CN112213718B - Networking radar node selection and radiation resource joint optimization method under multi-target tracking - Google Patents
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Abstract
The invention discloses a networking radar node selection and radiation resource joint optimization method under multi-target tracking, which comprises the following steps: s1, determining the composition of a networking radar system and a multi-target tracking task; s2, constructing a predicted Bayesian-Luo lower bound matrix of the target motion state estimation error by taking radar node selection, each radar dwell time and radiation power as independent variables, and taking the trace sum of the predicted Bayesian-Luo lower bound matrix of each target as a measurement index of multi-target tracking accuracy; s3, establishing a networking radar node selection and radiation resource joint optimization model under multi-target tracking; and S4, solving the networking radar node selection and radiation resource joint optimization model under multi-target tracking by using a two-step optimization algorithm. The method reduces the estimation error of the networking radar system on the motion state of each target, and effectively improves the multi-target tracking precision.
Description
Technical Field
The invention relates to a radar signal processing technology, in particular to a networking radar node selection and radiation resource joint optimization method under multi-target tracking.
Background
Radio frequency radiation resources are very important resources in radar systems. Therefore, the radio frequency radiation resource optimal allocation in a multi-target tracking scene or the radio frequency radiation resource optimal allocation in a networking radar tracking scene is a research hotspot problem at present.
The networking radar is a radar system of a new system developed on the basis of the traditional phased array radar, can realize the independent control of each radar transmitter and receiver, and synthesizes expected beams according to the total amount of radar system resources, battlefield environment, task types, quantity and the like so as to realize the organic allocation of the radio frequency radiation resources of the networking radar system.
In order to improve the utilization rate of radar radio frequency radiation resources, research institutions and colleges at home and abroad have already done a great deal of work, and a solid theoretical foundation is laid for subsequent research. However, no method for joint optimization of networking radar node selection and radiation resource under multi-target tracking exists in the prior art.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a networking radar node selection and radiation resource joint optimization method under multi-target tracking, which takes the radiation resources of a networking radar system as constraint conditions, takes the sum of traces of Bayesian-Luo lower bound matrixes predicted by each target at each moment as an optimization target, and establishes a networking radar node selection and radiation resource joint optimization model under multi-target tracking, thereby reducing the motion state estimation error of each target by the networking radar system and effectively improving the multi-target tracking precision.
The technical scheme is as follows: the invention discloses a networking radar node selection and radiation resource joint optimization method under multi-target tracking, which comprises the following steps:
s1, determining the composition of a networking radar system and a multi-target tracking task;
s2, constructing a prediction Bayes-Lame lower bound matrix of the target motion state estimation error by taking radar node selection, radar residence time and radiation power as independent variables, and taking the track sum of the prediction Bayes-Lame lower bound matrix of each target as a measurement index of multi-target tracking accuracy;
s3, establishing a networking radar node selection and radiation resource joint optimization model under multi-target tracking;
and S4, solving the networking radar node selection and radiation resource joint optimization model under multi-target tracking by using a two-step optimization algorithm.
Furthermore, in the step S1, a networking radar system formed by M phased array radars is considered to track Q targets, the M phased array radars can keep accurate time, space and frequency synchronization, and each phased array radar can only receive and process target echoes from its own transmitted signal.
