60 and the local residual covariance matrix block 70. In particular, the local state propagation block 60 adds the local update 46 to the estimated local state vectorTo determine an updated estimated local state vectorIt is expressed in equation 8 as:

local update 46 also applies to the local residual covariance matrixIn particular, the local residual covariance matrix block 70 adds the local update 46 to the local residual covariance matrixTo determine an updated residual covariance matrix P_i(k | k), which is expressed in equation 9 as:

P_i(k|k)＝(I-K_zi(k)H_zi(k))P_i(k | k-1) equation 9

Where I denotes an identity matrix.

The collaboration update 48 for an individual node 18i is now described. It should be appreciated that the estimator 40 may determine the local error covariance matrix P for the individual nodes 18i at the local error covariance block 62_i(K | K-1) is followed immediately by determining the collaborative update 48, or alternatively determining the local gain matrix K at the local gain matrix block 72_zi(k) Immediately thereafter, a collaboration update 48 is determined. However, if the estimator 40 determines the collaborative update 48 after the local update 46, the covariance matrix is updated firstAnd the estimator 40 may then determine the cooperative measurement result.

The estimator 40 includes a collaboration measurement block 76 and a collaboration update block 78 for determining the collaboration update 48. The cooperative measurement block 76 includes a cooperative measurement prediction block 80 and a cooperative residual block 82. As explained below, the cooperative measurement prediction block 80 predicts the estimated cooperative measurement result based on the cooperative measurement result between the individual node 18i and the cooperative node 18jIt should be understood that the cooperative measurement between individual nodes 18i and cooperative nodes 18j is measured relative to individual nodes 18 i. The cooperative node 18j may send its local measurement to the individual nodes 18i through the communication network 10 (fig. 1), or alternatively, the measurement devices 32 of the individual nodes 18i may collect the local measurement of the cooperative node 18 j.

The cooperative measurement prediction block 80 is based on a cooperative measurement result vector y_ij(k) Local state vector x for individual node 18i_i(k) And local state vector y of cooperative node 18j_i(k) Predicting estimated cooperative measurement resultsAnd is expressed by equation 10 as:

wherein h is_ijRepresents a function that models the cooperative measurement results at the individual nodes 18i as measured by the cooperative node 18i through cooperation of the node 18i with the node 18 j. Collaborative measurement vector y_ij(k) Representing the result of cooperative measurement between the individual node 18i and the cooperative node 18 j.

Collaborative residual v and estimated collaborative measurementAnd (4) associating. Specifically, the collaborative residual block 82 determines a collaborative residual v. The cooperation residual v represents a cooperation measurement vector y_ij(k) And estimated cooperative measurement resultsThe difference between, and expressed according to equation 11 as:

the collaborative update block 78 includes a collaborative measure sensitivity block 84, a collaborative covariance matrix block 86, and a collaborative gain matrix block 88. The cooperative measurement sensitivity block 84 determines a cooperative measurement sensitivity matrix H_yij(k) And a composite covariance matrixCooperative measurement sensitivity matrix H_yij(k) Representing a local state vector x based on individual nodes 18i of a collaborative measurement_i(k) The amount of change experienced by the corresponding change in (b). The composite covariance matrix when the effect of one or more states of the cooperative node 18j is modeled as random noiseUncertainty in the cooperative measurement is characterized. Cooperative measurement sensitivity matrix H_yij(k) Collaborative measurement based on estimationDetermined as expressed in equation 12:

the cooperative measurement sensitivity block 84 is also based on a cooperative measurement variance matrix R_yij(k) To determine a composite covariance matrix Represents the uncertainty of the state, anRepresents the uncertainty of the noise, and is expressed in equation 13 as:

the collaborative covariance matrix block 86 determines a collaborative error covariance matrix P of the collaborative residual v_υij. Covariance matrix of cooperative errors P_υijSensitivity matrix H based on cooperative measurement_yij(k) Co-operative measurement variance matrix R_yij(k) Composite covariance matrixCollaborative error covariance matrix P for individual nodes 18i_ii(k | k-1) and the cooperation error covariance matrix P of the cooperative node 18j_jj(k | k-1) and expressed in equation 14 as:

the cooperative gain matrix block 88 is based on the covariance matrix P of the cooperative residual v_υijCo-operative error covariance matrix P_ii(k | k-1) and a cooperative measurement sensitivity matrix H_yij(k) To determine a cooperative gain matrix K_yij(k) Which is expressed in equation 15 as:

k_yij(k)＝P_ii(k|k-1)H_yij ^T(k)B_υijequation 15

Wherein the covariance matrix P_υijInverse P of_υij ^-1Is expressed as B_υij. Cooperative gain matrix K_yij(k) Combined with the collaborative residual v to create a collaborative update 48. Specifically, the cooperation update 48 is a cooperation gain matrix K_yij(k) And the cooperative residual v. The local state propagation block 60 then applies the collaborative update 48 to the estimated local state vectorIn particular, the local state propagation block 60 adds the cooperation update 48 to the estimated local state vectorTo determine an updated estimated local state vectorIt is expressed in equation 16 as:

the local residual covariance matrix block 70 determines an updated residual covariance matrix P based on the local update 46_i(k | k), which is expressed in equation 17 as:

P_i(k|k)＝(I-K_yij(k)H_yij(k))P_i(k | k-1) equation 17

It should be understood that the method is applied to a composite covariance matrixIs decoupled. In other words, each node 18i, 18j is associated with a unique state vector. It should also be appreciated that the estimation error of the cooperative node 18j is modeled as noise. In particular, a collaborative measurement vector y_ij(k) Expressed in equation 18 as:

y_ij(k)＝h_ij(x_i(k)，x_j(k)，k)+s_ij(k) equation 18

Wherein s is_ij(k) Representing the random measurement noise vector for the individual node 18i at time k when cooperating with the cooperating node 18 j. Finally, it should be understood that the collaborative measurement vector y_ij(k) Is a unique measurement that is not locally independent. In other words, all of the remaining measurements described above are local measurements specific to the individual node 18i or the cooperative node 18 j.

