A multi-target tracking networking radar power distribution method for bidirectional data packet loss

Abstract

The application discloses a kind of multi-target tracking networking radar power distribution methods of two-way data packet loss, which includes: constructing system model;According to system model, state space model and measurement model are constructed, target motion equation is established, target covariance matrix and measurement covariance matrix are obtained;According to target covariance matrix and measurement covariance matrix, target tracking error covariance matrix is obtained, the lower bound of expected covariance matrix is obtained by taking expectation, as a measure standard, the lower bound of predicted expected covariance matrix is calculated, by iterating the expected covariance matrix forward, the approximate value of prediction error covariance is obtained, used as optimization criterion in power distribution method;Establish power distribution mathematical model;Solve power distribution mathematical model, obtain the result of multi-target tracking networking radar power distribution.The application improves the multi-target tracking performance of networking radar under the condition of two-way data packet loss.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and relates to a method for power distribution of a multi-target tracking networking radar with bidirectional data packet loss. BACKGROUND

[0002] A networking radar system is a radar system that synchronously transmits radar signals under the control of a fusion center by using multiple transmitters deployed in different places, simultaneously receives echo signals transmitted from targets by using multiple receivers, and centrally processes the signals.

[0003] Radar networking is currently the mainstream important tool for performing various military and civilian tasks, especially unmanned aerial vehicle networking. However, because unmanned aerial vehicle networking uses wireless communication, the communication signals are affected by factors such as Rayleigh fading in the transmission path, causing communication data loss, i.e., packet loss. Allocating radar networking resources without considering packet loss may result in inaccurate or incorrect allocation results, affecting the effectiveness of radar networking task execution. Therefore, it is urgent and important to invent a radar resource allocation algorithm that takes packet loss into account.

[0004] Currently, existing research results involve the transmission power allocation problem of networking radar multi-target tracking. Under the condition of satisfying the transmission resources of the networking radar, the radar selection and residence time are jointly optimized and designed, which improves the multi-target tracking accuracy of the networking radar system to a certain extent. However, there are also certain limitations.

[0005] Li Zhengjie et al. in "Power and bandwidth joint allocation algorithm based on centralized MIMO radar[J]. Systems Engineering and Electronics, 2020, 42(5): 1041-1049" predicted the posterior Cramer-Rao lower bound of the position error of each target to construct a cost function to establish an optimization model, thereby converting the resource allocation problem into a non-convex optimization problem. Then, the convex relaxation technique and the cyclic minimization algorithm were used to solve the non-convex optimization problem. Finally, the effectiveness of the proposed algorithm was verified through simulation. However, the power and bandwidth joint allocation algorithm does not consider the case of possible data loss between the transmitting and receiving beams.

[0006] In "Spectrum coexistence under multi-target tracking oriented networking radar power time joint optimization algorithm[J]. Journal of Radar: 2022, 11: 1-12", Shi Chen et al. proposed a networking radar power time joint optimization algorithm for multi-target tracking resource allocation in spectrum coexistence environment. The method sets the communication signal to tolerate the interference of radar signal less than the threshold value, which indicates that the communication function is normal, i.e. the communication function is not damaged. By allocating radar resources, the multi-target tracking performance of the networking radar system is improved under the condition of mutual interference between communication and radar. However, this method does not consider the case of damaged communication. SUMMARY

[0007] To solve the technical problem that the resource allocation model in the prior art is mismatched under the condition of packet loss, resulting in inaccurate allocation results or making wrong allocation results, the present application provides a multi-target tracking networking radar power allocation method for bidirectional data packet loss. The technical solution adopted by the present application is:

[0008] A multi-target tracking networking radar power allocation method for bidirectional data packet loss, comprising:

[0009] S1, a networking radar system composed of N radars is established, each radar independently detects and tracks multiple targets dispersedly deployed, a system model is constructed, and a target state is established;

[0010] S2, a state space model is constructed according to the system model, a target motion equation is established, the target state is predicted and updated according to the target motion equation, and a predicted target state and a target covariance matrix are obtained;

[0011] S3, a measurement model is constructed according to the system model, and a measurement covariance matrix is obtained according to the measurement model;

