阅读说明：本技术 组网雷达多目标跟踪时间资源与信号带宽联合优化方法 (Networking radar multi-target tracking time resource and signal bandwidth joint optimization method ) 是由 时晨光 仇伟 汪飞 李海林 周建江 夏伟杰 孔莹莹 于 2019-10-12 设计创作，主要内容包括：本发明公开了一种组网雷达多目标跟踪时间资源与信号带宽联合优化方法,不仅满足了多目标跟踪过程中各目标的跟踪精度,而且对多目标跟踪过程中照射目标选择、雷达分配方式和发射信号带宽等参数进行自适应动态优化,最大限度地减少了组网雷达系统在整个跟踪过程中的目标照射次数,从而有效提升了组网雷达系统多目标跟踪时的射频隐身性能。(The invention discloses a combined optimization method of multi-target tracking time resources and signal bandwidths of a networking radar, which not only meets the tracking precision of each target in the multi-target tracking process, but also carries out self-adaptive dynamic optimization on parameters such as irradiation target selection, radar distribution mode, emitted signal bandwidth and the like in the multi-target tracking process, reduces the target irradiation times of the networking radar system in the whole tracking process to the maximum extent, and thus effectively improves the radio frequency stealth performance of the networking radar system in the multi-target tracking process.)

1. The method for jointly optimizing the multi-target tracking time resource and the signal bandwidth of the networking radar is characterized by comprising the following steps of:

(1) considering a networking radar system consisting of N space, time and frequency synchronous two-coordinate phased array radars, when tracking multiple targets, each radar can only receive and process target echoes from self-transmitted signals, and simultaneously, each radar can only track one target at most at each moment;

(2) for a target which meets the requirement of tracking accuracy and does not need radar radiation, assuming that all airplanes in the airplane formation are provided with passive sensors, receiving radiation signals from the target, and utilizing the radiation signals of the target to carry out passive arrival time difference positioning;

(3) constructing a Bayesian Classman-Rou lower bound matrix for predicting target state estimation errors by taking an irradiation target index, a radar binary selection variable and a transmitted signal bandwidth as independent variables, and taking the Bayesian Classman-Rou lower bound matrix as a measurement index of the target tracking accuracy;

(4) at each observation moment, determining whether the target needs to be irradiated by starting the radar or not by judging whether the prediction tracking precision of the target meets the constraint condition or not; and selecting a radar and signal bandwidth distribution mode which enables the sum of the prediction and tracking accuracy of all targets to be minimum according to the prediction and tracking accuracy of different radars to the targets to irradiate.

2. The networking radar multi-target tracking time resource and signal bandwidth joint optimization method of claim 1, wherein in the step (2), for a target whose tracking accuracy meets the requirement and does not need radar radiation, it is assumed that all airplanes in an airplane formation are equipped with passive sensors, receive radiation signals from the target, and perform passive arrival time difference positioning by using the radiation signals of the target specifically:

let (x)_i,y_i) The position coordinates of the i (i is more than or equal to 1 and less than or equal to N) th passive sensor, and the distance between the target q and each passive sensor at the time k is as follows:

wherein the content of the first and second substances,

wherein c is an electromagnetic wave propagation velocity, and is obtained by substituting formula (1) into formula (2):

equation (3) is an equation of N-1 hyperbolas, determining the location of the target q at time k from the focus of the hyperbolas

in the formula (I), the compound is shown in the specification,

in the formula (I), the compound is shown in the specification,

3. The networking radar multi-target tracking time resource and signal bandwidth joint optimization method according to claim 1, wherein in the step (3), a Bayesian-Lame lower bound matrix for predicting target state estimation errors with an irradiation target index, a radar binary selection variable and a transmitted signal bandwidth as arguments is constructed, and the lower bound matrix is specifically used as a measurement index of the target tracking accuracy:

prediction Bayesian information matrix of target q at moment k

in the formula (I), the compound is shown in the specification,

(a) uniform motion model

(b) Turning model

Three object motion models are considered: a uniform motion model; with positive angular velocity omega₊The turning model of (1); having a negative angular velocity omega_-The turning model of (1); setting the motion model set of the target as M ═ M¹,m²,m³}，

in the formula (I), the compound is shown in the specification,

in the formula, the upper mark [. C]^-1The inverse of the matrix is represented and,

