CN114971283A - Resource optimization scheduling method for distributed networking radar multi-target tracking - Google Patents
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Abstract
The invention discloses a resource optimization scheduling method for distributed networking radar multi-target tracking, which comprises the following steps: s1, setting initial target node selection of the distributed networking radar system, and uniformly distributing bandwidth resources and residence time resources to each selected radar node; s2, selecting each radar node at the moment k to obtain a corresponding target measured value, and performing local filtering; s3, the fusion center fuses the results of the local filtering according to the covariance cross fusion criterion, and feeds the fusion results back to the selected radar nodes; s4, selecting the predicted Bayesian Classmen-Luo lower limit as an evaluation index of target tracking precision, and establishing an optimization model; and S5, allocating resources of bandwidth and residence time, and solving the established optimization model by using a circular minimum method and a minimum maximum method. The method can effectively reduce the tracking error of the worst target under the constraint of limited resources, and improve the tracking precision of multiple targets.
Description
Technical Field
The invention relates to the technical field of intelligent perception and processing, in particular to a resource optimization scheduling method for distributed networking radar multi-target tracking.
Background
With the rapid development of weaponry, the combat environment faced by modern radars is more and more complex. Stealth aircraft, electronic interference and other technologies pose a threat to modern radars. It becomes increasingly difficult to continuously track a target by means of conventional monostatic radar alone. In the networking radar technology which is developed in recent years, reasonable information fusion and resource management are carried out by combining a plurality of radars, so that the overall tracking performance of a radar system can be effectively improved.
For the research of networking radar, typical data fusion modes are mainly classified into centralized fusion and distributed fusion. The existing algorithm mainly adopts a measurement dimension-expanding algorithm in centralized fusion, and the algorithm concentrates measurement information of all sensors into an observation equation and finally outputs fusion state estimation. The fusion mode has small information loss, but has higher requirements on communication bandwidth and processing capacity of a fusion center, and can cause filter divergence when sensor abnormality exists. The distributed fusion is to preprocess the information measured by each sensor to generate a local track of the sensor, and then each sensor periodically sends the local track to a fusion center for fusion. The fusion mode has lower requirements on communication bandwidth and computing power of a fusion center, has stronger reliability and expandability and is less influenced by the abnormality of a single sensor. For the resource scheduling technology, the resource scheduling technology can be divided into two categories according to different optimization objectives: one is to minimize the resource consumption of the networking radar under the condition of meeting the target tracking precision requirement; and the other type is to maximally improve the target tracking performance under the condition that the transmission resources of the networking radar system are limited.
Most of the existing resource optimization configuration methods for target tracking of the networking radar system adopt a centralized information fusion technology, but the distributed information fusion technology for maneuvering multi-target tracking still involves less, and the resource optimization scheduling research for comprehensively considering node selection, bandwidth and residence time distribution to improve the overall tracking performance of the multi-target is still incomplete. Therefore, a resource optimization scheduling method oriented to distributed networking radar multi-target tracking is needed to be developed.
Disclosure of Invention
The invention aims to provide a resource optimization scheduling method for distributed networking radar multi-target tracking so as to overcome the defects in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a resource optimization scheduling method for distributed networking radar multi-target tracking comprises the following steps:
s1, setting initial target node selection of the distributed networking radar system, and uniformly distributing bandwidth resources and residence time resources to each selected radar node;
s2, selecting each radar node at the moment k to obtain a corresponding target measured value, and performing local filtering;
s3, the fusion center fuses the results of the local filtering according to the covariance cross fusion criterion, and feeds the fusion results back to the selected radar nodes;
s4, selecting the predicted Bayesian Classmen-Luo lower limit as an evaluation index of target tracking precision, and establishing an optimization model;
s5, selecting a sensor node, and adopting a Bayesian Clary-Rous lower limit trace as the tracking precision of the sensor node selection;
s6, solving the established optimization model by using a cyclic minimum method and combining a minimum maximum method to obtain the optimal solution of residence time distribution when the bandwidth is fixed
And an optimized objective function value fva T ；
S7 optimal solution distributed according to residence time
Fixing residence time, and adopting minimum maximum value method to obtain optimum solution of bandwidth allocation when residence time is fixed
And an optimized objective function value fva β ；
S8, if the absolute value of the tracking accuracy error obtained by the optimization in the steps S6 and S7 is less than the set threshold | fva T -fva β If | < epsilon, the optimization results of the node selection, the bandwidth and the residence time resource can be obtained, otherwise, the step S6 is carried out.
