Joint radar pulse data rate scheduling method based on multi-target tracking

Abstract

The invention relates to the technical field of radar system resource management, in particular to a joint radar pulse data rate scheduling method based on multi-target tracking. A joint radar pulse data rate allocation model based on quality of service is popularized to a more general and flexible model, a task utility function can be selected from a group of monotonically increasing convex functions, and the construction of an objective function is not limited to use of a specific filter to approach BCRLB; a more efficient nonlinear Bayesian filter is used; discrete variables are relaxed into variables of a continuous interval, the quasi-convexity of the non-convex joint radar pulse data rate scheduling problem based on the service quality framework is discussed, and an objective function is formed by the weighted sum of a group of separable quasi-convex functions; and the strong duality between the original non-convex problem and the duality problem after relaxation is deduced. And finally, under the condition that any approximation BCRLB is given, a DPSPA algorithm is provided to deal with the dual problem.

Description

Technical Field

[0001] The present invention relates to the technical field of radar system resource management, and in particular to a joint radar pulse data rate scheduling method based on multi-target tracking. Background Art

[0002] As the global security situation becomes increasingly complex, radar systems have become a key technology in the modern battlefield and civilian fields. Whether it is air warning and defense in military operations or meteorological monitoring and traffic management in civilian use, radar systems undertake vital tasks. Faced with these diverse application scenarios, radar systems not only need to have powerful detection capabilities, but also must be able to efficiently dispatch and manage system resources under limited resources to meet real-time mission requirements. Therefore, managing and dispatching radar system resources according to the external environment has broad research value.

[0003] For radar tracking systems, the scheduling of pulse width and data rate plays a vital role. Reasonable scheduling strategies can improve the overall performance of radar systems and enable them to flexibly respond to various challenges in a changing environment. The paper "Joint subcarrier assignment and power allocation strategy for integrated radar and communications system based on power minimization, IEEE Sensors J., vol. 19, no. 23, pp. 11 167–11 179, Dec. 2019" proposes a power allocation scheme for spectrum sharing between different wireless devices. In this scheme, the formulated optimization problem uses the sum of power consumption as the objective function and achieves an effective allocation solution. However, due to the strict constraints on the desired performance requirements, the above work is only applicable to ideal situations with sufficient resources. The paper "Robust power allocation for resource-aware multi-target tracking with colocated MIMO radars, IEEE Trans. Signal Process., vol. 69, pp. 443–458, 2021" proposes a robust power allocation method under the framework of quality of service. The BCRLB of the EKF is used as the performance indicator of each linear constant velocity (CV) model tracked target. Since the problem established is non-smooth, the authors approximate the original objective function by the weighted sum of polynomials. Since the optimization problem is non-convex, the optimality of the solution cannot be guaranteed. Summary of the invention

[0004] In view of the above problems, the purpose of the present invention is to provide a joint radar pulse data rate scheduling method based on multi-target tracking, which generalizes the allocation model based on the quality of service framework to a more general and flexible model. The technical solution is as follows:

[0005] A joint radar pulse data rate scheduling method based on multi-target tracking includes the following steps:

[0006] Step 1: Determine the topological structure of radar and target and the managed resource variables;

[0007] Suppose a radar system located at coordinates (x, y) tracks N targets distributed in the monitoring area. At the kth tracking moment, the state vector of target i is At each tracking moment, the radar beam transmits a set amount of pulses to the target to obtain target information and accumulates the pulses of the radar system for a certain period of time. and data rate As a managed resource variable;

[0008] Step 2: Determine the resource allocation model;

[0009] Determine the state vector The dynamic equation and measurement equation of the radar are proposed. The Bayesian CR lower bound is used as the evaluation index of the tracking performance. The approximate Bayesian CR lower bound is introduced to derive the tracking performance metric. The resource allocation model that meets the radar tracking accuracy requirements is established, and the allocated pulse accumulation time and data rate are optimized.

[0010] Step 3: Propose a pulse accumulation time and data rate scheduling strategy for the radar system. First, relax the original optimization problem and discuss the strong duality of the relaxed optimization problem. Then, solve the dual problem according to the optimization theory to obtain the allocation result.

