阅读说明：本技术 基于不完全量测下集员滤波的矿井人员安全状态估计方法 (Mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement ) 是由 白星振 张金昌 宋保业 刘洋 郑鑫磊 于 2020-04-24 设计创作，主要内容包括：本发明公开了一种基于不完全量测下集员滤波的矿井人员安全状态估计方法,该方法充分考虑到了无线传感器的非完全量测以及矿山环境中的未知但有界噪声,构造了基于不完全量测下的集员滤波器。其中,为了有效处理矿井作业人员定位系统中的非线性误差,本发明将系统量测方程进行线性化处理,采用缩放矩阵和未知矩阵来表示线性化误差,并利用粒子群算法对缩放矩阵进行处理,有效解决了系统的线性化问题,实现了矿井作业人员的精确定位。此外,本发明通过半正定规划确定各项滤波参数,并提出了递归滤波算法来计算包含矿井作业人员真实状态的最小状态估计椭球,提高了矿山作业人员定位系统的可靠性。(The invention discloses a mine personnel safety state estimation method based on collective filtering under incomplete measurement, which fully considers the incomplete measurement of a wireless sensor and unknown but bounded noise in a mine environment and constructs a collective filter based on the incomplete measurement. In order to effectively process the nonlinear error in the positioning system of the mine workers, the system measurement equation is subjected to linearization processing, a scaling matrix and an unknown matrix are adopted to represent the linearization error, and the scaling matrix is processed by utilizing a particle swarm algorithm, so that the problem of linearization of the system is effectively solved, and the accurate positioning of the mine workers is realized. In addition, the invention determines various filtering parameters through semi-positive planning, and provides a recursive filtering algorithm to calculate the minimum state estimation ellipsoid containing the real state of the mine operator, thereby improving the reliability of the positioning system of the mine operator.)

1. A mine personnel safety state estimation method based on incomplete measurement centralized filtering is characterized in that,

the method comprises the following steps:

I. arranging a plurality of wireless sensors above a mine working area, and collecting position and speed information of mine operators;

II, establishing a mine worker positioning system model;

the system model establishment process is as follows:

the state quantity x of the mine worker moving in the mine working area_kIncluding position and velocity, expressed as the following vector:

x_k＝[x_1,kv_1,kx_2,kv_2,k]^T(1)

wherein x is_kThe vector is a 4-dimensional vector and represents the state of the mine worker; (x)_1,k,x_2,k) Indicating mine operator at time t_kPosition coordinates of time; (v)_1,k,v_2,k) Indicating mine operator at time t_kA velocity coordinate of time;

giving out a dynamic state equation x of mine operators_k+1The following were used:

x_k+1＝A_kx_k+B_ku_k+ω_k(2)

wherein the content of the first and second substances,

wherein, Δ t_k＝t_k+1-t_kThe time interval between two continuous sampling moments in the mine worker positioning system consisting of the plurality of wireless sensors is shown; vector u_kRepresenting the variation trend of the state track; omega_kIs process noise;

defining the number of the wireless sensors as m, wherein m is a natural number greater than 0; wherein the ith wireless sensor is at time t_kIs measured as y_i,kI is more than 0 and less than or equal to m; the expression of the measurement equation is:

wherein the content of the first and second substances,for measuring noise v_kA component of (a); g_i(x_k) As a function of distance, g_i(x_k) The expression of (a) is:

wherein the content of the first and second substances,representing the position coordinates of the ith wireless sensor; to simplify the expression, let:

the measurement results were then rewritten as:

y_k＝g(x_k)+v_k(6)

wherein, y_k∈R^mIs an m-dimensional vector, an

Wherein the process noise omega_k∈RⁿFor n-dimensional vectors, n is taken to be 4, and the noise v is measured_k∈R^mIs an m-dimensional vector;

process noise omega_k∈RⁿAnd the measurement noise v_k∈R^mBelong to the following ellipsoid sets W and V, respectively:

wherein Q is_kAnd R_kIs a known positive definite symmetric matrix describing the size and shape of an ellipsoid;

constructing a centralized filter based on incomplete measurement according to the mine operator positioning system model;

III.1, constructing a transmission mechanism under incomplete measurement;

the wireless sensors are mutually independent and respectively adopt a transmission mechanism under incomplete measurement to transmit information; the transmission time sequence of the information defining the ith wireless sensor under incomplete measurement is expressed as:

wherein the content of the first and second substances,the information is transmitted for the t +1 th time at the k moment by the wireless sensor i; t is 0,1,2 …;

the following formula is defined:

wherein σ_i,kQuantity measurement representing previous transmission of ith wireless sensorMeasure y from the current quantity_i,kA difference of (d);

thus, the information transfer function f_i(-) is defined as follows:

wherein the content of the first and second substances,_idetermining a parameter for transmission of a wireless sensor i; according to the transmission scheme under incomplete measurement, the wireless sensor i sends the measurement to the ensemble filter only when equation (10) holds:

f_i(σ_i,k,_i)＞0 (10)

therefore, the transmission timing under incomplete measurement is shown in equation (11):

wherein the content of the first and second substances,the information is transmitted for the t +2 th time at the k moment by the wireless sensor i; inf { } represents the minimum value satisfying the constraint in brackets, and N represents a natural number; in addition, the information received by the collective filter from the wireless sensor i representsComprises the following steps:

thus, σ_i,kThe values are shown in formula (13):

order toThen:

wherein the content of the first and second substances,

III.2, constructing a centralized member filter based on incomplete measurement;

according to the transmission mechanism under incomplete measurement constructed in step iii.1, in combination with the formula (2) -formula (6) mentioned in step II, the structure of the membership filter based on incomplete measurement is proposed as follows:

wherein, among others,representing the center of the estimated ellipsoid at time k +1,representing the center of an estimated ellipsoid at the moment k;representing a predicted quantity measurement;K_ka filter gain matrix required to be solved for the collector filter;

then the state quantity x at the moment k +1_k+1In thatIn the indicated ellipsoid;

wherein, P_k+1Estimating a shape matrix of the ellipsoid for the state;

IV, carrying out linear processing on a measurement equation of the mine operator positioning system;

the estimated error e is obtained from the equations (2) and (15)_k+1Expressed as:

wherein the content of the first and second substances,according to equation (8), the amount of measurements received by the ensemble filter from the wireless sensor is expressed as:

and, using Taylor's expansion, the non-linear measurement equation g (x)_k) The linear representation is:

wherein the content of the first and second substances,L_αis a scaling matrix, Δ_αIs an unknown matrix, and | | | Δ_α||≤1；

Then, the formula (18) is substituted into the formula (6) to obtain:

in conjunction with equations (16) and (17), the estimation error is expressed as:

scaling matrix L_αThe method is obtained by a particle swarm optimization method, and comprises the following specific steps:

obtaining a scaling matrix by analyzing a linearization errorWherein E is_kFrom P_kIs decomposed to obtainP_kEstimate the shape matrix of the ellipsoid, | | E for the state_kI is E_kEuclidean norm of;

1,2, N for all i_iSatisfy the requirement of

Wherein the content of the first and second substances,is composed ofEuclidean norm of g_i(x_k) Is g (x)_k) The ith component of (a);

if presentAnd the existence of the parameter z ensures that the < I < Z > is less than or equal to 1, and the < I > z < I > is the Euclidean norm of z;

then equation (21) holds:

obviously, N_iIs affected by z, and thus the scaling matrix L_αTranslates into the following optimization problem:

wherein the content of the first and second substances,is composed ofEuclidean norm of;

in order to obtain the optimal solution of the formula (22) when the condition of < I < Z > is less than or equal to 1, solving by adopting a particle swarm algorithm;

in the particle swarm algorithm, the particles move according to a position and speed formula to obtain an optimal solution, wherein the position and speed formula is as follows:

wherein x is_l(s)＝[x_l1(s),...,x_ld(s)]Is the location of the ith particle in the s iteration;

v_l(s)＝[v_l1(s),...,v_ld(s)]the velocity of the l-th particle in the s-th iteration; w is the inertial weight;

two acceleration coefficients c₁And c₂Referred to as cognitive parameters and social parameters, respectively;

r₁and r₂Are respectively uniformly distributed in [0,1 ]]A random number in between;

p_l(s) and p_g(s) local optimal position and global optimal position of the population in the s-th iteration, respectively;

setting an initial time atA particles exist in a region expressed by | z | | < 1 at random;

the particles move according to the position and the quick-action formula shown in the formula (23), and the obtained global optimal position p is subjected to b times of iterative movement_g(b) Substituting in formula (22) to obtain N_iTo obtain a scaling matrix L at time k_α；

WhileRepresents g (x)_k) The high-order item in the Taylor expansion process completes the linearization of the measurement equation of the positioning system of the mine operating personnel; wherein a and b are both constants;

v, determining various filtering parameters of the collector filter;

v.1, determining constraint conditions met by various filtering parameters of the collector filter;

for the mine worker positioning system, the initial state of the system is set to be x₀The estimated value thereofSatisfies the following conditions:

wherein, P₀Is a given positive definite symmetric matrix;

and at time k, the state quantity x_kBelongs to the state estimation ellipsoid

Then, if there is a filter parameter P_k+1＞0，K_k，λ₁＞0，λ₂＞0，λ₃＞0，λ₄> 0 and lambda₅If > 0, the linear matrix inequality shown in the formula (25) is satisfied; then:

state quantity x at time k +1_k+1Belongs to the state estimation ellipsoid

Wherein the content of the first and second substances,i denotes an identity matrix, Π_k＝[0 (A_k-K_kG_k)E_k1 -K_kL_α-K_k-K_k]；