Further, the step S1 is specifically: the set networking radar system consists of M radars, and the coordinate of the mth radar is (x) m ,y m ) M1, 2.. gth, M, there are Q independent maneuvering targets in space, and the state of the Q (Q1, 2.. gth, Q) target at time k is
And
respectively representing the position, velocity and acceleration of the target, the equation of state of motion of the target q at time k is expressed as:
in the formula (I), the compound is shown in the specification,
for the state-transfer function of the target q,
representing zero mean gaussian white noise at time k-1.
Further, in the step S2:
the m-th radar obtains a measurement value of a target q at the time k and performs local filtering by using unscented Kalman filtering. The observation equation is expressed as:
wherein the content of the first and second substances,
the binary variable is used for characterizing the association state of the radar and the target, and the expression is as follows:
in the formula (I), the compound is shown in the specification,
radial distance from m part radar to target q at time k，
The doppler shift of the m-th radar and the target q due to relative motion at the time k,
for the m-th radar observation noise of the target q at time k,
and
for the distance and doppler measurement error of the mth radar to the target q at time k, the radial distance and doppler measurement error can be expressed as:
wherein c is the speed of light,
the effective bandwidth of the signal transmitted by the mth radar to the target q,
represents the dwell time of the mth radar irradiation target q at the time k,
the signal-to-noise ratio of the m-th radar irradiation target q at the time k.
Further, the step S3 is specifically: and after receiving the state estimation results of the radar nodes, the fusion center performs data fusion processing on the state estimation values of the radar nodes and the covariance matrixes thereof according to the distributed covariance cross fusion criterion with feedback, and then feeds back the state estimation results to the radar nodes.
Further, the expression of the optimization model in step S4 is:
in the formula (I), the compound is shown in the specification,
and a Bayesian information matrix representing the target q, wherein the expression is as follows:
in the formula (I), the compound is shown in the specification,
representing observation functions
A jacobian matrix of;
minimizing the predicted Bayesian Classmen-Rous lower limit of the worst target tracking error needing to be irradiated, and establishing an optimized model expression as follows:
in the formula, beta total Representing the total transmission bandwidth, T, of a networked radar system dw,total Representing the total dwell time of the radar at each time instant,
in the networking radar system for expressing the k +1 moment, each target is fixed by an L partThe radar is used for tracking the radar,
denotes that each radar tracks at most 1 target at the time k +1, beta min And beta max Respectively representing the lower and upper bounds of the radar transmission bandwidth, T dw,min And T dw,max Representing the lower and upper bounds of radar dwell time, respectively.
Further, the target function of selecting the predicted bayesian lower limit as the evaluation index of the target tracking accuracy in step S5 is as follows:
when node selection is carried out on each target, the other two variables are uniformly distributed, L nodes which improve the tracking performance of the system most are selected, and the generated subproblems are modeled after convex relaxation as follows:
after relaxation, solving by adopting a convex optimization algorithm; and after the optimal solution selected by the nodes is obtained, selecting the first L larger values, setting the corresponding nodes as 1 and the rest nodes as 0, removing the selected sensors, and repeating the steps by using the rest nodes until all targets are distributed.
Further, the optimization model obtained by fixing the bandwidth in step S6 is:
solving by adopting a minimum maximum value method to obtain fixed bandwidthOptimal solution for residence time distribution
And an optimized objective function value fva T 。
Further, the optimization model obtained by fixing the residence time in step S7 is:
adopting a minimum maximum value method to obtain an optimal solution of bandwidth allocation when the residence time is fixed
And an optimized objective function value fva β 。
Compared with the prior art, the invention has the advantages that: the resource optimization scheduling method for distributed networking radar multi-target tracking can effectively reduce the tracking error of the worst target under the constraint of limited resources and improve the tracking precision of multiple targets.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a block diagram of a covariance cross-fusion architecture with feedback according to the present invention.