Fig. 4 is an exemplary illustration of the PNT network 26 in which each node 18 represents a user. In the exemplary embodiment as shown in fig. 4, node 18 represents a land vehicle, a helicopter, or an aircraft. However, it should be understood that node 18 may also represent an individual. For example, in one embodiment, one or more nodes 18 represent individuals such as soldiers holding the PNT system. Referring to fig. 2 and 4, the measurement device 32 for each node 18 of the PNT network 26 is a PNT system that determines the location 90 of the respective node 18 in the earth reference frame. One example of an earth reference frame is an earth-centered fixed-on-earth (ECEF) reference frame. Alternatively, in another embodiment, latitude, longitude, and altitude may be used instead. In the illustrated embodiment, the dashed lines between nodes 18 represent wireless communication connections 92A. The thin solid lines between nodes 18 represent wireless communication connections 92B that include time transfer and range measurements. The thick solid lines between the nodes 18 represent the wireless communication connection 92C including time transfer, range measurements and (LOS) line-of-sight measurements.

Fig. 5A to 5C show exemplary cooperative measurement results based on the PNT network 26 shown in fig. 4. In the embodiment shown in fig. 5A, the cooperation measurements between the individual node 18i and the cooperative node 18j include relative distance measurements between the individual node 18i and the cooperative node 18j in combination with relative LOS measurements between the individual node 18i and the cooperative node 18 j. As seen in fig. 5A, the relative distance measurement results are represented by a first relative distance r measured between the individual node 18i and the cooperative node 18j as measured by the individual node 18i_ijAnd a second relative distance r measured between the individual node 18i and the cooperative node 18j as measured by the cooperative node 18j_jiTo indicate. The relative LOS measurement comprises a first relative LOS measurement as measured by the individual node 18iRepresented by a first unit vector pointing from an individual node 18i to a cooperative node 18j, with superscript B_iIndicating the ontology reference frame of the individual node 18 i. The relative LOS measurement further comprises a second relative LOS measurement as measured by the cooperative node 18jRepresented by a second unit vector pointing from cooperative node 18j to individual node 18i, with superscript B_jIndicating the ontology reference frame of the cooperative node 18 j.

Equation 19 TableThe position of the destination node 18i in the ECEF reference frame^ER_iAnd equation 20 expresses the position of the cooperative node 18j in the ECEF reference frame^ER_j：

WhereinRepresents a directional cosine matrix for transforming vectors from the ontology reference frame to the ECEF reference frame of the individual node 18i, anda direction cosine matrix is shown for transforming the vectors from the body reference frame of the cooperative node 18j to the ECEF reference frame. It should be appreciated that the cooperative measurements between the individual nodes 18i and the cooperative nodes 18j for the LWIN approach are node-centric. In other words, the cooperation measurement result between the individual node 18i and the cooperative node 18j is measured with respect to the individual node 18i or the cooperative node 18 j.

In another embodiment as shown in fig. 5B, the cooperative measurement between the individual node 18i and the cooperative node 18j is a relative LOS direction measurement, which indicates an angle measurement as measured relative to the individual node 18i or the cooperative node 18 j. In one example, the collaborative measurement is centered around an individual node 18i and includes a location of the individual node 18i^ER_iThe attitude r of the individual node 18i in the body reference system^BiFirst relative LOS direction measurement u_ijAnd a first LOS angle psi_LOSi. It will be appreciated that these measurements relate to two LOS angles, however for simplicity only a single angle is shown. Measuring a first between an individual node 18i and a cooperative node 18j relative to the individual node 18iRelative LOS direction measurement u_ijAnd relative to the individual node 18i and the first relative LOS direction measurement u_ijMeasuring the first LOS angle Ψ_LOSi. Equation 21 may be used to determine the pose r of an individual node 18i^BiAnd position^ER_iAnd is expressed as:

wherein z is_iijRepresents a measurement result for the individual node 18i as measured by cooperation between the individual node 18i and the cooperative node 18j by the individual node 18i, and v_iijRepresenting all measurement noise. In another example, instead of node-centric measurements, the location of the cooperative node 18j is used instead^ER_jThe attitude r of the cooperative node 18j in the body reference system^BjAnd a second relative LOS direction measurement u_ji. Measuring a second relative LOS direction measurement u between the individual node 18i and the cooperative node 18j relative to the cooperative node 18j_jiRelative to the cooperative node 18j and the second relative LOS direction measurement u_jiMeasuring a second LOS angle Ψ_LOSj. Location of cooperative node 18j^ER_jAnd posture r of cooperative node 18j^BjAnd a second relative LOS direction measurement u_jiTo individual nodes 18i via communication network 10 (fig. 1). Equation 22 may be used to determine the pose r of an individual node 18i^BiAnd position^ER_iAnd is expressed as:

wherein z is_ijiRepresents a measurement result for the individual node 18i as measured by cooperation between the cooperative node 18j and the individual node 18i by cooperation between the cooperative node 18j, and v_ijiRepresenting all measurement noise.

In yet another embodiment as shown in FIG. 5C, collaboration between an individual node 18i and a cooperative node 18jThe measurement result is a relative range measurement between the individual node 18i and the cooperative node 18j measured with respect to the individual node 18i or the cooperative node 18 j. In particular, fig. 5C shows a first relative range measurement d measured between an individual node 18i and a cooperative node 18j as measured relative to the individual node 18i_ijAnd a second relative range measurement d measured between the individual node 18i and the cooperative node 18j as measured relative to the cooperative node 18j_ji. In one example, a first relative range measurement d measured between an individual node 18i and a cooperating node 18j as measured relative to the individual node 18i_ijExpressed in equation 23 as:

d_ij＝||^ER_i-^ER_j||+v_ijequation 23

When the first relative range measures the result d_ijLinearized as δ d_ijIn time, equation 23 becomes equation 24, which is:

whereinAn estimate representing a first relative range measurement,representing vector magnitude, δ R_iRepresents the linearized position of the individual node 18i, and δ R_iIndicating the linearized position of the cooperative node 18 j. If the first relative LOS measurement resultExpressed in equation 25 as:

the linearized first relative range measurement δ d_ijCan be expressed in equation 26 as:

FIGS. 6A-6B illustrate exemplary process flow diagrams illustrating a method for updating estimated local state vectors for individual nodes 18iThe method of (1). Referring to fig. 2, 3, and 6A, the method 200 begins at block 202. In block 202, 220, the estimator 40 determines the local update 46. Specifically, in block 202, the local state propagation block 60 estimates an estimated local state vector for the individual node 18i based on the local measurementsThe method 200 may then proceed to block 204.