in the formula (I), the compound is shown in the specification,

defining binary variables

in the formula, E {. cndot } represents the mathematical expectation operation,

in the formula (I), the compound is shown in the specification,representing a target state vector

in the formula (x)_iYi) is the position coordinate of the ith radar,

in the formula (I), the compound is shown in the specification,

in the formula, β_i,q,kEffective bandwidth of the transmitted signal for radar i to target q, c 3 × 10⁸m/s is the speed of light, lambda is the radar operating wavelength, gamma is the antenna aperture,

in the formula, P_tDwell time of radar i on target q, T, for radar transmit power_rIs the pulse repetition period of the radar,

since the formula (12) contains the expectation, the Monte Carlo method is required for

similarly, for a target which does not need radar irradiation, the Fisher information matrix of the measured data of the passive detector is as follows:

combining the formula (18) and the formula (19) to obtain a Fisher information matrix of the target q measurement data at the time k

in summary, it can be seen that,

according to the formulas (10) and (20), for

4. the networking radar multi-target tracking time resource and signal bandwidth joint optimization method of claim 1, wherein in the step (4), at each observation time, whether the target needs to be irradiated by starting the radar is determined by judging whether the predicted tracking precision of the target meets a constraint condition; for a target needing radar irradiation, selecting a radar and signal bandwidth allocation mode which enables the sum of all target prediction tracking accuracies to be minimum according to the prediction tracking accuracies of different radars to the target to irradiate specifically comprises the following steps:

(41) illumination target selection

And (3) establishing an optimization model of the target irradiation index by taking the condition that the prediction tracking precision of all targets at the moment k meets the requirement as a constraint condition and the minimum number of the targets needing irradiation as a target function:

in the formula (I), the compound is shown in the specification,

F_maxis preset

(42) Radar selection and signal bandwidth allocation

According to v obtained in (41)_k,optAnd establishing an optimization model of radar selection and signal bandwidth allocation by taking the data processing capacity of the fusion center and radar emission resources as constraint conditions and the minimum sum of the prediction tracking precision of the target to be irradiated at the moment k as a target function:

in the formula (I), the compound is shown in the specification,

(43) solving the optimization models (22) and (24) by adopting an enumeration method, a two-step decomposition method and an interior point method;

(a) first, as long asIs established, then

the optimization model (22) can easily obtain the optimal result through an enumeration method;

(b) secondly, the constraint condition is satisfied for a given target q needing radar irradiation

in the formula, β_totalThe sum of the bandwidths of all the radar transmitting signals illuminating a single target; because the model (26) is a convex optimization problem of linear constraint and nonlinear programming, an optimal solution is obtained by adopting an interior point method and a gradient projection method;

(c) finally, selecting a radar selection which enables the sum of the target prediction tracking accuracy of the networking radar system to be minimum under the condition of no conflict of radar distribution according to the prediction tracking accuracy value of each target under the specified radar distribution mode and the bandwidth value of each radar transmission signal obtained by the interior point method

Technical Field

The invention relates to the technical field of radar signal processing, in particular to a method for jointly optimizing multi-target tracking time resources and signal bandwidth of a networking radar.

Background

In today's battlefield environment, phased array radars must be able to combat an enemy's interception receiver. Because the networking radar system can adaptively adjust the transmitting parameters, compared with the traditional phased array radar, the networking radar system has obvious advantages in the aspects of tracking precision, radio frequency stealth performance and the like during target tracking. At present, the radiation parameter design of the networking radar is more and more emphasized by scholars and research institutions at home and abroad. From the perspective of time resources, increasing the revisit time interval of each radar to the irradiation target is an important measure for improving the radio frequency stealth performance of the networking radar system.

Aiming at the problem of optimization design of sampling intervals, the existing research results are only limited in the scenes of single-radar single-target tracking, single-radar multi-target tracking and networking radar single-target tracking, the research under the scene of networking radar multi-target tracking is not involved, the influence of the bandwidth of a transmitted signal on the sampling intervals is not considered, and the method has certain limitation. In the prior art, a networking radar multi-target tracking time resource and signal bandwidth joint optimization method does not exist.

Disclosure of Invention

The technical problem to be solved by the invention is to provide a method for jointly optimizing the multi-target tracking time resource and the signal bandwidth of the networking radar, which can reduce the target irradiation times of the networking radar system in the whole tracking process to the maximum extent, thereby effectively improving the radio frequency stealth performance of the networking radar system during multi-target tracking.