[0012] S4, a target tracking error covariance matrix is obtained according to the target covariance matrix and the measurement covariance matrix, a lower bound of the expected covariance matrix is obtained by taking the expectation of the target tracking error covariance matrix, the lower bound of the expected covariance matrix is used as a measurement standard, the lower bound of the predicted expected covariance matrix is calculated using the state space model and the measurement model, and the lower bound of the predicted expected covariance matrix is iterated forward to obtain an approximate value of the prediction error covariance under the condition of bidirectional data packet loss, which is used as an optimization criterion in the power allocation method;

[0013] S5, the lower bound of the predicted covariance matrix is used as a cost function of power allocation, the total power of the networking radar system is limited as a constraint, and a power allocation mathematical model is established according to the optimization criterion;

[0014] S6, the power allocation mathematical model is solved to obtain the result of the multi-target tracking networking radar power allocation.

[0015] In one embodiment of the present application, the target motion equation established in S2 is:

[0016] x q,k =Fx q,k-1 +ε q,k-1

[0017] In the above formula, x q，k represents the target state vector at the kth moment in the monitoring area, (x q,k ,y q,k ) represents the position of the target q at the kth moment; represents the velocity of the target q at the kth moment; ΔT represents the tracking time interval; is the state transition matrix; represents the Kronecker product; I2 represents a 2-order unit matrix; ε q,k-1 represents a Gaussian process white noise with a mean of zero, and its covariance matrix Q q,k-1 represents:

[0018]

[0019] In the above formula, r q represents the process noise intensity.

[0020] In one embodiment of the present application, the measurement model constructed in S3 is:

[0021] z n.q,k =h n,q,k (x q,k )+w n,q,k

[0022]

[0023]

[0024] The fusion center can receive the measurement data from the radar n only when and only when the variables μ n,k ,β n,k are both 1;

[0025] In the above formula, h n,q,k (·) represents an observation function, denoted as h n,q,k (x q,k ) = [r n,q,k f n,q,k ] T :

[0026]

[0027] wherein r n,q,kand f n,q,k w represents distance and Doppler measurement, respectively. n,q,k The measurement error is represented by a Gaussian distribution with zero mean and a variance of R. n,q,k .

[0028] In one embodiment of the present invention, the method for calculating the variance of the measurement error in S3 is as follows:

[0029]

[0030] In the above formula, and Let the estimated variances of distance and Doppler measurements be represented, respectively, and approximately as follows:

[0031]

[0032] Where, α n,q,k ∝1 / (r n,q,k ) 4 Indicates path fading, |h n,q,k | 2 B is the target's radar cross section. n,k and T n,k Indicates the effective bandwidth and duration of the transmitted signal; P n,k It is the result of power scheduling, when μ n,k =1, Radar n successfully received the power allocation result P n,k Otherwise, P n,k Packet loss occurs when packets are lost during transmission.

[0033] In one embodiment of the present invention, S4 includes:

[0034] Using the lower bound E of the expected covariance matrix As a benchmark;

[0035] Based on Jensen's inequality theorem, if X is a random variable and φ is a convex function, then:

[0036] φ(E[X])≤E[φ(X)]

[0037] Therefore, we have:

[0038]

[0039] The lower bound of the predicted expected covariance matrix is ​​approximated using the state-space model and measurement model:

[0040]

[0041] In the formula, Indicates the predicted target state;

[0042] By iterating the predicted covariance matrix forward, an approximation of the prediction error covariance is obtained in the case of two-way data packet loss, which is used as an optimization criterion in the power allocation method.

[0043] In one embodiment of the present application, the target covariance matrix in S4 is:

[0044] x q,k|k-1 = Fx q,k-1

[0045]

[0046] The above formula is a prediction update of the target state according to the target motion equation, at the kth moment, the predicted state of the target q and the target covariance matrix;

[0047] When the system model is completely observable and there is no packet loss, according to the information filtering algorithm, the target tracking error covariance matrix is represented as:

[0048]

[0049] Wherein is the Jacobian matrix of the measurement function h z (x x ) with a dimension of n n,q,k ×n q,k ;

[0050] From the above formula, the target tracking error covariance matrix is related to the random packet loss variable β 1,k ,β 2,k ,K,β N,k and μ 1,k ,μ 2,k ,K,μ N,k , therefore, the target tracking error covariance matrix under two-way packet loss is represented as:

[0051]

[0052] The above formula shows that if there is packet loss in any process of the two-way transmission process of radar node i, the fusion center does not have all the measurement data of node i, and can only use other successfully received node measurements for updating;

[0053] Therefore, the above formula is rewritten as:

[0054]

[0055] In one embodiment of the present application, the measurement covariance matrix in S4 is:

[0056]

[0057] From the above equation, we obtain the measurement covariance matrix R. n,q,k It is inversely proportional to the power variable, where D n,q,k This represents the remaining parameter matrix.