FIG. 2 is a flowchart of a resource optimization scheduling method for distributed networking radar multi-target tracking according to the present invention.
FIG. 3 is a diagram of a motor scene networking radar and a target motion track distribution.
Fig. 4 is an experimental result of target tracking accuracy in a maneuvering scene.
Fig. 5 shows the results of radar selection and bandwidth allocation experiments for each target.
Fig. 6 shows the results of radar selection and residence time distribution experiments for each target.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the scope of the present invention will be more clearly and clearly defined.
Referring to FIG. 1, each sub-sensor uses unscented Kalman filter to obtain local state estimation through local filtering
Sum local estimation covariance matrix
And then, transmitting the state estimation result to a fusion center, and performing data fusion processing on the state estimation value of each radar node and a covariance matrix thereof by the fusion center according to a covariance cross fusion criterion:
in the formula (I), the compound is shown in the specification,
representing the state estimation covariance matrix of the target q after data fusion at the time k,
representing post-k-time data fusion targetsq, and outputting the state estimation value as a final state estimation result. And then, the fusion center feeds back the fused state estimation result to each radar node:
in the formula, alpha m Is an information distribution factor, and satisfies the following conditions:
α 1 +α 2 +...+α M ＝1
it can be seen that the state estimation value obtained by each radar node is the same as the result of the fusion center, but the fed-back covariance matrix is distributed according to the weight of each radar node.
Referring to fig. 2, the embodiment discloses a resource optimization scheduling method for distributed networking radar multi-target tracking, which includes the following steps:
and step S1, setting initial target node selection of the networking radar system, and uniformly distributing bandwidth resources and residence time resources to each selected radar node.
Specifically, the networking radar system is set to be composed of M radars, and the coordinate of the mth radar is (x) m ,y m ) M1, 2.. gth, M, there are Q independent maneuvering targets in space, and the state of the Q (Q1, 2.. gth, Q) target at time k is
And
respectively representing the position, velocity and acceleration of the target, the equation of state of motion of the target q at time k is expressed as:
in the formula (I), the compound is shown in the specification,
for the state-transfer function of the target q,
representing zero mean gaussian white noise at time k-1.
Step S2, the mth radar obtains a measurement value of the target q at time k, and performs local filtering using unscented kalman filtering. The observation equation is expressed as:
wherein the content of the first and second substances,
the binary variable is used for characterizing the association state of the radar and the target, and the expression is as follows:
in the formula (I), the compound is shown in the specification,
the radial distance from the m-th radar to the target q at the time k,
the doppler shift of the m-th radar and the target q due to relative motion at the time k,
for the m-th radar observation noise of the target q at time k,
and
for the distance and doppler measurement error of the mth radar to the target q at time k, the radial distance and doppler measurement error can be expressed as:
wherein c is the speed of light,
the effective bandwidth of the signal transmitted by the mth radar to the target q,
represents the dwell time of the mth radar irradiation target q at the time k,
the signal-to-noise ratio of the m-th radar irradiation target q at the time k.
And step S3, the fusion center fuses the results of the local filtering according to the covariance cross fusion criterion, and feeds the fusion results back to the selected radar nodes.
Specifically, after receiving the state estimation result of each radar node, the fusion center performs data fusion processing on the state estimation value of each radar node and the covariance matrix thereof according to the distributed covariance cross fusion criterion with feedback, and then feeds back the state estimation result to each radar node.
Step S4, the BCRLB (bayesian-solomon limit) provides a lower bound to the Mean Square Error (MSE) of the target state estimation problem, and this embodiment selects the predicted bayesian-solomon limit as the evaluation index of the target tracking accuracy, and establishes the optimization model.
The expression of the optimization model is:
in the formula (I), the compound is shown in the specification,
and a Bayesian information matrix representing the target q, wherein the expression is as follows:
in the formula (I), the compound is shown in the specification,
representing observation functions
A jacobian matrix.