In block 204, the local error covariance block 62 determines a local state vector for estimation based on the local measurementsLocal error covariance matrix P_i(k | k-1). Local error covariance matrix P_i(k | k-1) characterizing the estimated local state vectorThe error of (2). The method 200 may then proceed to block 206.

In block 206, the local measurement prediction block 64 is based on the local state vectorAnd local measurement prediction of the estimated local measurement of the individual node 18iIn which locality for individual nodes 18iResidual mu_iAnd estimated local measurementsAnd (4) associating. The method 200 may then proceed to block 208.

In block 208, the local residual block 66 determines local residuals μ for the individual nodes 18i_i. Local residuals μ for individual nodes 18i_iLocal measurement result representing estimationAnd local measurement result vector z_i(k) The difference between them. Method 200 may then proceed to block 210.

In block 210, the local measurement sensitivity block 68 determines a local measurement sensitivity matrix H_zi(k) Which means that the local measurement results are based on a local state vector x_i(k) The amount of change experienced. The method 200 may then proceed to block 212.

In block 212, the local measurement sensitivity block 68 determines a local measurement variance matrix R_zi(k) Which represents the uncertainty in the local measurement. The method 200 may then proceed to block 214.

In block 214, the local residual covariance matrix block 70 is based on the local error covariance matrix P_i(k | k-1) and the local measurement variance matrix R_zi(k) Determining the local residual mu_iLocal residual covariance matrix ofMethod 200 may then proceed to block 216.

In block 216, the local gain matrix block 72 bases on the local residual covariance matrixLocal error covariance matrix P_i(k | k-1) and local measurement sensitivity matrix H_zi(k) Determining a local gain matrix K_zi(k) In that respect The method 200 may then proceed to block 218.

In block 218, localThe gain matrix block 72 maps the local gain matrix K_zi(k) And local residual mu_iTo create local updates 46. The method 200 may then proceed to block 220.

In block 220, the local update 46 is applied to the estimated local state vector of the individual node 18iAnd local residual covariance matrixThe method 200 may then proceed to block 222.

FIG. 6B illustrates block 222-238 where the estimator 40 determines the collaborative update 48. Specifically, in block 222, the cooperative measurement prediction block 80 predicts the estimated cooperative measurement based on the cooperative measurement between the individual node 18i and the cooperative node 18jWherein the cooperation residual v is associated with the estimated cooperation measureAnd (4) associating. The method 200 may then proceed to block 224.

In block 224, the collaborative residual block 82 determines a collaborative residual v, which represents a collaborative measurement vector y_ij(k) And estimated cooperative measurement resultsThe difference between them. The method 200 may then proceed to block 226.

In block 226, the cooperative measurement sensitivity block 84 determines a cooperative measurement sensitivity matrix H_yij(k) Which means that the cooperation measure is based on the local state vector x of the individual node 18i_i(k) The amount of change experienced by the corresponding change in (b). The method 200 may then proceed to block 228.

In block 228, the cooperative measurement sensitivity block 84 also determines a composite covariance matrixThe composite covariance matrix characterizes the uncertainty in the cooperative measurements when the effect of one or more states of the cooperative node 18j is modeled as random noise. The method 200 may then proceed to block 230.

In block 230, the collaborative covariance matrix block 86 is based at least on the collaborative measurement sensitivity matrix H_yij(k) And a composite covariance matrixDetermining a collaborative error covariance matrix P of collaborative residuals upsilon_υij. The method 200 may then proceed to block 232.

In block 232, the cooperative gain matrix block 88 bases the covariance matrix P of the cooperative residual v_υijDetermining a cooperative gain matrix K_yij(k) In that respect The method 200 may then proceed to block 234.

In block 234, the cooperation gain matrix block 88 determines a cooperation update 48, the cooperation update 48 based on the estimated cooperation measurementAnd a collaborative residual v. In particular, the cooperative gain matrix K_yij(k) Combined with the collaborative residual v to create a collaborative update 48. The method 200 may then proceed to block 236.

In block 236, the cooperation update 48 is applied to the estimated local state vector of the individual node 18iThe method 200 may then terminate or return to block 202.

Fig. 7 is a schematic diagram of a plurality of nodes 18i, 18j, 18k, and 18n in wireless communication with the centralized portion 100 of the estimator 140 based on the ITNS approach. In the non-limiting embodiment as shown in fig. 7, the communication network 10 includes a distributed estimator 140, wherein a portion 98 of the estimator 140 is located at each node 18. In particular, the portion 98 of the estimator 140 at each node 18 includes the local state propagation block 60, the local error covariance block 62, and the local residual block 66. The estimator 140 also includes a centralized portion 100 that is in wireless communication with all nodes 18 that are part of the communication network 10. However, in an alternative embodiment, the communication network 10 includes a plurality of centralized portions 100, the centralized portions 100 in wireless communication with a sub-network or a portion of the aggregation node 18 that is part of the communication network 10. In the non-limiting embodiment as shown in FIG. 7, the centralized portion 100 of the estimator 140 is a stand-alone component. In other words, the centralized portion 100 of the estimator 140 is not part of any node 18. However, in an alternative embodiment, the centralized portion 100 of the estimator 140 is included in one of the plurality of nodes 18 of the communication network 10.