[0058] In one embodiment of the present invention, the power allocation mathematical model established in S5 is as follows:

[0059]

[0060] stP n,min ≤P n,k ≤P n,max

[0061]

[0062] Among them, P n,min and P n,max These are the lower and upper limits of the system power, P. tot For total power; F(P) k The overall performance of multi-target tracking is defined as the average of the lower bound traces of the expected covariance matrix, expressed as: Tr[·] represents the trace operation of a matrix.

[0063] In one embodiment of the present invention, the method for S6 to find the solution of the power allocation mathematical model is as follows:

[0064] If the objective function F(P) k If is a convex function, then finding the solution to the power allocation mathematical model is a convex optimization problem. A convex optimization algorithm is used to solve it, and P is used to replace P. k Let λ∈[0,1], then:

[0065]

[0066] F(λP1+(1-λ)P2)≤λF(P1)+(1-λ)F(P2)

[0067] The optimization problem in the above equation is a convex optimization problem with only one continuous power variable. It is solved using the convex optimization toolbox, and the solution obtained is the result of power allocation for multi-target tracking network radar.

[0068] The beneficial effects of this invention are:

[0069] The two-way data packet loss multi-target tracking networked radar power distribution method considers that the communication between networked radars is lossy, and part of data may be lost between nodes and fusion centers, causing packet loss, and derives statistical characteristics of an error covariance matrix under the condition of packet loss, so as to establish a radar power distribution mathematical model for an optimization objective function, and improve the multi-target tracking performance of networked radars under the condition of two-way data packet loss. BRIEF DESCRIPTION OF DRAWINGS

[0070] Figure 1 A flowchart of the two-way data packet loss multi-target tracking networked radar power distribution method provided by the embodiment of the present application is shown in the figure.

[0071] Figure 2 A radar and target spatial distribution diagram of the embodiment of the present application is shown in the figure.

[0072] Figure 3 A diagram of the relationship between packet loss probability and distance of the embodiment of the present application is shown in the figure.

[0073] Figure 4 A power distribution result diagram of 50 times of Monte Carlo of the power distribution algorithm of the embodiment of the present application which does not consider packet loss is shown in the figure.

[0074] Figure 5 A power distribution result diagram of 50 times of Monte Carlo of the power distribution algorithm of the embodiment of the present application which considers packet loss is shown in the figure.

[0075] Figure 6 A comparison diagram of the weighted average RMSE and ELBTEC of two targets changing with time under the power distribution algorithm of the embodiment of the present application and the power distribution algorithm and the uniform power distribution algorithm which do not consider packet loss is shown in the figure. DETAILED DESCRIPTION

[0076] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0077] The embodiment of the present application provides a two-way data packet loss multi-target tracking networked radar power distribution method, referring to the drawings Figure 1 The two-way data packet loss multi-target tracking networked radar power distribution method comprises the following steps:

[0078] S1, a networked radar system composed of N radars is established, each radar independently detects and tracks multiple targets dispersedly deployed, a system model is constructed, and a target state is established;

[0079] S2, constructing a state space model according to the system model, establishing a target motion equation, and predicting and updating the target state according to the target motion equation to obtain a predicted target state and a target covariance matrix;

[0080] S3, constructing a measurement model according to the system model, and obtaining a measurement covariance matrix according to the measurement model;

[0081] S4, obtaining a target tracking error covariance matrix according to the target covariance matrix and the measurement covariance matrix, taking an expectation of the target tracking error covariance matrix to obtain a lower bound of an expectation covariance matrix, taking the lower bound of the expectation covariance matrix as a measurement standard, calculating a predicted lower bound of the expectation covariance matrix by using the state space model and the measurement model, and obtaining an approximate value of a prediction error covariance by iteratively moving forward the predicted expectation covariance matrix, which is used as an optimization criterion in a power allocation method under a bidirectional data packet loss condition;

[0082] S5, taking the lower bound of the predicted covariance matrix as a cost function of power allocation, taking the limited total power of the networking radar system as a constraint, and establishing a power allocation mathematical model according to the optimization criterion;

[0083] S6, solving the power allocation mathematical model to obtain a result of the multi-target tracking networking radar power allocation.