In combination with the motion model of the target and the predicted BCRLB, the present embodiment aims to minimize the predicted BCRLB of the worst target tracking error that needs to be irradiated under limited bandwidth resources and residence time resources, so that the established optimization model is as follows:
in the formula, beta total Representing the total transmission bandwidth, T, of a networked radar system dw,total Representing the total dwell time of the radar at each time instant,
in the networking radar system for expressing the k +1 moment, each target is fixedly tracked by L radars,
denotes that each radar tracks at most 1 target at the time k + 1, beta min And beta max Respectively representing the lower and upper bounds of the radar transmission bandwidth, T dw,min And T dw,max Representing the lower and upper bounds of radar dwell time, respectively. It is easy to know that the established optimization problem is a mixed Boolean and non-convex optimization problem, and in consideration of the complexity of the exhaustive search algorithm calculation, the embodiment decomposes the optimization problem into two sub-problems, and provides a quick and efficient two-step solving method;
step S5, selecting sensor nodes, adopting the trace of Bayesian Clary-Roman lower limit (BCRLB) as the tracking precision of the selection of the sensor nodes, and selecting the target function as
When the node selection is carried out on each target, the other two variables are uniformly distributed, and L nodes which improve the system tracking performance most are selected. The generated subproblems after convex relaxation can be modeled as follows:
after relaxation, the optimization problem becomes a convex optimization problem, so a convex optimization algorithm can be adopted for solving; and after the optimal solution selected by the nodes is obtained, selecting the first L larger values, setting the corresponding nodes as 1, and setting the rest nodes as 0. Removing the selected sensor, and repeating the above steps with the remaining nodes until all targets are assigned;
step S6, solving the established optimization model by using a cyclic minimum method and combining a minimum maximum method to obtain the optimal solution of residence time distribution when the bandwidth is fixed
And an optimized objective function value fva T 。
Specifically, after the node is selected and given, the optimization problem in step S5 is still a non-convex optimization problem, and can be solved by heuristic algorithms such as genetic algorithm, particle swarm algorithm, and the like, but these algorithms have long operation time and are difficult to meet the real-time requirement, so the method utilizes a cyclic minimum method in combination with a minimum maximum method to solve, and fixes the value of the bandwidth, and the optimization model can be rewritten as:
the optimization model is a convex problem, and the embodiment solves the problem by adopting a minimum maximum method, namely, an optimal solution of residence time distribution when the bandwidth is fixed can be obtained
And an optimized objective function value fva T ；
Step S7, optimal solution distributed according to residence time
Fixed residence time, the optimization model can be written as:
obtaining the optimal solution of bandwidth allocation when the residence time is fixed by adopting the minimum maximum value method
And an optimized objective function value fva β 。
Step S8, if the absolute value of the tracking accuracy error obtained by the optimization in the steps S6 and S7 is less than the set threshold | fva T -fva β If | < epsilon, the optimization results of node selection, bandwidth and residence time resources can be obtained, otherwise, k ═ k +1 goes to step S6.
The invention is further described below by means of tests.
Considering a maneuvering scene, assuming that M-6 radars are placed in a monitoring area, the number of targets is Q-2, and each target is fixedly tracked by L-2 radar nodes at each sampling moment. Assuming that 29 frames of data are used for the simulation, the system parameters of all radars are the same, the sampling interval is T equal to 3s, and the total effective bandwidth beta of 6 radars is total 4MHz, the upper limit and the lower limit of the effective bandwidth of each radar are respectively beta max ＝0.8β total And beta min ＝0.1β total . The total residence time of 6 radars is T dw,total 0.1s, the upper and lower limits of the pulse number of each radar transmission are T dw,max ＝0.8T dw,total And T dw,min ＝0.1T dw,total 。
The initial state of the target is shown in table 1 below, and the spatial position relationship between the networking radar system and the motion trajectory of the target is shown in fig. 3.