The communication network 10 also includes one or more pairs of cooperating nodes 18i, 18 j. For example, in the non-limiting embodiment shown, the node 18i and the node 18j communicate wirelessly with each other, and there is a cooperative measurement between the pair of cooperating nodes 18i, 18 j. It should be understood that fig. 7 shows only one pair of cooperating nodes 18i, 18j for simplicity and ease of illustration. Each node 18 that is part of the communication network 10 may cooperate with each of the remaining nodes 18 that are part of the communication network 10. In other words, if there are n nodes 18 that are part of the communication network 10, there may be up to n x (n-1) pairs of cooperating nodes 18 included in the communication network 10.

With continued reference to FIG. 7, in the ITNS approach, each of the plurality of nodes 18 determines its own respective estimated local state vectorEstimated local measurementAnd a local residual mu. In other words, each node 18 includes a respective local state propagation block 60, a respective local measurement prediction block 64, and a respective local residual block 66. Each node 18 has its corresponding estimated local state vector via the communication network 10Corresponding estimated localMeasurement resultsThe corresponding local residuals μ and the corresponding local measurements are sent to the centralising portion 100 of the estimator 140. The centralized portion 100 of the estimator 140 receives a respective estimated local state vector from each of a plurality of nodes 18 that are part of the communication network 10Local measurement result of corresponding estimationCorresponding local residuals μ and local measurements. As explained below, the centering portion 100 of the estimator 140 bases the corresponding estimated local state vectorLocal measurement result of corresponding estimationThe respective local residuals μ and the respective local measurements determine a local update 146 for each node 18. The centralized portion 100 of the estimator 140 also determines a collaboration update 148 for each pair of collaboration nodes 18i, 18j that are part of the communication network 10.

Fig. 8 is a block diagram of the centralized portion 100 of the estimator 140. The centralized portion 100 of the estimator 140 includes a total error covariance block 162, a local measurement sensitivity block 168, a local residual covariance matrix block 170, and a local gain matrix block 172. The total error covariance block 162 is based on the respective estimated local state vectors for each of the plurality of nodes 18 that are part of the communication network 10 (fig. 7)An overall error covariance matrix for the entire communication network 10 is determined. The total error covariance matrix characterizes the errors for the entire communication network 10. That is, the total error covariance matrix characterization is based on the use ofEstimated local state vector for each node 18 that is part of communication network 10The error of (2). The total error covariance matrix is expressed in equation 27 as:

P(k|k-1)＝Φ(k-1)P(k-1|k-1)Φ^T(k-1) + Q (k) equation 27

Where P (k | k-1) is a total error covariance matrix when time equals (k-1) based on measurements up to (k-1), P (k-1| k-1) is a covariance matrix for the entire communication network 10 when time equals k based on measurements up to (k-1), Φ is a state transition matrix for each node 18 in the communication network 10^TRepresents the transposed state transition torque, and q (k) is the process noise covariance matrix for the entire communication network 10.

The local measurement sensitivity block 168 determines a corresponding local measurement sensitivity matrix H_z(k) And a corresponding local measurement variance matrix R for a particular node 18 that is part of the communication network 10 (fig. 7)_z(k) In that respect As described above, the corresponding local measurement sensitivity matrix H_z(k) Representing the amount of change experienced by the local measurement for a particular node 18 based on changes in the corresponding local state vector x (k), and the corresponding local measurement variance matrix R_z(k) Representing the uncertainty in the local measurements for a particular node 18. The local residual covariance matrix block 170 of the estimator 140 is based on the total error covariance matrix P for the entire communication network 10_i(k | k-1) and the local measurement variance matrix R_zi(k) Determining a corresponding local residual covariance matrix P for a particular node 18_μWhich is expressed in equation 6 above.

The local gain matrix block 172 of the centralized portion 100 of the estimator 140 is then based on the corresponding local residual covariance matrix P for the particular node 18_μAn overall error covariance matrix P (k | k-1) for the entire communication network 10 and a corresponding local measurement sensitivity matrix H for a particular node 18_z(k) Determining a corresponding local gain matrix K for a particular node 18_z(k) In that respect Corresponding local gain matrix K_z(k) Combined with the local residual mu to create a local update 146 for the particular node 18. In particular, the local update 146 for a particular node 18 is a respective local residual μ and a respective local gain matrix K for each node 18 that is part of the communication network 10_z(k) The product of (a). Thus, the local update 146 is determined based on the total error covariance matrix P (k | k-1) and the local residuals μ for the entire communication network 10.

Referring to fig. 7 and 8, the local update 146 is applied to an estimated local state vector for a particular node 18 that is part of the communication network 10To determine a corresponding updated estimated local state vectorThe local update 146 also applies to the covariance matrix P for a particular node 18_μ. It should be appreciated that the centralized portion 100 of the estimator 140 determines a unique local update 146 for each of the plurality of nodes 18 of the communication network 10. In other words, the centralized portion 100 of the estimator 140 is configured to determine n local updates 146, wherein each local update 146 corresponds to a particular one of the nodes 18 that are part of the communication network 10.

Collaboration update 148 is now described. There may be any number of pairs of cooperating nodes 18i, 18j that are part of the communication network 10. Thus, there may be up to n × n (n-1) collaborative updates 148 determined by the centralized portion 100 of the estimator 140. Further, the centralized portion 100 of the estimator 140 may determine the collaborative update 148 immediately after the total error covariance block 162 determines the total error covariance matrix P (k | k-1), or alternatively determine the collaborative update 148 immediately after the local gain matrix block 172 applies the local update 146. However, if the centralized portion 100 of the estimator 140 determines the collaborative update 148 after the local update 146, the total error covariance matrix P (k | k-1) is updated first, and then the centralized portion 100 of the estimator 140 may determine the collaborative measurement.