[0084] In an optional embodiment, a networking radar system composed of N radars is considered, each radar independently detects and tracks multiple targets scatteredly deployed, a system model is constructed, and a target state is established. The system model refers to a large scene of allocation, which influences the establishment of a state space model and a measurement model. The coordinates of the radar n are n = 1, 2, K, N, and the coordinates of the fusion center are It is assumed that each radar node can cover all targets. Each radar node uniformly encodes all the detected target measurements and sends them to the fusion center in the form of a single data packet. If the data packet is correctly received, the fusion center receives the complete measurement data of the node; if the data packet is lost, the fusion center loses all the measurement data of the node. The fusion center estimates the global state by fusing the received node measurements and performs resource scheduling, and finally feeds back the resource scheduling result to each radar node. If the radar node successfully receives the allocation result, it works according to the allocation result at the next moment; if it does not receive the allocation result, it maintains the on state at the next moment with a small power.

[0085] The radar and target space distribution diagram of the embodiment of the application is shown in Fig. 1. Figure 2 The relationship between the packet loss probability and the distance is shown in Fig. 2. Figure 3 .

[0086] Due to the existence of data packet loss phenomenon, the receiving process of data packet is usually represented as a random process, using Bernoulli variable β n,k and μ n,k represent the random packet loss variable, is the non-packet loss probability in the process of transmitting target measurement from radar n to fusion center at the kth moment, packet loss probability is the packet loss probability in the process of transmitting resource scheduling results from fusion center to radar n at the kth moment, packet loss probability In actual wireless communication network, due to the existence of path fading, the packet loss probability is related to the distance between radar node and fusion center.

[0087] For ease of description, it is assumed that the target state vector at the kth moment in the monitoring area is where (x q,k , y q,k ) represents the position of target q at the kth moment; represents the velocity of target q at the kth moment; ΔT represents the tracking time interval. According to the system model, the state space model is constructed, and the target motion equation is established. Assuming that the target moves at a constant speed in a straight line, the motion equation of the target is:

[0088] x q,k = Fx q,k-1 + ε q,k-1 (1)

[0089] In formula (1), is the state transition matrix; represents the Kronecker product; I2 represents a 2-order unit matrix; ε q,k-1 represents a Gaussian process white noise with zero mean, and its covariance matrix Q q,k-1 can be represented as:

[0090]

[0091] In formula (2), r q represents the process noise intensity.

[0092] According to the target motion equation, the target state is predicted and updated to obtain the predicted target state and target covariance matrix.

[0093] In an optional implementation, it is assumed that radar n tracks target q to generate a measurement vector z n.q,k , the local measurement received by the fusion center from radar n is Z n.k , and the transmission signal power of radar n is P n,kAccording to the system model, a measurement model is constructed, and the fusion center receives the measurement model in the case of packet loss in the data bidirectional transmission process:

[0094] z n.q,k = h n,q,k (x q,k ) + w n,q,k (3)

[0095]

[0096]

[0097] It can be concluded from formula (3) that the fusion center can receive the measurement data from radar n only when the variables μ n,k and β n,k are both 1.

[0098] In formula (3), h n,q,k (·) represents an observation function, denoted as h n,q,k (x q,k ) = [r n,q,k f n,q,k ] T :

[0099]

[0100] In formula (6), r n,q,k and f n,q,k represent the distance and Doppler measurement respectively, and w n,q,k represents the measurement error, which is subject to a zero-mean Gaussian distribution, and its variance is R n,q,k :

[0101]

[0102] In formula (7), σ r and σ f

[0103] represent the estimated variances of the distance and Doppler measurement respectively, which can be approximately represented as:

[0104] In formula (8), α n,q,k ∝1 / (r n,q,k ) 4 represents path loss, |h n,q,k | 2 is the target radar cross section (RCS). B n,k and T n,k represent the effective bandwidth and time width of the transmitted signal. As can be seen from the formula, the greater the power, the smaller the measurement noise w n,q,k . P n,kis the power scheduling result, when μ n,k = 1, the radar n successfully receives the power allocation result P n,k , otherwise, P n,k is lost in the transmission process, resulting in packet loss, and it can be obtained from formula (4) that the power variable is a random variable, and because the measurement noise is related to the power, the measurement noise also has randomness.