Further, step S2 specifically includes:
the Bayesian information matrix calculation expression of the qth target is as follows:
wherein, (. Cndot.) -1 The inverse operation of the matrix is represented,
a Bayesian information matrix for a qth target;
predicting the motion state vector of the qth object at time k for time k-1, wherein T Representing a transpose operation of a matrix or vector,
indicating the location of the qth object at time k-1 at which time k is predicted,
representing the motion speed of the qth target at the predicted k moment at the k-1 moment;
selecting variables for radar nodes when
When the target is shot and tracked by the nth radar at the time point k, the shot and the tracked target are shot and tracked
Then, the nth radar does not perform irradiation tracking on the qth target at the time k; q is a process noise covariance matrix, and the mathematical expression is as follows:
wherein, T 0 In order to be the sampling interval of the sample,
representing a matrix direct product operation, I 2 Is an identity matrix of order 2, r q Process noise strength for the qth target; f is a target state transition matrix, and the mathematical expression of the target state transition matrix is as follows:
wherein (x) n ,y n ) Position coordinates of the nth part of radar in the space;
the measured noise covariance matrix of the nth radar to the qth target is expressed by the following mathematical expression:
wherein, c =3 × 10 8 m/s, B is effective bandwidth of radar emission signal, lambda is radar working wavelength, and gamma isThe aperture of the antenna is set to be,
predicting the echo signal-to-noise ratio of the k moment to the q target for the nth radar k-1 moment, wherein the mathematical expression is as follows:
wherein,
and
respectively the dwell time and the radiation power of the nth radar irradiating the qth target at the time k, T r For each radar pulse repetition period, G t And G r For each radar transmit antenna gain and receive antenna gain,
radar cross section of the qth target relative to the nth radar, G RP Processing gain, k, for radar receivers 0 And T 0 Respectively Boltzmann constant and noise temperature of each radar receiver, B r Matching the filter bandwidth, F, for each radar receiver r Noise figure for each radar receiver;
predicting the distance between the k moment and the q target for the nth radar k-1 moment;
the formula (1) is inverted, namely a Bayesian Classmei-Rou lower bound matrix for predicting the estimation error of the q-th target motion state is obtained, and the mathematical expression is as follows:
here, bayesian clar is predicted using each targetMei-Luo lower bound matrix
The multi-target tracking precision is characterized by the sum of the traces of (1), namely:
wherein, tr (-) represents the trace operation of the matrix.
Further, step S3 specifically includes:
the method comprises the following steps of taking radiation resources of a networking radar system as constraint conditions, taking the sum of traces of a Bayesian Classman-Luo lower bound matrix for minimizing target prediction at each moment as an optimization target, and establishing a networking radar node selection and radiation resource combined optimization model under multi-target tracking as follows:
wherein, T d,min And T d,max Respectively the lower limit and the upper limit of the residence time of each radar; p min And P max Respectively the lower limit and the upper limit of the radiation power of each radar; t is a unit of total Is the total dwell time of the networked radar; p total Is the total radiated power of the networking radar; l is max And the number of radar nodes for carrying out irradiation tracking on the q-th target at the time k.
Further, step S4 specifically includes:
first, select
L with the largest value max The radar irradiates and tracks the q-th target and makes the corresponding target
Predicting the distance between the k moment and the q target for the nth radar k-1 moment;
and secondly, combining an interior point method and a cycle minimum method to obtain the residence time and radiation power optimal distribution result of each radar under the selection of the given radar node.
Furthermore, the specific steps of obtaining the residence time and the radiation power optimal distribution result of each radar under the selection of the given radar node by combining the interior point method and the cyclic minimum method are as follows:
(a) For the obtained radar node selection result, the networking radar node selection and radiation resource joint optimization model under multi-target tracking is simplified as follows:
(b) Order to
Adopting an interior point method in MATLAB software to call a function fmincon to calculate and solve the model simplified formula (10), namely obtaining an optimal solution of radiation power distribution when the residence time distribution of the networking radar is fixed
(c) Order to
Adopting an interior point method in MATLAB software to call a function fmincon to calculate and solve the model simplified formula (10), namely obtaining an optimal solution of residence time distribution when the distribution of the networking radar radiation power is fixed
(d) An optimal solution for assigning residence time
Substituting into a model simplified formula (10), jumping to the step (a), and circulating in sequence until the difference of the multi-target tracking precision obtained by two times of iterative calculation is less than a fixed value epsilon 0 At this time can be obtainedAnd determining the residence time and the radiation power optimization distribution result of each radar under the selection of the radar nodes.