Each filtering parameter satisfies the constraint shown in formula (25); in addition, the center of the state estimation ellipsoid is determined by equation (15);

v.2, determining each filtering parameter of the collector filter according to a semi-positive planning method;

determining an optimum state ellipsoid by applying a semi-positive definite programming method, and determining each filtering parameter by solving the following optimization problems:

wherein trace (P)_k+1) Representing the shape matrix P_k+1Each filter parameter of the trace (1) meets the constraint shown in the formula (25); obtaining the P through a semi-positive definite programming method_k+1The value of each filtering parameter when the trace of (A) is minimum;

substituting each filtering parameter into the step III to obtain a centralized filter based on incomplete measurement;

VI, positioning the mine operating personnel by using a centralized filter;

recursion of the collector filter is used for obtaining the positioning ellipsoid center at the k +1 momentAnd positioning the ellipsoid-shaped matrix P_k+1The state quantity x of the mine worker_k+1In thatIn the represented ellipsoid, a person position fix is achieved.

Technical Field

The invention relates to a mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement.

Background

In the technical field of mine industrial safety, a wireless positioning system has important application and has important practical significance for guaranteeing the safety of mine operators. The wireless positioning system generally adopts advanced wireless transmission network information facilities, and the wireless intelligent node senses data locally and cooperates with other sensors to exchange relevant information of a monitored object.

In actual engineering, a wireless positioning system is used for tracking and positioning personnel on an industrial site, so that the sensing capability of the industrial monitoring system on safety information is improved. However, the energy supply of wireless sensors is rather limited. If the wireless sensor periodically transmits the measured signal according to the traditional time-based communication scheme, a large amount of unnecessary transmission on a wireless network can be caused, so that the energy consumption of the wireless sensor is overlarge, and the service life of the wireless sensor is greatly shortened.

In addition, the wireless communication environment of the mine site is relatively complex, and various measurement noises and interferences exist. And the distance between the wireless sensor and the target is usually modeled by a certain nonlinear function. Therefore, various non-linear filters (e.g., extended kalman filter, unscented kalman filter) have emerged to address the estimation problem in wireless positioning systems. However, these filters need to assume that the noise sources are random white noise and gaussian noise. However, in the practical application of the wireless positioning system, the probability assumption of the system noise sometimes does not meet the real situation, and the more reasonable assumption is that the system noise is unknown but bounded.

In summary, it is more practical to consider the incomplete measurement of the wireless sensor and the unknown but bounded noise in the mine environment.

Disclosure of Invention

The invention aims to provide a mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement, so that the position positioning of mine operation personnel can be accurately realized under the condition of incomplete measurement.

In order to achieve the purpose, the invention adopts the following technical scheme:

the mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement comprises the following steps:

I. arranging a plurality of wireless sensors above a mine working area, and collecting position and speed information of mine operators;

II, establishing a mine worker positioning system model;

the system model establishment process is as follows:

the state quantity x of the mine worker moving in the mine working area_kIncluding position and velocity, expressed as the following vector:

x_k＝[x_1,kv_1,kx_2,kv_2,k]^T(1)

wherein x is_kThe vector is a 4-dimensional vector and represents the state of the mine worker; (x)_1,k,x_2,k) Indicating mine operator at time t_kPosition coordinates of time; (v)_1,k,v_2,k) Indicating mine operator at time t_kA velocity coordinate of time;

giving out a dynamic state equation x of mine operators_k+1The following were used:

x_k+1＝A_kx_k+B_ku_k+ω_k(2)

wherein the content of the first and second substances,

wherein, Δ t_k＝t_k+1-t_kThe time interval between two continuous sampling moments in the mine worker positioning system consisting of the plurality of wireless sensors is shown; vector u_kRepresenting the variation trend of the state track; omega_kIs process noise;

defining the number of the wireless sensors as m, wherein m is a natural number greater than 0; wherein the ith wireless sensor is at time t_kIs measured as y_i,kI is more than 0 and less than or equal to m; the expression of the measurement equation is:

wherein the content of the first and second substances,for measuring noise v_kA component of (a); g_i(x_k) As a function of distance, g_i(x_k) The expression of (a) is:

wherein the content of the first and second substances,representing the position coordinates of the ith wireless sensor; to simplify the expression, let:

the measurement results were then rewritten as:

y_k＝g(x_k)+v_k(6)

wherein, y_k∈R^mIs an m-dimensional vector, an

Wherein the process noise omega_k∈RⁿFor n-dimensional vectors, n is taken to be 4, and the noise v is measured_k∈R^mIs an m-dimensional vector;

process noise omega_k∈RⁿAnd the measurement noise v_k∈R^mBelong to the following ellipsoid sets W and V, respectively:

wherein Q is_kAnd R_kIs a known positive definite symmetric matrix describing the size and shape of an ellipsoid;

constructing a centralized filter based on incomplete measurement according to the mine operator positioning system model;