[0105] Because of the existence of double-sided random data packet loss, the transmission power of the radar node and the received measurement of the fusion center have randomness. Embodiments of the present application study the tracking performance criterion of a discrete random system with double-sided random packet loss.

[0106] Embodiments of the present application construct a tracking optimization criterion under the condition of bidirectional random packet loss. For an ideal communication network without packet loss, the stability of the matrix (F, Q q,k ) and the detectability of the matrix (F, H n,q,k ) ensure that the error covariance matrix converges to a unique value from any initial condition. However, because of the randomness of the power and the measurement, there is no longer a unique deterministic error covariance matrix at the steady state. The present application studies the statistical properties of the error covariance matrix under the condition of random loss of the power variable and the measurement due to the existence of packet loss.

[0107] According to the motion equation, the target state is updated, and at the kth moment, the predicted target state of the target q and the target covariance matrix are:

[0108] x q,k|k-1 = Fx q,k-1

[0109]

[0110] When the system is completely observable and there is no packet loss, according to the information filtering algorithm, the target tracking error covariance matrix can be expressed as:

[0111]

[0112] In formula (10), is the Jacobian matrix of the measurement function h z (x x ) with a dimension of n n,q,k × n q,k .

[0113] From formula (9) and formula (10), it can be obtained that the covariance matrix is related to the random packet loss variables β 1,k , β 2,k , K, β N,k and μ 1,k , μ 2,k , K, μN,k The target tracking error covariance matrix under the bidirectional packet loss can be expressed as:

[0114]

[0115] Equation (11) shows that if there is packet loss in any process of the bidirectional transmission process of radar node i, the fusion center does not have all the measurement data of node i, and can only update using other successfully received node measurements.

[0116] Therefore, equation (11) can be rewritten as:

[0117]

[0118] From equation (12), the measurement covariance matrix R n,q,k is inversely proportional to the power variable, and equation (12) can be rewritten as:

[0119]

[0120] Equation (13) is the measurement covariance matrix. In equation (13), D n,q,k represents the remaining parameter matrix.

[0121] Since the covariance matrix includes random packet loss variables (β n,k ,μ n,k ), the covariance matrix is a random process that changes over time and cannot be used as a standard for measuring target tracking error. Therefore, the lower bound of the expected covariance matrix (ELBTEC) E is used as a measurement standard.

[0122] Based on the Jensen inequality theorem, if X is a random variable and φ is a convex function, then:

[0123] φ(E[X])≤E[φ(X)] (14)

[0124] Therefore, there is a lower bound of the expected covariance matrix:

[0125]

[0126] Using the prior information of target motion (including the predicted target state and the predicted covariance matrix derived from the state space model and the measurement covariance matrix constructed from the measurement model) can approximately calculate the predicted ELBTEC:

[0127]

[0128] In equation (16), represents the predicted target state.

[0129] The predicted covariance uses the expected covariance of the previous time step to predict the expected covariance of the next time step. By iterating forward the predicted ELBTEC, an approximation of the future state error covariance is given in the presence of random packet loss; furthermore, it is a function of the adjustable power variable and can be directly used as an optimization criterion in power allocation strategies.

[0130] This invention proposes a power allocation algorithm for networked radar systems under bidirectional packet loss conditions. The aim is to rationally set the radar transmit power at each moment, thereby minimizing resource consumption. As described above, ELBTEC provides a theoretical lower bound for target tracking error under packet loss conditions, and the ELBTEC at the next moment can be predicted given the transmit parameters. Using this as the cost function for power allocation, and constrained by the finite total transmit power of the networked radar system, a power optimization mathematical model is established.

[0131] The overall performance of multi-target tracking is defined as the average of the ELBTEC traces, expressed as:

[0132]

[0133] In formula (17), Tr[·] represents the trace operation of a matrix.