For purposes of illustration, nodes 18i and 18j (FIG. 7) represent a pair of cooperating nodes. Specifically, the node 18i represents an individual node, and the node 18j represents a cooperative node, with respect to which cooperative measurement is performed. However, it should be understood that each node 18 that is part of the communication network 10 may cooperate with each remaining node 18 that is part of the communication network 10 to determine cooperative measurements. The centralized portion 100 of the estimator 140 includes a collaborative measurement block 176 and a collaborative update block 178. The cooperative measurement block 176 includes a cooperative measurement prediction block 180 and a cooperative residual block 182. The cooperative measurement prediction block 180 is based on the local state vector x of the cooperative nodes 18i, 18j_i(k)、y_i(k) And a collaborative measurement vector y_ij(k) Predicting estimated cooperative measurement resultsAnd is expressed by equation 10 above. Collaborative measurement with estimationThe associated cooperation residual v represents the cooperation measurement and the estimated cooperation measurementThe difference therebetween, and is determined based on equation 11 above.

The collaborative update block 178 includes a collaborative measure sensitivity block 184, a collaborative covariance matrix block 186, and a collaborative gain matrix block 188. The cooperative measurement sensitivity block 184 determines a cooperative measurement sensitivity matrix H_yij(k) And a composite covariance matrixCooperative measurement sensitivity matrix H_yij(k) Local state vector x representing cooperation measurement results based on node 18i_i(k) Is experienced with respect to the node 18i, wherein the cooperation measure is made with respect to the node 18 i. Compounding when the effect of one or more states of a cooperative node 18j of a pair of cooperative nodes 18i, 18j is modeled as random noiseCovariance matrixUncertainty in the cooperative measurement is characterized. Cooperative measurement sensitivity matrix H_yij(k) Expressed in equation 12 above, and the composite covariance matrixExpressed in equation 13 above.

The collaborative covariance matrix block 186 determines a collaborative error covariance matrix P of the collaborative residual v_υijAnd is determined based on equation 14 above. The cooperative gain matrix block 188 based on the cooperative residual upsilon cooperative error covariance matrix P_υijDetermining a cooperative gain matrix K_yij(k) In that respect Determining the cooperative gain matrix K based on equation 15 above_yij(k) In that respect Cooperative gain matrix K_yij(k) Combined with the cooperative residual v to create a cooperative update 148 for a pair of cooperative nodes 18i, 18 j. Specifically, the cooperation update 148 is a cooperation gain matrix K_yij(k) And the cooperative residual v. Referring to fig. 7 and 8, the cooperation update 48 is applied to the respective estimated local state vectors of the nodes 18i, 18j of a pair of cooperating nodesThe collaborative update 148 is also applied to the total error covariance matrix P (k | k-1) of the communication network 10.

In one embodiment, the communication network 10, including the centralized portion 100 of the estimator 140, is part of the PNT network 26 (FIG. 4). Thus, in the embodiment shown in FIG. 5A, the cooperative measurement between the individual node 18i and the cooperative node 18j comprises a combination of a relative distance measurement between the individual node 18i and the cooperative node 18j in combination with a relative LOS measurement between the individual node 18i and the cooperative node 18 j. As described above, the relative distance measurement results are represented by a first relative distance r measured between the individual node 18i and the cooperative node 18j as measured by the individual node 18i_ijAnd a second relative distance measured between the individual node 18i and the cooperative node 18j as measured by the cooperative node 18jr_jiTo indicate. The relative LOS measurement comprises a first relative LOS measurement as measured by the individual node 18iRepresented by a first unit vector pointing from individual node 18i to cooperative node 18 j. The relative LOS measurement further comprises a second relative LOS measurement as measured by the cooperative node 18jRepresented by a second unit vector pointing from the cooperative node 18j to the individual node 18 i.

Referring to fig. 5B, in another embodiment, the cooperative measurement between the individual node 18i and the cooperative node 18j is a relative LOS direction measurement, which indicates an angle measurement as measured relative to the individual node 18i or the cooperative node 18 j. In one example, the cooperative measurement results include the location of individual nodes 18i^ER_iThe attitude r of the individual node 18i in the body reference system^BiAnd a first relative LOS direction measurement u_ij. Equation 28 may be used to determine the pose r of an individual node 18i^BiAnd position^ER_iAnd is expressed as:

wherein z is_ijRepresenting measurements for individual nodes 18i through cooperation between the individual nodes 18 i. In another example, the cooperative measurement result includes a location of the cooperative node 18j^ER_jThe attitude r of the cooperative node 18j in the body reference system^BjAnd a second relative LOS direction measurement u_ji. Equation 29 may be used to determine the pose r of an individual node 18i^BiAnd position^ER_iAnd is expressed as:

wherein z is_jiRepresents a measurement result for the cooperative node 18j through cooperation between the cooperative node 18j and the individual node 18i, and v_ijiRepresenting all measurement noise.

In yet another embodiment as shown in fig. 5C, the cooperative measurement is a relative range measurement between an individual node 18i and a cooperative node 18j that is measured relative to the individual node 18i or the cooperative node 18 j. In particular, fig. 5C shows a first relative range measurement d measured between an individual node 18i and a cooperative node 18j as measured relative to the individual node 18i_ijAnd a second relative range measurement d measured between the individual node 18i and the cooperative node 18j as measured relative to the cooperative node 18j_ji。

Fig. 9A-9B illustrate an exemplary process flow diagram illustrating a method 300 for updating estimated local state vectors for a plurality of nodes 18 that are part of a communication network 10. Referring to fig. 7, 8, and 9A, the method 300 begins at block 302. In block 302 and 316, the centralized portion 100 of the estimator 140 determines the local update 146. Specifically, in block 302, the centralized portion 100 of the estimator 140 receives a respective estimated local state vector from each of a plurality of nodes 18 that are part of a communication networkLocal measurement result of corresponding estimationAnd the corresponding local residual mu. The method 300 may then proceed to block 304.

In block 304, the total error covariance block 162 of the centralized portion 100 of the estimator 140 is based on the respective estimated local state vectors for each of the plurality of nodes 18 that are part of the communication network 10An overall error covariance matrix P (k | k-1) for communication network 10 is determined.The method 300 may then proceed to block 306.

In block 306, the total measured sensitivity block 168 determines a corresponding local measured sensitivity matrix H_z(k) Which represents the amount of change experienced by the local measurement for a particular node 18 based on changes in the corresponding local state vector x (k). The method 300 may then proceed to block 308.