In order to solve the technical problem, the invention provides a method for jointly optimizing multi-target tracking time resources and signal bandwidth of a networking radar, which comprises the following steps:

(1) considering a networking radar system consisting of N space, time and frequency synchronous two-coordinate phased array radars, when tracking multiple targets, each radar can only receive and process target echoes from self-transmitted signals, and simultaneously, each radar can only track one target at most at each moment;

(2) for a target which meets the requirement of tracking accuracy and does not need radar radiation, assuming that all airplanes in the airplane formation are provided with passive sensors, receiving radiation signals from the target, and utilizing the radiation signals of the target to carry out passive arrival time difference positioning;

(3) constructing a Bayesian Classman-Rou lower bound matrix for predicting target state estimation errors by taking an irradiation target index, a radar binary selection variable and a transmitted signal bandwidth as independent variables, and taking the Bayesian Classman-Rou lower bound matrix as a measurement index of the target tracking accuracy;

(4) at each observation moment, determining whether the target needs to be irradiated by starting the radar or not by judging whether the prediction tracking precision of the target meets the constraint condition or not; and selecting a radar and signal bandwidth distribution mode which enables the sum of the prediction and tracking accuracy of all targets to be minimum according to the prediction and tracking accuracy of different radars to the targets to irradiate.

Preferably, in step (2), for a target that does not require radar for radiation when the tracking accuracy meets the requirement, assuming that all the airplanes in the formation of airplanes are equipped with passive sensors, receiving a radiation signal from the target, and performing passive time difference of arrival positioning by using the radiation signal of the target specifically:

let (x)_i,y_i) The position coordinates of the i (i is more than or equal to 1 and less than or equal to N) th passive sensor, and the distance between the target q and each passive sensor at the time k is as follows:

wherein the content of the first and second substances,the position of the target q at the moment k; assuming that the passive sensor 1 is a master station and the other passive sensors are auxiliary stations, the time difference between the arrival of the signal radiated by the target q at the moment k at the master station and the arrival at each auxiliary station is as follows:

where c is the electromagnetic wave propagation velocity. The formula (1) can be substituted into the formula (2):

it can be seen that equation (3) is an equation for N-1 hyperbolae, and that the location of the target q at time k can be determined from the focus of the hyperbolaeAs an observation value of the passive sensor networking observation model, the observation model is expressed as:

in the formula (I), the compound is shown in the specification,

for the passive sensor network at the moment k to measure the error of the target q,is a mean of zero and a variance of

White gaussian noise of (1);

in the formula (I), the compound is shown in the specification,

is composed of

The standard deviation of the observed error of (a),

is composed ofAnd

the correlation coefficient of (2).

Preferably, in the step (3), constructing a bayesian krame-ro lower bound matrix for predicting target state estimation errors by using the irradiation target index, the radar binary selection variable and the transmitted signal bandwidth as independent variables, and taking the bayesian krame-ro lower bound matrix as a measurement index of the target tracking accuracy specifically comprises the following steps:

prediction Bayesian information matrix of target q at moment k

Can be expressed as:

in the formula (I), the compound is shown in the specification,

is the predicted state vector of the target q at time k, with the superscript [ ·]^TWhich represents the operation of transposition by means of a transposition operation,

representing the predicted position of the target q at time k,

representing the predicted movement speed of the target q at the moment k; assuming that the motion trajectory of the maneuvering target is composed of a Constant Velocity (CV) model and a turning (CT) model, the corresponding target state transition matrices are respectively expressed as: (a) uniform motion model

(b) Turning model

Three object motion models are considered: a uniform motion model; with positive angular velocity omega₊The turning model of (1); having a negative angular velocity omega_-The turning model of (1); setting a possible motion model set of the target as M ═ M¹,m²,m³}，The motion model representing the object q at time k is m^j(j is more than or equal to 1 and less than or equal to 3); model slave

To

Has a transition probability of

The motion model of the target q at the moment k is m^jThe prediction probability of (c) is:

in the formula (I), the compound is shown in the specification,

representing the target q motion model at the k-1 moment as m^jProbability of (c), thus, a prediction Fisher information matrix of the k-time prior information