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) The invention provides a method for joint optimization of node selection and radiation resources of networking radar under multi-target tracking, which completes the main task of tracking multiple targets by considering a networking radar system consisting of a plurality of phased array radars, wherein the radars can keep accurate time, space and frequency synchronization, and each radar can only receive and process target echoes of self-transmitted signals. Firstly, constructing a prediction Bayesian-Lame lower bound matrix of a target motion state estimation error by taking radar node selection, radar residence time and radiation power as independent variables, and taking the sum of trails of the prediction Bayesian-Lame lower bound matrix of each target as a measurement index of multi-target tracking accuracy; secondly, by taking the radiation resources of the networking radar system as constraint conditions, and by taking the sum of the traces of the Bayesian-Luo lower bound matrix for minimizing the prediction of each target at each moment as an optimization target, a networking radar node selection and radiation resource combined optimization model under multi-target tracking is established, so that the motion state estimation error of each target by the networking radar system is reduced, and the multi-target tracking precision is effectively improved.
The method has the advantages that the radiation resource of the networking radar system can be met, the motion state estimation error of the networking radar system on each target can be reduced, and the multi-target tracking precision of the networking radar system is effectively improved. The method takes the radiation resources of a networking radar system as a constraint condition, takes the sum of the traces of a Bayesian-Ro lower bound matrix for each target prediction at each moment as an optimization target, and establishes a networking radar node selection and radiation resource combined optimization model under multi-target tracking. By adopting a two-step optimization algorithm to solve the optimization model, a networking radar node selection, residence time and radiation power combined optimization result meeting constraint conditions can be obtained, and therefore the multi-target tracking precision of the networking radar system is effectively improved.
(2) Compared with the prior art, the networking radar node selection and radiation resource joint optimization method under multi-target tracking provided by the invention not only can meet the radiation resource requirement of a networking radar system, but also can reduce the motion state estimation error of each target of the networking radar system, thereby effectively improving the multi-target tracking precision.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
The invention provides a networking radar node selection and radiation resource combined optimization method under multi-target tracking based on the current military application requirements, and establishes a networking radar node selection and radiation resource combined optimization model under multi-target tracking by taking the radiation resources of a networking radar system as constraint conditions and minimizing the sum of the traces of Bayesian-Rale lower bound matrixes predicted by each target at each moment as an optimization target, so that the motion state estimation error of each target by the networking radar system is reduced, and the multi-target tracking precision of the networking radar system is effectively improved.
As shown in fig. 1, the method for jointly optimizing networking radar node selection and radiation resources under multi-target tracking of the present invention includes the following steps:
s1, determining the composition of a networking radar system and a multi-target tracking task;
a networking radar system consisting of M phased array radars is considered to track Q targets, the radars can keep accurate time, space and frequency synchronization, and each radar can only receive and process target echoes from own transmitted signals.