[0134] The mathematical model for power allocation is expressed as follows:

[0135]

[0136] stP n,min ≤P n,k ≤P n,max

[0137]

[0138] In formula (18), P n,min and P n,max These are the lower and upper limits of the system power, P. tot This represents the total power.

[0139] Finally, the mathematical problem is solved, namely, the mathematical model for power optimization.

[0140] From formula (18), it can be concluded that since all constraints are linear constraints, if the objective function F(P) k If is a convex function, then the problem is a convex optimization problem and can be solved using a convex optimization algorithm. For ease of explanation, the proof will use P instead of P. k Let λ∈[0,1].

[0141]

[0142] The existing technology has been disclosed.

[0143] F (λP1+ (1-λ)P2) ≤ λF (P1) + (1-λ)F (P2) (20)

[0144] Therefore, the optimization problem of formula (19) is a convex optimization problem including only one power continuous variable, which can be solved by using the CVX convex optimization toolbox, and the obtained solution is the result of power distribution of the multi-target tracking networked radar.

[0145] The power distribution result graph of the power distribution algorithm without considering packet loss in 50 Monte Carlo is referred to the attached Figure 4 The attached Figure 4 It is shown that the power distribution algorithm without considering packet loss is only related to the distance of the target and the radar and the observation angle. The power distribution result graph of the power distribution algorithm considering packet loss in 50 Monte Carlo is referred to the attached Figure 5 The attached Figure 5 It is shown that the algorithm of the application equally considers the radar and target distance, the observation angle and the power distribution of each radar packet loss probability.

[0146] The curve comparison graph of the weighted average root mean square error (RMSE) of two targets and the lower bound of the expected covariance matrix (ELBTEC) changing with time under the power distribution algorithm without considering packet loss and the uniform power distribution algorithm is referred to the attached Figure 6 The attached Figure 6 It is shown that compared with the other two algorithms, the two-way data packet loss multi-target tracking networked radar power distribution method of the application can well match the real packet loss environment, the target tracking error is the lowest and closest to the theoretical lower bound ELBTEC curve, the target tracking accuracy is improved, and the accuracy of radar power distribution in the two-way data random packet loss environment is ensured.

[0147] The above only describes the preferred embodiments of the application and is not used to limit the application, and any content not departing from the technical scheme of the application should be included in the protection scope of the application.

Claims

1. A method for power allocation of a bi-directional data packet missing multi-target tracking networking radar, characterized in that, The method comprises the following steps: S1, establishing a networked radar system composed of N radars, each radar independently detecting and tracking multiple targets dispersedly deployed, constructing a system model, and establishing a target state; S2, constructing a state space model according to the system model, establishing a target motion equation, and performing a prediction update on the target state according to the target motion equation to obtain a predicted target state and a target covariance matrix; S3, constructing a measurement model according to the system model, and obtaining a measurement covariance matrix according to the measurement model; S4, obtaining a target tracking error covariance matrix according to the target covariance matrix and the measurement covariance matrix, obtaining a lower bound of an expected covariance matrix by taking an expectation of the target tracking error covariance matrix, taking the lower bound of the expected covariance matrix as a measurement standard, calculating a predicted lower bound of the expected covariance matrix by using the state space model and the measurement model, and obtaining an approximate value of a prediction error covariance by iteratively moving forward the predicted covariance matrix, which is used as an optimization criterion in a power allocation method under a bidirectional data packet loss condition; S5, taking the lower bound of the predicted covariance matrix as a cost function of power allocation, taking a total power limit of the networked radar system as a constraint, and establishing a power allocation mathematical model according to the optimization criterion; S6, solving the power allocation mathematical model to obtain a result of the multi-target tracking networked radar power allocation.

2. The method of claim 1, wherein, The target motion equation established in S2 is: x q,k = Fx q,k-1 + ε q,k-1 In the above equation, x q，k represents the target state vector at the kth moment in the monitoring area, (x q,k , y q,k ) represents the position of the target q at the kth moment; represents the velocity of the target q at the kth moment; ΔT represents the tracking time interval; is a state transition matrix; represents the Kronecker product; I2 represents a 2-order unit matrix; ε q,k-1 represents a Gaussian process white noise with a mean of zero, and its covariance matrix Q q,k-1 is represented as: In the above equation, r q represents the process noise intensity.