In block 308, the local measurement sensitivity block 168 determines a corresponding local measurement variance matrix R_z(k) Which represents the uncertainty in the local measurements for a particular node 18. Method 300 may then proceed to block 310.

In block 310, the local residual covariance matrix block 170 is based on the total error covariance matrix P (k | k-1) and the corresponding local measurement covariance matrix R for the entire communication network 10_z(k) Determining a respective local residual covariance matrix P for each of a plurality of nodes 18 that are part of a communication network 10_μ. The method 300 may then proceed to block 312.

In block 312, the local gain matrix block 172 bases the respective local residual covariance matrix P for the particular node 18_μAn overall error covariance matrix P (k | k-1) for the entire communication network 10 and a corresponding local measurement sensitivity matrix H for a particular node 18_z(k) Determining a corresponding local gain matrix K for a particular node 18_z(k) In that respect The method 300 may then proceed to block 314.

In block 314, the collaborative update block 178 combines the local gain matrix K_z(k) Combined with the respective local residuals μ for the particular node 18 to create respective local updates 146 for the particular node 18. In particular, the local update 146 for a particular node 18 is a respective local residual μ and a respective local gain matrix K for each node 18 that is part of the communication network 10_z(k) The product of (a). The method 300 may then proceed to block 316.

In block 316, the local update 146 is applied to the estimated local state vector for the particular node 18 that is part of the communication network 10To determine a corresponding updated estimated local state vectorThe local update 146 also applies to the cooperative error covariance matrix P for a particular node 18_μ. The method 300 may then proceed to block 318.

FIG. 9B illustrates block 318-332 in which the collaboration update 148 is determined. Specifically, in block 318, the cooperative measurement prediction block 180 predicts an estimated cooperative measurement based on a cooperative measurement between a pair of cooperating nodes 18i, 18j that are part of the communication network 10Wherein the cooperation residual is associated with the estimated cooperation measurement. In particular, as described above, the estimated cooperative measurement resultLocal state vector x based on cooperative nodes 18i, 18j_i(k)、y_i(k) And a collaborative measurement vector y_ij(k) In that respect The method 300 may then proceed to block 320.

In block 320, the collaborative residual block 182 determines a collaborative residual v, which represents a collaborative measurement vector y_ij(k) And estimated cooperative measurement resultsThe difference between them. The method 300 may then proceed to block 322.

In block 322, the cooperative measurement sensitivity block 184 determines a cooperative measurement sensitivity matrix H_yij(k) Indicating that the cooperative measurement result is based on the local state vector x of the node 18i_i(k) Is experienced with respect to the node 18i, wherein the cooperation measure is made with respect to the node 18 i. The method 300 may then proceed to block 324.

In block 324, the cooperative measurement sensitivity block 184 determines a composite covariance matrixThe composite covariance matrix characterizes the uncertainty in the cooperative measurement when the effect of one or more states of a cooperative node 18j of a pair of cooperative nodes 18i, 18j is modeled as random noise. The method 300 may then proceed to block 326.

In block 326, the collaborative covariance matrix block 186 bases at least on the collaborative measurement sensitivity matrix H_yij(k) And a composite covariance matrixDetermining a collaborative error covariance matrix P of collaborative residuals upsilon_υij. The method 300 may then proceed to block 328.

In block 328, the cooperative gain matrix block 188 determines a cooperative error covariance matrix P based on the cooperative residual v_υijAnd co-operative measurement sensitivity matrix H_yij(k) Determining a cooperative gain matrix K_yij(k) In that respect The method 300 may then proceed to block 330.

In block 330, the cooperative gain matrix block 188 combines the cooperative gain matrix K_yij(k) Combined with the collaborative residual v to create a collaborative update 148. Thus, it should be appreciated that collaboration update 148 is based on estimated collaboration measurementsCollaborative measurement with collaborative residual estimationTo be determined. The method 300 may then proceed to block 332.

In block 332, the cooperation update 148 is applied to the respective estimated local state vectors of the two nodes 18i, 18j of the pair of cooperating nodesThe collaborative update 148 is also applied to the total error covariance matrix P (k | k-1) of the communication network 10. The method 300 may then terminate or return to block 302 (shown in fig. 9A).

Referring to the drawings in general, the present disclosure provides various technical effects and benefits. In particular, the present disclosure describes an estimator that determines local updates and collaborative updates of estimated local state vectors applied to individual nodes. The local updates are determined based on local measurements, while the collaborative updates are based on collaborative measurements between individual nodes and collaborative nodes. In one decentralized approach, the estimator can be included as part of each node that is part of the communication network. Such an approach may require less computing power when compared to a centralized approach. Alternatively, in another approach, the estimation is done at a centralized location, which may result in improved accuracy. However, this approach may require additional computational power when compared to the decentralized approach. Both the centralised approach and the decentralized approach may improve the accuracy of the estimated local state vector for each node, since the update is not only based on local measurements, but also on cooperative measurements between nodes.

Referring to FIG. 10, the computing system 30 (FIG. 2) and the centralized portion 100 (FIG. 7) of the estimator 140 are implemented on one or more computer devices or systems, such as the exemplary computer system 1030. Computer system 1030 includes a processor 1032, a memory 1034, a mass storage memory device 1036, an input/output (I/O) interface 1038, and a human-machine interface (HMI) 1040. Computer system 1030 is operatively coupled to one or more external resources 1042 via network 1026 or I/O interfaces 1038. External resources may include, but are not limited to, servers, databases, mass storage devices, peripherals, cloud-based network services, or any other suitable computer resources that may be used by computer system 1030.

The processor 1032 includes one or more devices selected from microprocessors, microcontrollers, digital signal processors, microcomputers, central processing units, field programmable gate arrays, programmable logic devices, state machines, logic circuits, analog circuits, digital circuits, or any other devices that manipulate signals (analog or digital) based on operational instructions stored in the memory 1034. Memory 1034 includes a single memory device or multiple storage devices including, but not limited to, Read Only Memory (ROM), Random Access Memory (RAM), volatile memory, non-volatile memory, Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), flash memory, cache memory, or any other device capable of storing information. Mass storage memory device 1036 includes a data storage device, such as a hard disk drive, optical disk drive, tape drive, volatile or non-volatile solid state device, or any other device capable of storing information.