The calculation can be made by:

in the formula, the upper mark [. C]^-1The inverse of the matrix is represented and,

BIM, F for target q State at time k-1^jIs a model m^jCorresponding state transition matrix, Q^qIs the variance of the target q process noise and can be expressed as:

in the formula (I), the compound is shown in the specification,

the process noise intensity of the target q is shown, and T is a target observation time interval;

defining binary variables

Is the target irradiation index,

indicating that the target q needs to be illuminated at time k,

indicating that the target q is not required to be irradiated at time k; defining a binary variable for a target requiring radar illumination

Assign an index to the radar when

When the time indicates that the radar i irradiates the target q at the time k, when

The time indicates that the radar i does not irradiate the target q at the time k;

and a Fisher information matrix representing the measured data of the target q by the radar i is calculated by the following formula:

in the formula, E {. cndot } represents the mathematical expectation operation,

as a function of non-linear measurement

Expressed as:

in the formula (I), the compound is shown in the specification,

representing a target state vector

The first-order partial derivative is obtained,

expressed as:

in the formula (x)_i,y_i) Is the position coordinate of the ith radar,

for the predicted distance between radar i and target q at time k,the predicted azimuth angle of the target q relative to the radar i at the moment k;

representing the first partial derivatives of the predicted position and predicted speed of movement of the target relative to the radar predicted distance,

representing a first partial derivative of the predicted position and predicted movement speed of the target relative to the radar predicted azimuth;

the predicted covariance matrix for the metrology noise is expressed as:

in the formula (I), the compound is shown in the specification,

andthe estimated mean square errors, which represent the predicted distance and the predicted azimuth of the target, respectively, are calculated by the following equation:

in the formula, β_i,q,kEffective bandwidth of the transmitted signal for radar i to target q, c 3 × 10⁸m/s is the speed of light, lambda is the radar operating wavelength, gamma is the antenna aperture,

the predicted echo signal-to-noise ratio of the target q irradiated by the radar i at the time k is expressed as:

in the formula, P_tDwell time of radar i on target q, T, for radar transmit power_rIs the pulse repetition period of the radar,is a signal propagation attenuation parameter;

since the formula (12) contains the expectation, the Monte Carlo method is required for

Solving is carried out; in order for the algorithm to meet the real-time requirement, equation (12) is approximately expressed as:

similarly, for a target which does not need radar irradiation, the Fisher information matrix of the measured data of the passive detector is as follows:

combining the formula (18) and the formula (19) to obtain a Fisher information matrix of the target q measurement data at the time k

Comprises the following steps:

in summary, it can be seen that,

the prediction Fisher information matrix of the first item of prior information is only related to the Bayesian information matrix of the target state at the previous moment, the motion model of the target and the observation time interval; for the target needing radar radiation, the selection mode of the prediction Fisher information matrix of the second measurement data and the radar at the k moment is related to the bandwidth of a transmitted signal;

according to the formulas (10) and (20), for

And obtaining a prediction Bayesian Classmei-Rou lower bound matrix of the target motion state estimation error by inversion, namely:

preferably, in the step (4), at each observation time, whether the target needs to be irradiated by starting the radar is determined by judging whether the prediction tracking precision of the target meets the constraint condition; for a target needing radar irradiation, selecting a radar and signal bandwidth allocation mode which enables the sum of all target prediction tracking accuracies to be minimum according to the prediction tracking accuracies of different radars to the target to irradiate specifically comprises the following steps:

(41) illumination target selection

And (3) establishing an optimization model of the target irradiation index by taking the condition that the prediction tracking precision of all targets at the moment k meets the requirement as a constraint condition and the minimum number of the targets needing irradiation as a target function:

in the formula (I), the compound is shown in the specification,

the lower bound of the mean square error of the predicted position estimation of the target q at the moment k is only related to the BIM of the target state at the moment k-1, and the calculation process is as follows:

F_maxis preset

The result of all target tracking indexes at the moment k is obtained by solving the formula (22)

(42) Radar selection and signal bandwidth allocation

According to v obtained in (41)_k,optTo fuse the data throughput and radar emission resources of the centerAnd (3) as a constraint condition, establishing an optimization model of radar selection and signal bandwidth allocation by taking the minimum sum of the prediction tracking accuracy of the target to be irradiated at the moment k as a target function:

in the formula (I), the compound is shown in the specification,

the data quantity which is required to be transmitted to the fusion center and is related to the target q for the radar i at the moment k, rho & gt1 is an oversampling coefficient, V is a given observation area, epsilon is the sampling data quantity required by each target, β_minAnd β_maxRespectively representing the upper limit and the lower limit of the transmission signal bandwidth;

indicating that each radar tracks at most one target at time k;indicating that each target is tracked by M radars at time k;

(43) the optimization models (22) and (24) are solved by an enumeration method, a two-step decomposition method and an interior point method.