III.1, constructing a transmission mechanism under incomplete measurement;

the wireless sensors are mutually independent and respectively adopt a transmission mechanism under incomplete measurement to transmit information; the transmission time sequence of the information defining the ith wireless sensor under incomplete measurement is expressed as:

wherein the content of the first and second substances,the information is transmitted for the t +1 th time at the k moment by the wireless sensor i; t is 0,1,2 …;

the following formula is defined:

wherein σ_i,kQuantity measurement representing previous transmission of ith wireless sensorMeasure y from the current quantity_i,kA difference of (d);

thus, the information transfer function f_i(-) is defined as follows:

wherein the content of the first and second substances,_idetermining a parameter for transmission of a wireless sensor i; according to the transmission scheme under incomplete measurement, the wireless sensor i sends the measurement to the ensemble filter only when equation (10) holds:

f_i(σ_i,k,_i)＞0 (10)

therefore, the transmission timing under incomplete measurement is shown in equation (11):

wherein the content of the first and second substances,the information is transmitted for the t +2 th time at the k moment by the wireless sensor i; inf { } represents the minimum value satisfying the constraint in brackets, and N represents a natural number; in addition, the information received by the collective filter from the wireless sensor i representsComprises the following steps:

thus, σ_i,kThe values are shown in formula (13):

order toThen:

wherein the content of the first and second substances,

III.2, constructing a centralized member filter based on incomplete measurement;

according to the transmission mechanism under incomplete measurement constructed in step iii.1, in combination with the formula (2) -formula (6) mentioned in step II, the structure of the membership filter based on incomplete measurement is proposed as follows:

wherein, among others,representing the center of the estimated ellipsoid at time k +1,representing the center of an estimated ellipsoid at the moment k;representing a predicted quantity measurement;K_ka filter gain matrix required to be solved for the collector filter;

then the state quantity x at the moment k +1_k+1In thatIn the indicated ellipsoid;

P_k+1estimating a shape matrix of the ellipsoid for the state;

IV, carrying out linear processing on a measurement equation of the mine operator positioning system;

the estimated error e is obtained from the equations (2) and (15)_k+1Expressed as:

wherein the content of the first and second substances,according to equation (8), the amount of measurements received by the ensemble filter from the wireless sensor is expressed as:

and, using Taylor's expansion, the non-linear measurement equation g (x)_k) The linear representation is:

wherein the content of the first and second substances,L_αis a scaling matrix, Δ_αIs an unknown matrix, and | | | Δ_α||≤1；

Then, the formula (18) is substituted into the formula (6) to obtain:

in conjunction with equations (16) and (17), the estimation error is expressed as:

scaling matrix L_αThe method is obtained by a particle swarm optimization method, and comprises the following specific steps:

obtaining a scaling matrix by analyzing a linearization errorWherein E is_kFrom P_kIs decomposed to obtainP_kEstimate the shape matrix of the ellipsoid, | | E for the state_kI is E_kEuclidean norm of;

1,2, N for all i_iSatisfy the requirement of

Wherein the content of the first and second substances,is composed ofEuclidean norm of g_i(x_k) Is g (x)_k) To (1) ai components;

if presentAnd the existence of the parameter z ensures that the < I < Z > is less than or equal to 1, and the < I > z < I > is the Euclidean norm of z;

then equation (21) holds:

obviously, N_iIs affected by z, and thus the scaling matrix L_αTranslates into the following optimization problem:

wherein the content of the first and second substances,is composed ofEuclidean norm of;

in order to obtain the optimal solution of the formula (22) when the condition of < I < Z > is less than or equal to 1, solving by adopting a particle swarm algorithm;

in the particle swarm algorithm, the particles move according to a position and speed formula to obtain an optimal solution, wherein the position and speed formula is as follows:

wherein x is_l(s)＝[x_l1(s),...,x_ld(s)]Is the location of the ith particle in the s iteration;

v_l(s)＝[v_l1(s),...,v_ld(s)]the velocity of the l-th particle in the s-th iteration; w is the inertial weight;

two acceleration coefficients c₁And c₂Referred to as cognitive parameters and social parameters, respectively;

r₁and r₂Are respectively uniformly distributed in [0,1 ]]A random number in between;

p_l(s) and p_g(s) local optimal position and global optimal position of the population in the s-th iteration, respectively;

setting an initial time atA particles exist in a region expressed by | z | | < 1 at random;

the particles move according to the position and the quick-action formula shown in the formula (23), and the obtained global optimal position p is subjected to b times of iterative movement_g(b) Substituting in formula (22) to obtain N_iTo obtain a scaling matrix L at time k_α；