3. The method of claim 1, wherein, The measurement model constructed in S3 is: z n.q,k = h n,q,k (x q,k ) + w n,q,k The fusion center can receive the measurement data from the radar n if and only if the variables μ n,k ,β n,k are all 1. In the above equation, h n,q,k (·) denotes an observation function, denoted by h n,q,k (x q,k ) = [r n,q,k f n,q,k ] T : where r n,q,k and f n,q,k denote the range and Doppler measurements, w n,q,k denotes the measurement error, which is assumed to be zero-mean Gaussian with variance R n,q,k .

4. The bi-static data-drop multi-target tracking networked radar power allocation method of claim 1, wherein, The variance calculation method of the measurement error in S3 is: In the above equations, and denote the estimated variances of the range and Doppler measurements, respectively, and are approximated as: wherein α n,q,k ∝1 / (r n,q,k ) 4 represents path fading, |h n,q,k | 2 is the target radar cross section; B n,k and T n,k represent the effective bandwidth and time width of the transmitted signal; P n,k is the power scheduling result, when μ n,k = 1, the radar n successfully receives the power allocation result P n,k , otherwise, P n,k is lost in the transmission process, resulting in packet loss.

5. The bi-static data-drop multi-target tracking networked radar power allocation method of claim 1, wherein, S4 comprises: Adopting lower bound of desired covariance matrix As a measure; Based on the Jensen inequality theorem, if X is a random variable and φ is a convex function, then: φ(E[X])≤E[φ(X)] Therefore, there is: The lower bound of the predicted expected covariance matrix is approximately calculated by using the state space model and the measurement model: In the formula, represents the predicted target state; The approximate value of the prediction error covariance is obtained by iteratively moving forward the predicted covariance matrix under the bidirectional data packet loss condition, which is used as the optimization criterion in the power allocation method.

6. The bi-static data-drop multi-target tracking networked radar power allocation method of claim 1, wherein, The target covariance matrix in S4 is: x q,k|k-1 = Fx q,k-1 The above formula is used to predict and update the target state according to the target motion equation, and the predicted state of the target q and the target covariance matrix at the kth moment; When the system model is completely observable and there is no packet loss, the target tracking error covariance matrix is represented as: wherein is the Jacobian matrix of the measurement function h z (x x ) of dimension n n,q,k x n q,k . The target tracking error covariance matrix is derived from the above equation with the random packet loss variable β 1,k , β 2,k , K, β N,k , and μ 1,k , μ 2,k , K, μ N,k , and thus the target tracking error covariance matrix under bi-directional packet loss is represented as: The above formula shows that if there is packet loss in any process of the bidirectional transmission of the radar node i, the fusion center does not have all the measurement data of the node i, and can only use the measurement of other successfully received nodes for updating; Therefore, the above formula is rewritten as:

7. The bi-static data-drop multi-target tracking networked radar power allocation method of claim 1, wherein, The measurement covariance matrix in S4 is: From the above, the measurement covariance matrix R n,q,k is inversely proportional to the power variable, where D n,q,k denotes the residual parameter matrix.

8. The bi-static data-drop multi-target tracking networked radar power allocation method of claim 1, wherein, The power allocation mathematical model established in S5 is: s.t.P n,min ≤P n,k ≤P n,max where P n,min and P n,max are the lower and upper system power limits, respectively, and P tot is the total power; F(P k ) is the overall performance of the multi-target tracking, defined as the average of the lower bound trace of the expected covariance matrix, denoted as: Tr[·] denotes the trace operation of a matrix.

9. The bi-static data-drop multi-target tracking networked radar power allocation method of claim 1, wherein, The method for solving the solution of the power allocation mathematical model in S6 is: If the objective function F(P) k If is a convex function, then finding the solution to the power allocation mathematical model is a convex optimization problem. A convex optimization algorithm is used to solve it, and P is used to replace P. k Let λ∈[0,1], then: The optimization problem of the above formula is a convex optimization problem including only one continuous power variable, and the solution obtained by using a convex optimization toolbox is the result of the multi-target tracking networked radar power allocation.

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