(a) First, as long as

Is established, then

It must be true that the optimization model (22) is equivalent to:

the optimization model (22) can easily obtain the optimal result through an enumeration method;

(b) secondly, the constraint condition is satisfied for a given target q needing radar irradiation

The optimization model (24) is rewritten to contain only the variable β_m,q,kIn the form of (1), the model (24) is simplified to:

in the formula, β_totalThe sum of the bandwidths of all the radar transmitting signals illuminating a single target; because the model (26) is a convex optimization problem of linear constraint and nonlinear programming, an optimal solution is obtained by adopting an interior point method and a gradient projection method;

(c) finally, selecting a radar selection which enables the sum of the target prediction tracking accuracy of the networking radar system to be minimum under the condition of no conflict of radar distribution according to the prediction tracking accuracy value of each target under the specified radar distribution mode and the bandwidth value of each radar transmission signal obtained by the interior point method

And transmit signal bandwidth β_m,q,kAs an optimal solution for the model (24).

The invention has the beneficial effects that: the method not only meets the tracking precision of each target in the multi-target tracking process, but also carries out self-adaptive dynamic optimization on parameters such as irradiation target selection, radar distribution mode, emission signal bandwidth and the like in the multi-target tracking process, and reduces the target irradiation times of the networking radar system in the whole tracking process to the maximum extent, thereby effectively improving the radio frequency stealth performance of the networking radar system in the multi-target tracking process.

Drawings

FIG. 1 is a schematic diagram of multi-target motion trajectory and spatial distribution of networking radar in the invention.

Fig. 2 is a schematic diagram of radar selection and signal bandwidth allocation of the target 1 of the present invention.

Fig. 3 is a schematic diagram of radar selection and signal bandwidth allocation of target 2 of the present invention.

Fig. 4 is a comparison diagram of sampling intervals of the target 1 under different algorithms.

Fig. 5 is a comparison diagram of sampling intervals of the target 2 under different algorithms.

FIG. 6 is a diagram illustrating comparison of multi-target tracking errors under different algorithms.

Detailed Description

A method for jointly optimizing multi-target tracking time resources and signal bandwidth of a networking radar comprises the following steps:

(1) considering a networking radar system consisting of N space, time and frequency synchronous two-coordinate phased array radars, when tracking multiple targets, each radar can only receive and process target echoes from self-transmitted signals, and simultaneously, each radar can only track one target at most at each moment;

(2) for a target which meets the requirement of tracking accuracy and does not need radar radiation, assuming that all airplanes in the airplane formation are provided with passive sensors, receiving radiation signals from the target, and utilizing the radiation signals of the target to carry out passive arrival time difference positioning;

(3) constructing a Bayesian Classman-Rou lower bound matrix for predicting target state estimation errors by taking an irradiation target index, a radar binary selection variable and a transmitted signal bandwidth as independent variables, and taking the Bayesian Classman-Rou lower bound matrix as a measurement index of the target tracking accuracy;

(4) at each observation moment, determining whether the target needs to be irradiated by starting the radar or not by judging whether the prediction tracking precision of the target meets the constraint condition or not; and selecting a radar and signal bandwidth distribution mode which enables the sum of the prediction and tracking accuracy of all targets to be minimum according to the prediction and tracking accuracy of different radars to the targets to irradiate.

1. Determining the composition and working parameters of a networking radar system:

considering a networking radar system consisting of a plurality of space, time and frequency synchronous two-coordinate phased array radars, when tracking multiple targets, each radar can only receive and process target echoes from self-emitted signals, and meanwhile, each radar can only track one target at most at each moment. In addition, radar operating parameters, target tracking accuracy thresholds and the like are set.