S2, constructing a predicted Bayesian-Luo lower bound matrix of the target motion state estimation error by taking radar node selection, radar dwell time and radiation power as independent variables, and taking the track sum of the predicted Bayesian-Luo lower bound matrix of each target as a measurement index of the multi-target tracking accuracy, wherein the measurement index is as follows:
the Bayesian information matrix calculation expression of the qth target is as follows:
wherein, (.) -1 The inverse operation of the matrix is represented,
a Bayesian information matrix for a qth target;
predicting the motion state vector of the qth target at time k for time k-1, wherein · T Representing a transpose operation of a matrix or vector,
indicating the position of the qth object at time k-1,
representing the motion speed of the qth target at the predicted k moment at the k-1 moment;
selecting variables for radar nodes when
When the target is located at the k time, the nth radar performs irradiation tracking on the qth target
Then, the nth radar does not perform irradiation tracking on the qth target at the time k; q is a process noise covariance matrix, and the mathematical expression of the process noise covariance matrix is as follows:
wherein, T 0 In order to be the sampling interval of the sample,
representing a matrix direct product operation, I 2 Is an identity matrix of order 2, r q Process noise strength for the qth target; f is a target state transition matrix, and the mathematical expression of the target state transition matrix is as follows:
wherein (x) n ,y n ) Position coordinates of the nth part of radar in the space;
the measured noise covariance matrix of the nth radar to the qth target is expressed by the following mathematical expression:
wherein, c =3 × 10 8 m/s, B is the effective bandwidth of the radar emission signal, lambda is the radar operating wavelength, gamma is the antenna aperture,
predicting the echo signal-to-noise ratio of the k moment to the q target at the k-1 moment of the nth radar, wherein the mathematical expression is as follows:
wherein,
and
respectively the dwell time and the radiation power of the nth radar irradiating the qth target at the time k, T r For each radar pulse repetition period, G t And G r For each radar transmit antenna gain and receive antenna gain,
radar cross section of the qth target relative to the nth radar, G RP Processing gain, k, for radar receivers 0 And T 0 Respectively Boltzmann constant and noise temperature of each radar receiver, B r Matching the filter bandwidth, F, for each radar receiver r For each of the radar receiver noise figure(s),
predicting the distance between the k moment and the q target for the nth radar k-1 moment; .
The formula (1) is inverted, so that a Bayesian Classmen-Rou lower bound matrix for predicting the estimation error of the q-th target motion state can be obtained, and the mathematical expression is as follows:
here, a Bayesian-Lame lower bound matrix is predicted using each target
The multi-target tracking precision is characterized by the sum of the traces of (1), namely:
wherein, tr (·) represents a trace operation of matrix calculation.
S3, establishing a networking radar node selection and radiation resource joint optimization model under multi-target tracking, as follows:
by taking the radiation resources of the networking radar system as constraint conditions and taking the sum of the traces of the Bayesian-Ro lower bound matrix for minimizing the prediction of each target at each moment as an optimization target, a networking radar node selection and radiation resource combined optimization model under multi-target tracking is established, and is as follows:
wherein, T d,min And T d,max Respectively the lower limit and the upper limit of the residence time of each radar; p min And P max Respectively the lower limit and the upper limit of the radiation power of each radar; t is total Is the total dwell time of the networked radar; p total Is the total radiated power of the networking radar; l is max And the number of radar nodes for carrying out irradiation tracking on the q-th target at the time k.
S4, solving a networking radar node selection and radiation resource combined optimization model under multi-target tracking by using a two-step optimization algorithm, namely a formula (9):
first, select
L with the largest value max The radar irradiates the q-th targetShoot-follow and order the corresponding
And secondly, combining an interior point method and a cycle minimum method to obtain the residence time and radiation power optimal distribution result of each radar under the selection of the given radar node.
(a) For the obtained radar node selection result, the model for jointly optimizing networking radar node selection and radiation resources under multi-target tracking, namely the formula (9), can be simplified as follows:
(b) Order to
Adopting an interior point method in MATLAB software to call a function fmincon to calculate and solve the model simplified formula (10), and obtaining an optimal solution of radiation power distribution when the residence time distribution of the networking radar is fixed
(c) Order to
Adopting an interior point method in MATLAB software to call a function fmincon to calculate and solve the model simplified formula (10), namely obtaining an optimal solution of residence time distribution when the distribution of the networking radar radiation power is fixed
(d) An optimal solution for assigning residence time
Substituting into a model simplified formula (10), jumping to the step (a), and circulating in sequence until the difference of the multi-target tracking precision obtained by two times of iterative calculationLess than a fixed value epsilon 0 And at the moment, the residence time and radiation power optimization distribution result of each radar under the selection of the given radar node can be obtained.