WhileRepresents g (x)_k) The high-order item in the Taylor expansion process completes the linearization of the measurement equation of the positioning system of the mine operating personnel; wherein a and b are both constants;

v, determining various filtering parameters of the collector filter;

v.1, determining constraint conditions met by various filtering parameters of the collector filter;

for the mine worker positioning system, the initial state of the system is set to be x₀The estimated value thereofSatisfies the following conditions:

wherein, P₀Is a given positive definite symmetric matrix;

and at time k, the state quantity x_kBelongs to the state estimation ellipsoid

Then, if there is a filter parameter P_k+1＞0，K_k，λ₁＞0，λ₂＞0，λ₃＞0，λ₄> 0 and lambda₅If > 0, the linear matrix inequality shown in the formula (25) is satisfied; then:

state quantity x at time k +1_k+1Belongs to the state estimation ellipsoid

Wherein the content of the first and second substances,i denotes an identity matrix, Π_k＝[0 (A_k-K_kG_k)E_k1 -K_kL_α-K_k-K_k]；

Each filtering parameter satisfies the constraint shown in formula (25); in addition, the center of the state estimation ellipsoid is determined by equation (15);

v.2, determining each filtering parameter of the collector filter according to a semi-positive planning method;

determining an optimum state ellipsoid by applying a semi-positive definite programming method, and determining each filtering parameter by solving the following optimization problems:

wherein trace (P)_k+1) Representing the shape matrix P_k+1Each filter parameter of the trace (1) meets the constraint shown in the formula (25); obtaining the P through a semi-positive definite programming method_k+1The value of each filtering parameter when the trace of (A) is minimum;

substituting each filtering parameter into the step III to obtain a centralized filter based on incomplete measurement;

VI, positioning the mine operating personnel by using a centralized filter;

recursion of the collector filter is used for obtaining the positioning ellipsoid center at the k +1 momentAnd positioning the ellipsoid-shaped matrix P_k+1The state quantity x of the mine worker_k+1In thatIn the represented ellipsoid, a person position fix is achieved.

The invention has the following advantages:

as described above, the present invention provides a mine personnel safety state estimation method based on incomplete measurement centralized filtering, which fully considers the incomplete measurement of a wireless sensor and unknown but bounded noise in a mine environment, and constructs a centralized filter based on incomplete measurement according to a mine operator positioning system model. In order to effectively process nonlinear errors in the mine operator positioning system, the measurement equation of the mine operator positioning system is subjected to linearization processing, a scaling matrix and an unknown matrix are adopted to express the linearization errors in the linearization processing, and the scaling matrix is processed by using a particle swarm algorithm, so that the linearization problem of the system is effectively solved, and the accurate positioning of the position of the mine operator is realized; in addition, the method determines various filtering parameters through semi-positive definite planning, and provides a recursive filtering algorithm to calculate a minimum state estimation ellipsoid containing the real state of the mine operator, so that the reliability of the positioning system of the mine operator is improved.

Drawings

Fig. 1 is a flowchart of a mine personnel safety state estimation method based on incomplete measurement centralized filtering in the invention.

Fig. 2 is a schematic layout diagram of wireless sensors according to an embodiment of the present invention.

Fig. 3 is a schematic diagram of transmission timings of the sensors when the transmission determination parameter is 0.6 according to the embodiment of the present invention.

FIG. 4 is a schematic diagram showing a comparison between a real trajectory and an estimated trajectory of a mine operator in an embodiment of the invention.

FIG. 5 is a schematic diagram illustrating a comparison between the real state coordinate value and the estimated state coordinate value of the mine operator according to an embodiment of the present invention.

FIG. 6 is a diagram illustrating a comparison of the actual status and estimated boundaries of mine workers in an embodiment of the present invention.

Detailed Description

The invention is described in further detail below with reference to the following figures and detailed description:

as shown in fig. 1, the mine personnel safety state estimation method based on collective filtering under incomplete measurement includes the following steps:

I. a plurality of wireless sensors are arranged above a mine working area, and position and speed information of mine operators is collected.

As shown in fig. 2, in order to improve the safety monitoring capability of the mine workers, for example, 6 wireless sensors may be deployed above the mine working area, so as to perform safety monitoring on the workers in the area.

The wireless sensors are respectively used for collecting information such as the position and the speed of mine workers. And this information will be transmitted to the filter for personnel (security status or) location estimation, in selected parts, by means of a transmission mechanism under incomplete measurement.

Of course, the number of wireless sensors in the present embodiment is not limited to the above 6, and is only exemplified here.

And II, after receiving the position and speed information of the mine operating personnel, establishing a mine operating personnel positioning system model.

The system model establishment process is as follows:

setting the state quantity x of the mine operator when the mine operator moves in the mine working area_kIncluding position and velocity, expressed as the following vector:

x_k＝[x_1,kv_1,kx_2,kv_2,k]^T(1)

wherein x is_kIs a 4-dimensional vector and represents the mine operating personnelA state; (x)_1,k,x_2,k) Indicating mine operator at time t_kPosition coordinates of time; (v)_1,k,v_2,k) Indicating mine operator at time t_kThe velocity coordinate of time.