2. Establishing an observation model of the passive detector:

for targets with satisfactory tracking accuracy and without the need for radar radiation, it is assumed that all aircraft in the formation of aircraft are equipped with passive sensors, and can receive radiation signals from the targets and use the radiation signals of the targets for passive Time Difference of Arrival (TDOA) positioning. Let (x)_i,y_i) The position coordinates of the i (i is more than or equal to 1 and less than or equal to N) th passive sensor, and the distance between the target q and each passive sensor at the time k is as follows:

wherein the content of the first and second substances,

the position of the target q at the moment k; assuming that the passive sensor 1 is a master station and the other passive sensors are auxiliary stations, the time difference between the arrival of the signal radiated by the target q at the moment k at the master station and the arrival at each auxiliary station is as follows:

where c is the electromagnetic wave propagation velocity. The formula (1) can be substituted into the formula (2):

it can be seen that equation (3) is an equation for N-1 hyperbolae, and that the location of the target q at time k can be determined from the focus of the hyperbolaeAs an observation value of the passive sensor networking observation model, the observation model is expressed as:

in the formula (I), the compound is shown in the specification,

for the passive sensor network at the moment k to measure the error of the target q,

is a mean of zero and a variance of

White gaussian noise of (1);

in the formula (I), the compound is shown in the specification,

is composed of

The standard deviation of the observed error of (a),

is composed of

And

the correlation coefficient of (2).

3. Constructing a Bayesian Classman-Rou lower bound matrix for predicting target state estimation errors by taking an irradiation target index, a radar binary selection variable and a transmitted signal bandwidth as independent variables, and taking the Bayesian Classman-Rou lower bound matrix as a measurement index of target tracking accuracy, wherein the measurement index is as follows:

prediction Bayesian information matrix of target q at moment k

Can be expressed as:

in the formula (I), the compound is shown in the specification,

is the predicted state vector of the target q at time k, with the superscript [ ·]^TWhich represents the operation of transposition by means of a transposition operation,

representing the predicted position of the target q at time k,representing the predicted movement speed of the target q at the moment k; assuming that the motion trajectory of the maneuvering target is composed of a Constant Velocity (CV) model and a turning (CT) model, the corresponding target state transition matrices are respectively expressed as:

(a) uniform motion model

(b) Turning model

Three object motion models are considered: a uniform motion model; with positive angular velocity omega₊The turning model of (1); having a negative angular velocity omega_-The turning model of (1); setting a possible motion model set of the target as M ═ M¹,m²,m³}，

The motion model representing the object q at time k is m^j(j is more than or equal to 1 and less than or equal to 3); model slave

To

Has a transition probability of

The motion model of the target q at the moment k is m^jThe prediction probability of (c) is:

in the formula (I), the compound is shown in the specification,

representing the target q motion model at the k-1 moment as m^jProbability of (c), thus, a prediction Fisher information matrix of the k-time prior information

The calculation can be made by:

in the formula, the upper mark [. C]^-1The inverse of the matrix is represented and,

BIM, F for target q State at time k-1^jIs a model m^jCorresponding state transition matrix, Q^qIs the variance of the target q process noise and can be expressed as:

in the formula (I), the compound is shown in the specification,the process noise intensity of the target q is shown, and T is a target observation time interval;

defining binary variables

Is the target irradiation index,

indicating that the target q needs to be illuminated at time k,indicating that the target q is not required to be irradiated at time k; defining a binary variable for a target requiring radar illuminationAssign an index to the radar when

When the time indicates that the radar i irradiates the target q at the time k, when

The time indicates that the radar i does not irradiate the target q at the time k;and a Fisher information matrix representing the measured data of the target q by the radar i is calculated by the following formula:

in the formula, E {. cndot } represents the mathematical expectation operation,

as a function of non-linear measurement

Expressed as:

in the formula (I), the compound is shown in the specification,

representing a target state vector

The first-order partial derivative is obtained,

expressed as:

in the formula (x)_i,y_i) Is the position coordinate of the ith radar,

for the predicted distance between radar i and target q at time k,the predicted azimuth angle of the target q relative to the radar i at the moment k;

representing the first partial derivatives of the predicted position and predicted speed of movement of the target relative to the radar predicted distance,

representing a first partial derivative of the predicted position and predicted movement speed of the target relative to the radar predicted azimuth;

the predicted covariance matrix for the metrology noise is expressed as:

in the formula (I), the compound is shown in the specification,and

the estimated mean square errors, which represent the predicted distance and the predicted azimuth of the target, respectively, are calculated by the following equation:

in the formula, β_i,q,kEffective bandwidth of the transmitted signal for radar i to target q, c 3 × 10⁸m/s is the speed of light, lambda is the radar operating wavelength, gamma is the antenna aperture,the predicted echo signal-to-noise ratio of the target q irradiated by the radar i at the time k is expressed as:

in the formula, P_tDwell time of radar i on target q, T, for radar transmit power_rIs the pulse repetition period of the radar,

is a signal propagation attenuation parameter;

since the formula (12) contains the expectation, the Monte Carlo method is required forSolving is carried out; in order for the algorithm to meet the real-time requirement, equation (12) is approximately expressed as:

similarly, for a target which does not need radar irradiation, the Fisher information matrix of the measured data of the passive detector is as follows:

combining the formula (18) and the formula (19) to obtain a Fisher information matrix of the target q measurement data at the time k

Comprises the following steps:

in summary, it can be seen that,the prediction Fisher information matrix of the first item of prior information is only related to the Bayesian information matrix of the target state at the previous moment, the motion model of the target and the observation time interval; for the target needing radar radiation, the selection mode of the prediction Fisher information matrix of the second measurement data and the radar at the k moment is related to the bandwidth of a transmitted signal;

according to the formulas (10) and (20), for

And obtaining a prediction Bayesian Classmei-Rou lower bound matrix of the target motion state estimation error by inversion, namely:

4. establishing a networking radar multi-target tracking sampling interval optimization model based on radio frequency stealth:

at each observation moment, determining whether the target needs to be irradiated by starting the radar or not by judging whether the prediction tracking precision of the target meets the constraint condition or not; and selecting a radar and signal bandwidth distribution mode which enables the sum of the prediction and tracking accuracy of all targets to be minimum according to the prediction and tracking accuracy of different radars to the targets to irradiate. The specific steps are as follows:

(41) illumination target selection

And (3) establishing an optimization model of the target irradiation index by taking the condition that the prediction tracking precision of all targets at the moment k meets the requirement as a constraint condition and the minimum number of the targets needing irradiation as a target function:

in the formula (I), the compound is shown in the specification,the lower bound of the mean square error of the predicted position estimation of the target q at the moment k is only related to the BIM of the target state at the moment k-1, and the calculation process is as follows:

F_maxis preset

The result of all target tracking indexes at the moment k is obtained by solving the formula (22)

(42) Radar selection and signal bandwidth allocation

According to v obtained in (41)_k,optAnd establishing an optimization model of radar selection and signal bandwidth allocation by taking the data processing capacity of the fusion center and radar emission resources as constraint conditions and the minimum sum of the prediction tracking precision of the target to be irradiated at the moment k as a target function:

in the formula (I), the compound is shown in the specification,for the data quantity which needs to be transmitted to the fusion center and is related to the target q by the radar i at the moment k, rho is more than or equal to 1 and is an oversampling coefficient, and V is a given observationArea of region, epsilon is the amount of sampled data required for each object β_minAnd β_maxRespectively representing the upper limit and the lower limit of the transmission signal bandwidth;

indicating that each radar tracks at most one target at time k;indicating that each target is tracked by M radars at time k;

(43) the optimization models (22) and (24) are solved by an enumeration method, a two-step decomposition method and an interior point method.

(a) First, as long as

Is established, then

It must be true that the optimization model (22) is equivalent to:

the optimization model (22) can easily obtain the optimal result through an enumeration method;

(b) secondly, the constraint condition is satisfied for a given target q needing radar irradiation

The optimization model (24) is rewritten to contain only the variable β_m,q,kIn the form of (1), the model (24) is simplified to:

in the formula, β_totalThe sum of the bandwidths of all the radar transmitting signals illuminating a single target; since the model (26) is a convex optimization problem for linear constraint, non-linear programming, interior point methods and ladders are usedObtaining an optimal solution by a degree projection method;

(c) finally, selecting a radar selection which enables the sum of the target prediction tracking accuracy of the networking radar system to be minimum under the condition of no conflict of radar distribution according to the prediction tracking accuracy value of each target under the specified radar distribution mode and the bandwidth value of each radar transmission signal obtained by the interior point method

And transmit signal bandwidth β_m,q,kAs an optimal solution for the model (24).