The working principle and the working process of the invention are as follows:
the invention considers that a networking radar system formed by a plurality of phased array radars tracks multiple targets, the radars can keep accurate time, space and frequency synchronization, and each radar can only receive and process target echoes of self-transmitted signals. Firstly, constructing a predicted Bayesian-Luo lower bound matrix of a target motion state estimation error by taking radar node selection, each radar dwell time and radiation power as independent variables, and taking the trace sum of the predicted Bayesian-Luo lower bound matrix of each target as a measurement index of multi-target tracking accuracy; secondly, by taking the radiation resources of the networking radar system as constraint conditions and taking the sum of the traces of the Bayesian-Rauwolf lower bound matrix for predicting each target at each moment as an optimization target, a networking radar node selection and radiation resource combined optimization model under multi-target tracking is established, so that the motion state estimation error of each target by the networking radar system is reduced, and the multi-target tracking precision of the networking radar system is effectively improved; and finally, solving the optimization model by adopting a two-step optimization algorithm to obtain a networking radar node selection, residence time and radiation power combined optimization result which meets the constraint condition.
The invention is characterized in that:
1. tracking multiple targets by a networking radar system consisting of multiple phased array radars, wherein the radars can keep accurate time, space and frequency synchronization, and each radar can only receive and process target echoes of a signal transmitted by the radar; constructing a prediction Bayesian-Lame lower bound matrix of a target motion state estimation error by taking radar node selection, radar residence time and radiation power as independent variables, and taking the sum of traces of the prediction Bayesian-Lame lower bound matrix of each target as a measurement index of multi-target tracking accuracy;
2. the method comprises the steps of taking radiation resources of a networking radar system as constraint conditions, taking the sum of the traces of a Bayesian-Luo lower bound matrix of target prediction at each moment as an optimization target, establishing a networking radar node selection and radiation resource combined optimization model under multi-target tracking, solving the optimization model by adopting a two-step optimization algorithm, and determining the networking radar node selection, residence time and radiation power which enable the sum of the traces of the Bayesian-Luo lower bound matrix of target prediction to be minimized as an optimal solution.
Claims (2)
1. The method for jointly optimizing networking radar node selection and radiation resources under multi-target tracking is characterized by comprising the following steps:
s1, determining the composition of a networking radar system and a multi-target tracking task, and tracking Q targets by considering the networking radar system consisting of M phased array radars;
s2, constructing a predicted Bayesian-Luo lower bound matrix of the target motion state estimation error by taking radar node selection, each radar dwell time and radiation power as independent variables, and taking the trace sum of the predicted Bayesian-Luo lower bound matrix of each target as a measurement index of multi-target tracking accuracy; the method specifically comprises the following steps:
the Bayesian information matrix calculation expression of the qth target is as follows:
wherein, (.) -1 The inverse operation of the matrix is represented,
a Bayesian information matrix for a qth target;
predicting the motion state vector of the qth object at time k for time k-1, wherein T Representing a transpose operation of a matrix or vector,
indicating the location of the qth object at time k-1 at which time k is predicted,
representing the motion speed of the qth target at the predicted k moment at the k-1 moment;
selecting variables for radar nodes when
When the target is located at the k time, the nth radar performs irradiation tracking on the qth target
When the target is shot, the nth radar does not carry out irradiation tracking on the qth target at the moment k; q is a process noise covariance matrix, and the mathematical expression is as follows:
wherein, T 0 In order to be the sampling interval of the sample,
representing a matrix direct product operation, I 2 Is an identity matrix of order 2, r q Process noise strength for the qth target; f is a target state transition matrix, and the mathematical expression of the target state transition matrix is as follows:
wherein (x) n ,y n ) Position coordinates of the nth part of radar in the space;
the measured noise covariance matrix of the nth radar to the qth target is expressed by the following mathematical expression:
wherein, c =3 × 10 8 m/s, B is the effective bandwidth of the radar emission signal, lambda is the radar operating wavelength, gamma is the antenna aperture,
predicting the echo signal-to-noise ratio of the k moment to the q target at the k-1 moment of the nth radar, wherein the mathematical expression is as follows:
wherein,
and
respectively the dwell time and the radiation power of the nth radar irradiating the qth target at the time k, T r For each radar pulse repetition period, G t And G r For each radar transmit antenna gain and receive antenna gain,
radar cross section of the qth target relative to the nth radar, G RP Processing gain, k, for radar receivers 0 And T 0 Respectively Boltzmann constant and noise temperature of each radar receiver, B r Matching the filter bandwidth, F, for each radar receiver r Noise figure for each radar receiver;
predicting the distance between the k moment and the q target for the nth radar k-1 moment;
the formula (1) is inverted, namely a Bayesian Classmei-Rou lower bound matrix for predicting the estimation error of the q-th target motion state is obtained, and the mathematical expression is as follows:
here, a Bayesian-Lame lower bound matrix is predicted using each target
The multi-target tracking precision is characterized by the sum of the traces of (1), namely:
wherein, tr (-) represents the trace operation of matrix calculation;
s3, establishing a networking radar node selection and radiation resource joint optimization model under multi-target tracking; the method specifically comprises the following steps:
the method comprises the following steps of taking radiation resources of a networking radar system as constraint conditions, taking the sum of traces of a Bayesian Classman-Luo lower bound matrix for minimizing target prediction at each moment as an optimization target, and establishing a networking radar node selection and radiation resource combined optimization model under multi-target tracking as follows:
wherein, T d,min And T d,max Respectively the lower limit and the upper limit of the residence time of each radar; p min And P max Respectively the lower limit and the upper limit of the radiation power of each radar; t is a unit of total Total residence time for the networked radar; p total Is the total radiated power of the networking radar; l is max The number of radar nodes for performing irradiation tracking on the q-th target at the time k;
s4, solving a networking radar node selection and radiation resource joint optimization model under multi-target tracking by using a two-step optimization algorithm; the method comprises the following specific steps:
first, select
L with the largest value max The radar irradiates and tracks the q-th target and makes the corresponding target
Predicting the distance between the k moment and the q target for the nth radar k-1 moment;
secondly, combining an interior point method and a cycle minimum method to obtain the residence time and radiation power optimal distribution result of each radar under the selection of the given radar node;
the method comprises the following specific steps of combining an interior point method and a cycle minimum method to obtain the residence time and radiation power optimal distribution result of each radar under the condition that a given radar node is selected:
(a) For the obtained radar node selection result, the networking radar node selection and radiation resource joint optimization model under multi-target tracking is simplified as follows:
(b) Order to
Adopting an interior point method in MATLAB software to call a function fmincon to calculate and solve the model simplified formula (10), namely obtaining an optimal solution of radiation power distribution when the residence time distribution of the networking radar is fixed
(c) Order to
Adopting an interior point method in MATLAB software to call a function fmincon to calculate and solve the model simplified formula (10), namely obtaining an optimal solution of residence time distribution when the distribution of the networking radar radiation power is fixed
(d) An optimal solution for assigning residence time
Substituting the model into a simplified formula (10), skipping to the step (a), and circulating in sequence until the difference of the multi-target tracking precision obtained by two times of iterative computation is less than a fixed value epsilon 0 At this time, can be obtainedAnd determining the residence time and the radiation power optimization distribution result of each radar under the selection of the radar nodes.
2. The method for joint optimization of node selection and radiation resource of networking radar under multi-target tracking according to claim 1, wherein in the step S1, the M phased array radars can keep accurate time, space and frequency synchronization, and each phased array radar can only receive and process target echoes from its own transmitted signal.
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| CN110412515B (en) * | 2019-08-19 | 2023-02-03 | 南京航空航天大学 | Multi-target tracking transmission power distribution method for networking radar based on radio frequency stealth |
| CN111025275B (en) * | 2019-11-21 | 2021-10-08 | 南京航空航天大学 | Multi-base radar radiation parameter multi-target joint optimization method based on radio frequency stealth |
| CN111323773A (en) * | 2020-02-20 | 2020-06-23 | 南京航空航天大学 | Networking radar power and bandwidth joint optimization distribution method based on radio frequency stealth |
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