TABLE 1 (target initial state)
| Target number | Initial position (Km) | Initial velocity (m/s) | Acceleration (m/s) 2 ) |
| 1 | (10,70) | (150,-800) | (2,7) |
| 2 | (70,10) | (-150,800) | (-2,-8) |
In order to better understand that the target tracking performance is improved in the present embodiment, a Root Mean Square Error (RMSE) of target tracking in the worst case at the time k is used to characterize the overall tracking accuracy of the system at the time k, and the expression is as follows:
wherein the Monte Carlo simulation frequency Nmont is 100,
which represents the true position of the target q,
the position estimate of the target q at time k obtained in the mth monte carlo experiment is shown. Fig. 4 is a time-dependent variation curve of worst-case target tracking RMSE and BCRLB in a maneuvering scenario, where uniform resource allocation indicates that a networking radar system performs radar node selection, but does not perform allocation of bandwidth and residence time resources. The results show that the BCRLB is always less than or equal to the corresponding RMSE, and the RMSE of the target tracking gradually approaches the BCRLB with the time, thereby verifying the correctness of the embodiment. Compared with the uniform resource distribution, the method effectively reduces the RMSE and BCRLB of target tracking.
In order to better understand the law of radar node selection and bandwidth and residence time resource allocation in this embodiment, fig. 5 shows the results of radar node selection and bandwidth resource allocation of the next two targets in this embodiment, fig. 6 shows the results of radar node selection and residence time resource allocation of the next two targets in this embodiment, two on the left side in the four graphs are for target 1, and two on the right side are for target 2. As can be seen from fig. 5 and fig. 6, the rule of allocating the bandwidth resource and the residence time resource is similar, and the analysis is performed by taking the result of allocating the bandwidth resource of fig. 5 as an example. For target 1, in the first 42s, the system allocates the 1 st and 2 nd radar shots closest to it, while allocating more bandwidth resources to the 2 nd radar, and as the target moves, the 4 th and 5 th radars gradually replace the 1 st and 2 nd radars; for target 2, the first 21s, the system selects the 5 th and 6 th radar shots, and as time progresses, the 3 rd radar gradually replaces the 5 th radar and the 2 nd radar replaces the 6 th radar. It can be seen that the networking radar system preferentially selects a radar node which is close to the target and has a good relative position to irradiate the target, and when the target is close to the radar and has a poor relative position, the system selects another radar node which is far from the target and has a good relative position to irradiate the target.
Through analysis, the networking radar system preferentially selects the radar nodes which are close to the target and have good relative positions to irradiate the target, and allocates more bandwidth resources and dwell time resources to the radar which is far away from the target and has poor relative positions, so that the overall tracking accuracy of the system is improved. That is to say, through implementation of the embodiment, resource optimization scheduling in a distributed networking radar multi-target tracking scene can be realized, requirements on communication bandwidth and computing power of a fusion center are reduced, multi-target tracking accuracy is improved, and the method can be widely applied to the distributed networking radar multi-target tracking scene.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, various changes or modifications may be made by the patentees within the scope of the appended claims, and within the scope of the invention, as long as they do not exceed the scope of the invention described in the claims.
Claims (8)
1. A resource optimization scheduling method for distributed networking radar multi-target tracking is characterized by comprising the following steps:
s1, setting initial target node selection of the distributed networking radar system, and uniformly distributing bandwidth resources and residence time resources to each selected radar node;
s2, selecting each radar node at the moment k to obtain a corresponding target measured value, and performing local filtering;
s3, the fusion center fuses the results of the local filtering according to the covariance cross fusion criterion, and feeds the fusion results back to the selected radar nodes;
s4, selecting the predicted Bayesian Classmen-Luo lower limit as an evaluation index of target tracking precision, and establishing an optimization model;
s5, selecting a sensor node, and adopting a Bayesian Clary-Rous lower limit trace as the tracking precision of the sensor node selection;
s6, solving the established optimization model by using a minimum method and combining with a minimum maximum method to obtain the optimal solution of residence time distribution when the bandwidth is fixed
And after optimizationTarget function value fva T ；
S7 optimal solution distributed according to residence time
Fixing residence time, and adopting minimum maximum value method to obtain optimum solution of bandwidth allocation when residence time is fixed
And an optimized objective function value fva β ；
S8, if the absolute value of the tracking accuracy error obtained by the optimization of the steps S6 and S7 is less than the set threshold | fva T -fva β If | < epsilon, the optimization results of node selection, bandwidth and residence time resources can be obtained, and the next moment is reached. Otherwise go to step S6.