The number of the radars in the networking radar system is assumed to be N-6, the number of the targets is Q-2, and the working parameters of the radars are the same. The remaining parameter settings are shown in table 1.

Table 1 simulation parameter settings

The duration of the airborne radar networking tracking process is assumed to be 100 s.

The multi-target motion trajectory and networking radar space distribution diagram is shown in fig. 1, the radar selection and signal bandwidth allocation diagram of the target 1 is shown in fig. 2, and the radar selection and signal bandwidth allocation diagram of the target 2 is shown in fig. 3. As can be seen from fig. 2 and 3, in the target tracking process, along with the movement of the target, the networking radar system preferentially selects two radars which are closer to the target and have better relative positions to irradiate the target; meanwhile, more signal bandwidth resources tend to be allocated to the part of the selected radar farther away from the target, so that the sum of the target prediction and tracking accuracy of the networking radar system is ensured to be minimum.

A comparison graph of the sampling intervals of the target 1 under the different algorithms is shown in fig. 4, and a comparison graph of the sampling intervals of the target 2 under the different algorithms is shown in fig. 5. As can be seen from fig. 4 and 5, compared with the bandwidth uniform distribution method, the method provided by the patent enables the irradiation interval time of the networking radar system to the same target to be longer, thereby further improving the radio frequency stealth performance of the networking radar during multi-target tracking. In order to more intuitively embody the improvement of the proposed algorithm on the sampling interval, the total number of times of irradiation of the radar networking on the target 1 and the target 2 in the whole tracking process under different methods is counted, as shown in table 2:

TABLE 2 comparison of target irradiation times under different methods

As can be seen from table 2, compared with the bandwidth uniform allocation method, in the method provided by the present invention, the number of times that the radar networking irradiates the target 1 and the target 2 in the tracking process of 100s is significantly reduced, and the total number of times of irradiation is reduced by approximately 19%, which fully indicates that the method of the present invention further improves the radio frequency stealth performance of the networking radar during multi-target tracking.

The multi-target tracking Error pair under different methods is shown in fig. 6, wherein a target tracking Root Mean Square Error (RMSE) is defined as:

in the formula, N_MCFor the number of monte carlo experiments,

is the estimated position of the target obtained in the nth Monte Carlo experiment, where N is set_MC100. As can be seen from fig. 1 and fig. 6, the method provided by the present invention can better meet the tracking accuracy requirements of all targets while saving more radiation resources.

According to the simulation result, the combined optimization method of the multi-target tracking time resource and the signal bandwidth of the networking radar can adaptively optimize and adjust parameters such as irradiation target selection, radar distribution mode, emission signal bandwidth and the like in the multi-target tracking process under the condition of meeting the target prediction tracking precision, the fusion center data processing amount and the radar emission resource constraint at the next observation moment, and the target irradiation times of the networking radar system in the whole tracking process are reduced to the maximum extent, so that the radio frequency stealth performance of the networking radar system in the multi-target tracking process is effectively improved.

The invention considers a networking radar system consisting of a plurality of space, time and frequency synchronous two-coordinate phased array radars, when tracking multiple targets, each radar can only receive and process target echoes from self-emitted signals, and simultaneously, each radar can only track one target at most at each moment. Firstly, selecting the target needing radar radiation at the next observation moment according to the predicted value of the target tracking precision, and minimizing the number of the targets needing radiation while meeting the requirements of all target prediction and tracking precision. Aiming at the targets needing radiation, a combined optimization method of the multi-target tracking time resources and the signal bandwidth of the networking radar is established by taking the data processing amount of a fusion center and the radar emission resources as constraint conditions and taking the sum of the prediction tracking precision of all the radiation targets as an optimization target, irradiation target selection, radar selection and signal bandwidth emission in the multi-target tracking process are adaptively optimized and adjusted, the radar radiation frequency of the radar networking in the tracking process is minimum, and the radio frequency stealth performance of the radar networking is improved.

The invention provides a method for jointly optimizing networking radar multi-target tracking time resources and signal bandwidth based on practical engineering application requirements. And then, updating the target state of the target radiated by the radar by using the radar measurement information, and updating the target state estimation obtained by the target without the radar radiation by using the arrival time difference of the target radiation signal received by the passive sensor of the aircraft platform.