Processor 1032 operates under the control of an operating system 1046 resident in memory 1034. Operating system 1046 manages computer resources such that computer program code embodied in one or more computer software applications, such as application programs 1048 resident in memory 1034, may have instructions executed by processor 1032. In alternative examples, processor 1032 may directly execute application programs 1048, in which case operating system 1046 may be omitted. One or more data structures 1049 are also resident in the memory 1034 and may be used by the processor 1032, the operating system 1046, or the application programs 1048 to store or manipulate data.

I/O interface 1038 provides a machine interface that operatively couples processor 1032 to other devices and systems, such as network 1026 or external resources 1042. The application programs 1048 thus operate in conjunction with the network 1026 or external resources 1042 by communicating via the I/O interfaces 1038 to provide various features, functions, applications, procedures, or modules that comprise examples of the disclosure. Application programs 1048 also include program code that is executed by one or more external resources 1042 or otherwise rely on functionality or signals provided by other system or network components external to computer system 1030. Indeed, given the almost limitless possible hardware and software configurations, those of ordinary skill in the art will appreciate that examples of the disclosure can include applications external to computer system 1030, applications distributed among multiple computers or other external resources 1042, or applications provided by computing resources (hardware and software) provided as a service (such as a cloud computing service) over a network.

The HMI 1040 is operatively coupled to a processor 1032 of the computer system 1030 in a known manner to allow a user to interact directly with the computer system 1030. HMI 1040 may include a video or alphanumeric display, a touch screen, a speaker, and any other suitable audio and visual indicators capable of providing data to a user. HMI 1040 also includes input devices and controls, such as an alphanumeric keyboard, pointing device, keypad, buttons, control knobs, microphone, etc., that are capable of accepting commands or input from a user and communicating entered input to processor 1032.

A database 1044 may reside on the mass storage memory device 1036 and may be used to collect and organize data used by the various systems and modules described herein. The database 1044 may include both data and supporting data structures that store and organize the data. In particular, the database 1044 may be arranged with any database organization or structure including, but not limited to, a relational database, a hierarchical database, a network database, or a combination thereof. A database management system in the form of a computer software application executing as instructions on processor 1032 may be used to access information or data stored in records of database 1044 in response to queries, which may be dynamically determined and executed by operating system 1046, other applications 1048, or one or more modules.

Further, the present disclosure includes embodiments according to the following clauses:

clause 1. an estimator (140) as part of a communication network (10) comprising a plurality of nodes (18), wherein a centralized portion (100) of the estimator (140) comprises:

one or more processors (1032) in wireless communication with the plurality of nodes (18) that are part of the communication network (10), wherein the communication network (10) includes one or more pairs of cooperating nodes (18i, 18 j); and

a memory (1034) coupled to the one or more processors (1032), the memory (1034) storing data as a database (1044) and program code that, when executed by the one or more processors (1032), causes the centralized portion (100) of the estimator (140) to:

receiving, from each of the plurality of nodes (18) that are part of the communication network (10), a respective estimated local state vector, a respective estimated local measurement, a respective local residual, and a respective local measurement;

determining an overall error covariance matrix for the communication network (10) based on the respective estimated local state vector for each of the plurality of nodes (18) that are part of the communication network (10);

determining a respective local update (146) based on the total error covariance matrix and the local residuals for each of the plurality of nodes (18), wherein the respective local update (146) applies to the respective estimated local state vector for a particular node (18 i);

predicting an estimated cooperation measurement based on a cooperation measurement between a pair of cooperating nodes (18i, 18j) that are part of the communication network (10), wherein a cooperation residual is associated with the estimated cooperation measurement; and is

Determining a cooperation update (148) based on the estimated cooperation measure and the cooperation residual, wherein the cooperation update (148) is applied to the respective estimated local state vector of both nodes of the pair of cooperating nodes (18i, 18 j).

Clause 2. the estimator (140) according to clause 1, wherein the estimated cooperative measurement is based on a local state vector and a cooperative measurement vector for each node that is part of the pair of cooperative nodes (18i, 18 j).

Clause 3. the estimator (140) according to clause 2, wherein the cooperation residual represents a difference between the cooperation measurement vector and the estimated cooperation measurement.

Clause 4. the estimator (140) according to clause 1, wherein the one or more processors (1032) execute instructions to:

determining a cooperative measurement sensitivity matrix representing an amount of change experienced by the cooperative measurement result based on a corresponding change in a local state vector of a node (18i) with respect to which the cooperative measurement is made;

determining a composite covariance matrix that characterizes an uncertainty in the cooperative measurement when an effect of one or more states of a cooperative node (18j) of the pair of cooperative nodes (18i, 18j) is modeled as random noise; and is

Determining a cooperative error covariance matrix of the cooperative residuals based at least on the cooperative measurement sensitivity matrix and the composite covariance matrix.

Clause 5. the estimator (140) according to clause 4, wherein the one or more processors (1032) execute instructions to:

determining a cooperation gain matrix based on the cooperation error covariance matrix and the cooperation measurement sensitivity matrix of the cooperation residual; and is

Combining the cooperation gain matrix with the cooperation residual to create the cooperation update (148).

Clause 6. the estimator (140) according to clause 5, wherein the cooperation update (148) is a product of the cooperation gain matrix and the cooperation residual.

Clause 7. the estimator (140) according to clause 1, wherein the centralized portion (100) of the estimator (140) is included in one of the plurality of nodes (18) of the communication network (10).

The estimator (140) of clause 1, wherein the one or more processors (1032) execute instructions to:

determining a respective local measurement sensitivity matrix representing an amount of change experienced by a local measurement result for a particular node (18i) based on a change in a respective local state vector for the particular node (18 i);

determining a respective local measurement variance matrix representing an uncertainty in the local measurement for the particular node (18 i); and is

Determining a respective local residual covariance matrix for each of the plurality of nodes (18) that are part of the communication network (10) based on the total error covariance matrix and the respective local measurement variance matrix for the communication network (10).