2. The method for optimizing and scheduling resources for multi-target tracking of distributed networking radars according to claim 1, wherein the step S1 specifically comprises: the networking radar system is set to be composed of M radars, and the coordinate of the mth radar is (x) m ,y m ) M1, 2.. gth, M, there are Q independent maneuvering targets in space, and the state of the Q (Q1, 2.. gth, Q) target at time k is
And
respectively representing the position, velocity and acceleration of the target, the equation of state of motion of the target q at time k is expressed as:
in the formula (I), the compound is shown in the specification,
for the state-transfer function of the target q,
representing zero mean gaussian white noise at time k-1.
3. The method for optimally scheduling resources for multi-target tracking of distributed networking radars according to claim 1, wherein in the step S2:
the m-th radar obtains a measurement value of a target q at the time k and performs local filtering by using unscented Kalman filtering. The observation equation is expressed as:
wherein the content of the first and second substances,
the binary variable is used for characterizing the association state of the radar and the target, and the expression is as follows:
in the formula (I), the compound is shown in the specification,
the radial distance from the m-th radar to the target q at the time k,
the doppler shift of the m-th radar and the target q due to relative motion at the time k,
for the m-th radar observation noise of the target q at time k,
and
for the distance and doppler measurement error of the mth radar to the target q at time k, the radial distance and doppler measurement error can be expressed as:
wherein c is the speed of light,
the effective bandwidth of the signal transmitted by the mth radar to the target q,
represents the dwell time of the mth radar irradiation target q at the time k,
the signal-to-noise ratio of the m-th radar irradiation target q at the time k.
4. The method for optimizing and scheduling resources for multi-target tracking of distributed networking radars according to claim 1, wherein the step S3 specifically comprises: and after receiving the state estimation results of the radar nodes, the fusion center performs data fusion processing on the state estimation values of the radar nodes and the covariance matrixes thereof according to the distributed covariance cross fusion criterion with feedback, and then feeds back the state estimation results to the radar nodes.
5. The method for optimizing and scheduling resources for multi-target tracking of distributed networking radar according to claim 1, wherein the expression of the optimization model in the step S4 is as follows:
in the formula (I), the compound is shown in the specification,
and a Bayesian information matrix representing the target q, wherein the expression is as follows:
in the formula (I), the compound is shown in the specification,
representing observation functions
A jacobian matrix of;
minimizing the predicted Bayesian Classmen-Rous lower limit of the worst target tracking error needing to be irradiated, and establishing an optimized model expression as follows:
in the formula, beta total Representing the total transmission bandwidth, T, of a networked radar system dw,total Representing the total dwell time of the radar at each time instant,
in the networking radar system for expressing the k +1 moment, each target is fixedly tracked by L radars,
denotes that each radar tracks at most 1 target at the time k +1, beta min And beta max Respectively representing the lower and upper bounds of the radar transmission bandwidth, T dw,min And T dw,max Representing the lower and upper bounds of radar dwell time, respectively.
6. The method for optimizing and scheduling resources for multi-target tracking of distributed networking radars according to claim 1, wherein the objective function of selecting the predicted bayesian krame-roche lower limit as the evaluation index of the target tracking accuracy in step S5 is as follows:
when node selection is carried out on each target, the other two variables are uniformly distributed, L nodes which improve the tracking performance of the system most are selected, and the generated subproblems are modeled after convex relaxation as follows:
after relaxation, solving by adopting a convex optimization algorithm; and after the optimal solution selected by the nodes is obtained, selecting the first L larger values, setting the corresponding nodes as 1 and the rest nodes as 0, removing the selected sensors, and repeating the steps by using the rest nodes until all targets are distributed.
7. The method for optimizing and scheduling resources for multi-objective tracking of distributed networking radar according to claim 1, wherein the optimization model obtained by fixing the bandwidth in step S6 is as follows:
solving by adopting a minimum maximum method to obtain the optimal solution of residence time distribution when the bandwidth is fixed
And an optimized objective function value fva T 。
8. The method for optimizing and scheduling resources for multi-objective tracking of distributed networking radar according to claim 1, wherein the optimization model obtained by fixing the residence time in step S7 is as follows:
obtaining the optimal solution of bandwidth allocation when the residence time is fixed by adopting the minimum maximum value method
And an optimized objective function value fva β 。
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