Giving out a dynamic state equation x of mine operators_k+1The following were used:

x_k+1＝A_kx_k+B_ku_k+ω_k(2)

wherein the content of the first and second substances,

wherein, Δ t_k＝t_k+1-t_kThe time interval between two continuous sampling moments in the mine worker positioning system consisting of the plurality of wireless sensors is shown; vector u_kRepresenting the variation trend of the state track; omega_kIs process noise.

The number of the wireless sensors is defined as m, and m is a natural number greater than 0. Wherein the ith wireless sensor is at time t_kIs measured as y_i,kI is more than 0 and less than or equal to m; the expression of the measurement equation is:

wherein the content of the first and second substances,for measuring noise v_kA component of (a); g_i(x_k) As a function of distance, g_i(x_k) The expression of (a) is:

wherein the content of the first and second substances,indicating the location coordinates of the ith wireless sensor. To simplify the expression, let:

the measurement results were then rewritten as:

y_k＝g(x_k)+v_k(6)

wherein, y_k∈R^mIs an m-dimensional vector, an

Wherein the process noise omega_k∈RⁿFor n-dimensional vectors, n is taken to be 4, and the noise v is measured_k∈R^mIs an m-dimensional vector; process noise omega_k∈RⁿAnd the measurement noise v_k∈R^mBelong to the following ellipsoid sets W and V, respectively:

wherein Q is_kAnd R_kIs a known positive definite symmetric matrix describing the size and shape of the ellipsoid.

And III, constructing a centralized filter based on incomplete measurement according to the mine operator positioning system model.

The construction process of the membership filter based on incomplete measurement proposed in the embodiment can be divided into the following two steps:

and III.1, constructing a transmission mechanism under incomplete measurement.

After the wireless sensor collects the position and speed equivalent measurement information of the mine operation personnel, the measurement information needs to be transmitted to the filter for personnel positioning processing. In order to achieve the purpose of energy saving, the measured signals on the wireless sensors cannot be transmitted completely. In the case of such incomplete measurement, a special information transmission mechanism is proposed.

And each wireless sensor judges whether the current measurement is sent to the filter or not according to the difference value between the previous transmitted measurement and the current measurement. In this way, the wireless sensor can adjust its own transmission rate according to the dynamic change of the sensing signal, thereby reducing the data amount transmitted to the filter. In addition, in order to improve the energy efficiency of the sensors and ensure the estimation performance of the positioning system, each wireless sensor can independently execute the transmission strategy without considering the consistency with other sensors in the cluster.

The transmission mechanism under the incomplete measurement can effectively reduce energy consumption and obviously prolong the service life of the wireless sensor.

The transmission time sequence of the information defining the ith wireless sensor under incomplete measurement is expressed as:

wherein the content of the first and second substances,the information is transmitted for the t +1 th time at the k moment by the wireless sensor i; t is 0,1,2 ….

The following formula is defined:

wherein σ_i,kQuantity measurement representing previous transmission of ith wireless sensorMeasure y from the current quantity_i,kThe difference of (a).

Thus, the information transfer function f_i(-) is defined as follows:

wherein the content of the first and second substances,_ithe parameters are judged for the transmission of the wireless sensor i. According to the transmission scheme under incomplete measurement, the wireless sensor i sends the measurement to the ensemble filter only when equation (10) holds:

f_i(σ_i,k,_i)＞0 (10)

therefore, the transmission timing under incomplete measurement is shown in equation (11):

wherein the content of the first and second substances,the wireless sensor i transmits information for the t +2 th time at the k moment, inf { } represents the minimum value meeting the constraint in brackets, and N represents a natural number. In addition, the information received by the collective filter from the wireless sensor i representsComprises the following steps:

thus, σ_i,kThe values are shown in formula (13):

order toThen:

wherein the content of the first and second substances,

the transmission mechanism in this embodiment can adjust the transmission frequency of the information according to the variation characteristic of the measurement, thereby ensuring the transmission performance. Compared with the traditional time-based transmission scheme, the transmission mechanism in the embodiment improves the resource utilization efficiency by reasonably reducing redundant transmission, and simultaneously ensures the required filtering performance.

And III.2, constructing a membership filter based on incomplete measurement.

The collective filtering is to describe the true state of the system by a collection of outer bounding ellipsoids that contain the model structure, measurement data, and noise boundaries of the system, resulting in a set of feasible states for the state information.

The set of feasible states consists of the state and measurement equations of the system, noise boundaries, measurement outputs and initial state values.

Compared with methods such as Kalman filtering and the like which need to know the statistical characteristics of the noise, the method adopts the centralized filtering which only needs to know the boundary of the noise, so that the method is more suitable for processing unknown bounded noise in the mine environment.