Clause 9. the estimator (140) according to clause 8, wherein the one or more processors (1032) execute instructions to:

determining a respective local gain matrix for the particular node (18i) based on the respective local residual covariance matrix for the particular node (18i), the total error covariance matrix for the communication network (10), and the respective local measurement sensitivity matrix for the particular node (18 i); and is

Combining the local residuals for the particular node (18i) with the respective local gain matrix to create the respective local update (146).

Clause 10. the estimator (140) according to clause 9, wherein the respective local update (146) is a product of the respective local residual corresponding to the particular node (18i) and the respective local gain matrix.

Clause 11. the estimator (140) according to clause 1, wherein the respective local residual for the particular node (18i) represents a difference between a local measurement vector for the particular node (18i) and the respective estimated local measurement.

Clause 12. the estimator (140) according to clause 1, wherein the communication network (10) is part of a collaborative positioning, navigation, and timing (PNT) system (26).

Clause 13. the estimator (140) according to clause 1, wherein the cooperative measurement between an individual node (18i) and a cooperative node (18j) comprises a relative distance measurement between the individual node (18i) and the cooperative node (18j) in combination with a relative line of sight (LOS) measurement between the individual node (18i) and the cooperative node (18 j).

Clause 14. the estimator (140) according to clause 13, wherein the relative distance measurement is represented by a first relative distance measured between the individual node (18i) and the cooperative node (18j) as measured by the individual node (18i) and a second relative distance measured between the individual node (18i) and the cooperative node (18j) as measured by the cooperative node (18 j).

Clause 15. the estimator (140) according to clause 13, wherein the relative LOS measurement comprises:

a first relative LOS measurement represented by a first unit vector pointing from the individual node (18i) to the cooperative node (18j), wherein the first relative LOS measurement is measured by the individual node (18 i); and

a second relative LOS measurement represented by a second unit vector pointing from the cooperating node (18j) to the individual node (18i), wherein the second relative LOS measurement is measured by the cooperating node (18 j).

Clause 16. the estimator (140) according to clause 12, wherein the cooperative measurement comprises a first relative range measurement measured between an individual node (18i) and a cooperative node (18j) as measured with respect to the individual node (18i), and a second relative range measurement measured between the individual node (18i) and the cooperative node (18j) as measured with respect to the cooperative node (18 j).

Clause 17. a method (300) for updating, by a centralized portion (100) of an estimator (140), estimated local state vectors for a plurality of nodes (18) that are part of a communication network (10), the method (300) comprising:

receiving, by the centralized portion (100) of the estimator (140), from each of the plurality of nodes (18) that are part of the communication network (10), a respective estimated local state vector, a respective estimated local measurement, a respective local residual, and a respective local measurement;

determining, by the centralized portion (100) of the estimator (140), an overall error covariance matrix for the communication network (10) based on the respective estimated local state vector for each of the plurality of nodes (18) that are part of the communication network (10);

determining, by the centralising portion (100) of the estimator (140), a respective local measurement sensitivity matrix representing an amount of change experienced by the local measurement result for a particular node (18i) based on a change in the respective local state vector for the particular node (18 i);

determining, by the centralising portion (100) of the estimator (140), a respective local measurement variance matrix representing an uncertainty in the local measurement for the particular node (18 i);

determining, by the centralized portion (100) of the estimator (140), a respective local residual covariance matrix for each node of the plurality of nodes (18) that are part of the communication network (10) based on the total error covariance matrix and the respective local measurement variance matrix for the communication network (10);

determining, by the centralizing part (100) of the estimator (140), a respective local gain matrix for the particular node (18i) based on the respective local residual covariance matrix for the particular node (18i), the total error covariance matrix for the communication network (10), and the respective local measurement sensitivity matrix for the particular node (18 i);

combining, by the centering portion (100) of the estimator (140), the local residuals of the particular node (18i) with the respective local gain matrix to create respective local updates (146);

predicting, by a centralising portion (100) of the estimator (140), an estimated cooperation measure based on a cooperation measure between a pair of cooperating nodes (18i, 18j) being part of the communication network (10), wherein a cooperation residual is associated with the estimated cooperation measure;

determining, by the centralising portion (100) of the estimator (140), a cooperative measurement sensitivity matrix representing an amount of change experienced by the cooperative measurement result based on a corresponding change in the respective local state vector for the particular node (18i) with respect to which the cooperative measurement is being made;

determining, by the centralized portion (100) of the estimator (140), a composite covariance matrix characterizing uncertainty in the cooperative measurements when an effect of one or more states of a cooperative node (18j) of the pair of cooperative nodes (18i, 18j) is modeled as random noise;

determining, by the centralizing part (100) of the estimator (140), a cooperative error covariance matrix of the cooperative residual based on at least the cooperative measurement sensitivity matrix and the composite covariance matrix;

determining, by the centering portion (100) of the estimator (140), a cooperative gain matrix based on the cooperative error covariance matrix and the cooperative measurement sensitivity matrix of the cooperative residuals; and

combining, by the centering portion (100) of the estimator (140), the cooperation gain matrix with the cooperation residual to create the cooperation update (148).

Clause 18. the method (300) of clause 17, further comprising:

applying, by the centralising portion (100) of the estimator (140), the collaborative update (148) to the respective estimated local state vectors of both nodes of the pair of collaborative nodes (18i, 18 j).

Clause 19. the method (300) of clause 17, further comprising:

applying, by the centralising portion (100) of the estimator (140), the respective local update (146) to the respective estimated local state vector of the particular node (18 i).

Clause 20. the method (300) of clause 17, wherein the collaborative residual represents a difference between a collaborative measurement vector and the estimated collaborative measurement.

The description of the disclosure is merely exemplary in nature and variations that do not depart from the gist of the disclosure are intended to be within the scope of the disclosure. Such variations are not to be regarded as a departure from the spirit and scope of the disclosure.