According to the transmission mechanism under incomplete measurement constructed in step iii.1, in combination with the formula (2) -formula (6) mentioned in step II, the structure of the membership filter based on incomplete measurement is proposed as follows:

wherein the content of the first and second substances,representing the center of the estimated ellipsoid at time k +1,representing the center of an estimated ellipsoid at the moment k;representing a predicted quantity measurement;K_kthe filter gain matrix that needs to be solved for the ensemble filter.

And IV, carrying out linearization processing on the measurement equation of the mine operator positioning system.

In the embodiment, the measurement equation of the system mine operator positioning system is a nonlinear function, and if the nonlinear terms involved are processed according to the traditional extended kalman filter algorithm, the high-order terms generated by the taylor expansion are simply ignored, and the conservatism is inevitably caused in some cases, so that the precision is reduced.

When the measurement equation of the positioning system of the mine workers is subjected to linearization processing, the embodiment adopts the scaling matrix and the unknown matrix to express the linearization error, and utilizes the particle swarm algorithm to process the scaling matrix, so that the linearization problem of the positioning system of the mine workers is effectively solved, and the positioning accuracy of the mine workers is improved.

The estimated error e is obtained from the equations (2) and (15)_k+1Expressed as:

wherein the content of the first and second substances,according to equation (8), the amount of measurements received by the ensemble filter from the wireless sensor is expressed as:

and, using Taylor's expansion, the non-linear measurement equation g (x)_k) The linear representation is:

wherein the content of the first and second substances,L_αis an indeterminate scaling matrix, Δ_αIs an unknown matrix, and | | | Δ_α||≤1。

Then, the formula (18) is substituted into the formula (6) to obtain:

in conjunction with equations (16) and (17), the estimation error is expressed as:

scaling matrix L_αThe method is obtained by a particle swarm optimization method, and comprises the following specific steps:

obtaining a scaling matrix by analyzing a linearization errorWherein E is_kFrom P_kIs decomposed to obtainP_kEstimate the shape matrix of the ellipsoid, | | E for the state_kI is E_kEuclidean norm of.

1,2, N for all i_iSatisfy the requirement of

Wherein the content of the first and second substances,is composed ofEuclidean norm of g_i(x_k) Is g (x)_k) The ith component of (a).

If presentAnd the parameter z is present to ensure that the | z | is less than or equal to 1, and the | z | is the Euclidean norm of z.

Then equation (21) holds:

obviously, N_iIs affected by z, therefore, the scaling matrix L_αTranslates into the following optimization problem:

wherein the content of the first and second substances,is composed ofEuclidean norm of.

In order to obtain the optimal solution of the formula (22) when the condition of < i > z < i > is less than or equal to 1, a particle swarm algorithm is adopted for solving.

In the particle swarm algorithm, the particles move according to a position and speed formula to obtain an optimal solution, wherein the position and speed formula is as follows:

wherein x is_l(s)＝[x_l1(s),...,x_ld(s)]Is the location of the ith particle in the s iteration;

v_l(s)＝[v_l1(s),...,v_ld(s)]the velocity of the l-th particle in the s-th iteration; w is the inertial weight;

two acceleration coefficients c₁And c₂Referred to as cognitive parameters and social parameters, respectively;

r₁and r₂Are respectively uniformly distributed in [0,1 ]]A random number in between;

p_l(s) and p_g(s) are the local optimal location and global optimal location of the population in the s-th iteration, respectively.

Setting an initial time atA particles exist in a region expressed by | z | | < 1 at random;

the particles move according to the position and quick-action formula shown in (23), and the global optimal position p is obtained after b times of iterative movement_g(b) Into formula (22) to obtain N_iThe value is obtained.

Wherein a and b are constants, and the values of a and b are determined according to time and precision requirements and actual conditions.

By means of particle swarm algorithm, obtaining accurate N_iThe value, and hence the scaling matrix L at time k_αTo do soRepresents g (x)_k) And (4) completing linearization of a measurement equation of the positioning system of the mine workers by using a high-order term in the Taylor expansion process.

In the embodiment, the measurement equation of the positioning system of the mine workers is subjected to linear processing, which is determined by the accurate positioning requirement of the mine environment on the mine workers, so that the safety of the mine workers is ensured.

Conventionally, the higher order terms of the Taylor expansion are ignored, which inevitably reduces the accuracy of the state estimation, and the embodiment of the present invention takes this point into account, and uses the higher order termsAnd (4) showing.

Albeit Δ_αIs unknown, but it satisfies | | | Δ_α| | < 1, i.e. Δ_αIs bounded, and then getsIs bounded.

The embodiment makes full use of the boundedness of the high-order item, can more accurately obtain the filtering parameters of the collector filter, further improves the filtering performance of the filter, and finally is beneficial to improving the positioning accuracy of mine workers.

V. determining the filter parameters of the ensemble filter. The determination of the filter parameters can be divided into the following two steps:

and V.1, determining the constraint conditions met by each filtering parameter of the member filter.

For the mine worker positioning system, the initial state of the system is set to be x₀The estimated value thereofSatisfies the following conditions:

wherein, P₀Is a given positive definite symmetric matrix.

And at time k, the state quantity x_kBelongs to the state estimation ellipsoid

Then, if there is a filter parameter P_k+1＞0，K_k，λ₁＞0，λ₂＞0，λ₃＞0，λ₄> 0 and lambda₅If > 0, the linear matrix inequality shown in the formula (25) is satisfied; then:

state quantity x at time k +1_k+1Belongs to the state estimation ellipsoid

Wherein the content of the first and second substances,i denotes an identity matrix, Π_k＝[0 (A_k-K_kG_k)E_k1 -K_kL_α-K_k-K_k]。

Each filtering parameter satisfies the constraint shown in formula (25); in addition, the center of the state estimation ellipsoid is determined by equation (15).

V.2, determining each filtering parameter of the collector filter according to a semi-positive planning method;

determining an optimal state estimation ellipsoid by applying a semi-positive definite programming method, and determining each filtering parameter by solving the following optimization problems:

wherein trace (P)_k+1) Representing the shape matrix P_k+1Each filter parameter of the trace (1) meets the constraint shown in the formula (25); obtaining the P through a semi-positive definite programming method_k+1The value of each filtering parameter when the trace of (A) is minimum;

and substituting each filtering parameter into the step III to obtain the centralized filter based on incomplete measurement.

VI, positioning mine operating personnel according to the filter algorithm;

recursion of the collector filter is used for obtaining the positioning ellipsoid center at the k +1 momentAnd positioning the ellipsoid-shaped matrix P_k+1The state quantity x of the mine worker_k+1In thatIn the represented ellipsoid, a person position fix is achieved.

Compared with the traditional Kalman filtering method and the like which need to know the statistical characteristics of the noise, the centralized filtering adopted by the embodiment of the invention only needs to know the boundary of the noise, so that the method and the device are more suitable for processing the unknown bounded noise in the mine environment.

In addition, considering that the energy supply of the wireless sensor is quite limited, the information obtained by the wireless sensor is not sent to the filter completely, but is transmitted through a transmission mechanism under incomplete measurement, so that the limited energy of the wireless sensor is saved, the service life of the sensor is longer, the filter obtains useful information as much as possible, and the estimation precision is ensured.

In addition, in consideration of the nonlinearity of the system measurement equation, the embodiment of the invention adopts the scaling matrix and the unknown matrix to express the high-order item in the linearization process of the measurement equation instead of simply neglecting the high-order item, thereby reducing the linearization error, improving the estimation precision of the collective filter, further being beneficial to improving the positioning precision of the mine operators and ensuring the safety of the mine operators.

Fig. 3 shows the times when the six wireless sensors S1 to S6 transmit data when the transmission determination parameter is 0.6. As can be seen from fig. 3, the wireless sensor does not transmit all the information to the collector filter, but selectively transmits the information, so that the energy consumption is reduced, and the service life of the wireless sensor is effectively prolonged. The six wireless sensors are mutually independent and adopt a transmission mechanism under incomplete measurement to transmit information, so the information transmission moments of the six wireless sensors are different, the information transmitted to the filter by each wireless sensor can be effectively complemented, and the situation that the 6 wireless sensors cannot transmit the information to the filter at a certain moment is avoided as much as possible.

Fig. 4 is a schematic diagram comparing the real track and the estimated track of the mine worker. By comparison, the centralized member filter can well estimate the track of the mine worker. FIG. 5 is a schematic diagram showing the comparison between the real state coordinate value and the estimated state coordinate value of the mine operator. Wherein (x1, x2) represents the position coordinates of the mine worker, and the coordinates are compared when the sampling time is from 0 to 200. As can be seen from fig. 5, the state coordinate values estimated by the ensemble filter are very different from the true state coordinate values. Through the comparison, the method disclosed by the invention has a good effect on the estimation of the safety state of the mine personnel. This is because although the information obtained by the membership filter is reduced in the case of incomplete measurement, the wireless sensor selects more effective information for transmission by the transmission mechanism under incomplete measurement proposed by the present invention. Therefore, the invention can reasonably reduce redundant transmission and improve the resource utilization efficiency on the basis of ensuring the required filtering performance.

Fig. 6 is a schematic diagram comparing the actual state and estimated boundaries of the mine operator. Where (x1, x2) represents the position coordinates of the mine worker. As can be seen from fig. 6, when the sampling time is from 0 to 200, the real state of the mine worker is always between the estimated boundaries obtained by the membership filter constructed in the embodiment of the present invention, and it is ensured that the real value is always within the estimated range, thereby facilitating more reasonable and effective safety management for the mine worker.

It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.