[0011] Furthermore, the step 2 is specifically as follows:

[0012] Step 2.1: Determine the state vector of target i at the kth tracking moment Dynamic equation and measurement equation:

[0013]

[0014] Among them, f k，i (·) is the state transfer function, process noise is zero and has a variance of Gaussian white noise, To extract the distance and angle information between the target and the radar system from the echo signal, measure the noise is zero and has a variance of Gaussian white noise; is the observation vector;

[0015] Step 2.2: The Bayesian CR lower bound, which is used as the lower bound of the mean square error of the estimation error, is used as the evaluation indicator of the tracking performance, expressed as:

[0016]

[0017] in, represents the Fisher information matrix; is the state estimation vector of the i-th target at the k-th moment; It means taking the expectation of the following random variable;

[0018] Step 2.3: Use the approximate Bayesian CR lower bound To approximate the theoretical Bayesian CR lower bound, the trace of the approximate Bayesian CR lower bound matrix is ​​used as the tracking performance metric, that is,

[0019]

[0020] Where Tr means finding the trace of the matrix; := means defining as a symbol;

[0021] To obtain the tracking error and the pulse accumulation time more intuitively and data rate The decreasing nature of the relationship between Written in the following form:

[0022]

[0023] in, represents the estimated performance index calculated from prior information and historical data, taking into account the information of past time steps; It is related to the pulse accumulation time and data rate, reflecting the influence of pulse accumulation time and data rate on estimation accuracy; specifically:

[0024]

[0025]

[0026] in, Describe the impact of state transitions on estimation errors; and Quantify the coupling effects between state transfer equations and observation noise; Describes the impact of the observation equation on the current state estimate; is the approximate Bayesian CR lower bound at the -1th tracking moment;

[0027] For any nonlinear dynamic system, the tracking performance of each target is measured as Simplified to the following form:

[0028]

[0029] Among them, the matrix and From Unitary decomposition of and From orthogonal decomposition The definition is For the matrix The element corresponding to the mth row and mth column, n is the dimension of the target state vector;

[0030] Step 2.4: Using the quality of service resource allocation framework, establish a resource allocation model that meets the radar tracking accuracy requirements and optimize the pulse accumulation time and data rate allocated to the target. The optimization problem is as follows:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] i=1,2,…,N

[0037] in: is the specified tracking accuracy of the i-th target at time k, and τ represents the pulse accumulation vector of N targets, i.e. d represents the data rate vector of N targets, i.e. f i is the utility function, α i is the weight corresponding to the utility function, η is the total resources, is the signal-to-noise ratio;

[0038] The first constraint indicates that the resources consumed by all targets do not exceed the total resources η; the second constraint indicates that the pulse accumulation time allocated to the target must make the signal-to-noise ratio not less than 13dB; the third constraint indicates the optional range of the pulse accumulation time of the target; the fourth constraint indicates that the data rate of the target is a positive integer;

[0039] Simplify tracking performance metrics Substituting into the objective function:

[0040]

[0041] Furthermore, the approximate Bayesian CR lower bound is calculated by the following formula:

[0042]

[0043]

[0044] In the formula, is the approximate Bayesian CR lower bound at the initial tracking moment; is the state vector of target i at the initial tracking moment; represents the second-order gradient of the function; p(·) is the probability density function;

[0045] Using different nonlinear filter predictions, we obtain the following approximations of the Bayesian CR lower bound:

[0046] 1) Bayesian CR lower bound approximated by extended Kalman filter:

[0047] The state estimation of the previous moment and the current moment is obtained by extended Kalman filtering, which are recorded as and but:

[0048]

[0049]

[0050]

[0051] in, and They are the state transfer functions in And the observation function is The Jacobian matrix at ; represents the first-order gradient of the function; h k,i (·) is the observation function;

[0052] 2) Bayesian CR lower bound approximated by unscented Kalman filter:

[0053] The state estimate of the previous moment obtained by unscented Kalman filtering is The estimated error covariance matrix is The corresponding sigma point is expressed as The predicted sigma point obtained by the state transfer function is but:

[0054]

[0055]

[0056]

[0057] in, The observation function is The Jacobian matrix at .

[0058] Furthermore, the step 3 is specifically as follows:

[0059] Step 3.1: Relaxation and strong duality;

[0060] Relax the discrete optimization variables in the optimization problem into continuous variables with values ​​in a closed interval Right now At the same time, the Lagrange multiplier function is introduced to obtain the optimization problem after relaxing the discrete variables:

[0061]

[0062]

[0063] in, λ ≥ 0 is the Lagrange multiplier;

[0064] The Lagrangian function of the optimization problem is:

[0065]

[0066] Its dual function is:

[0067]

[0068] The dual problem about the Lagrange multiplier λ is:

[0069]

[0070] Ignoring the constant term, since about is quasi-convex; therefore, the strong duality of the relaxed optimization problem holds, that is, the optimal solution of the problem is obtained by solving its dual problem;

[0071] Step 3.2: Efficient solution algorithm for resource optimization problem;

[0072] The dual problem is:

[0073]

[0074] First, for each target, we solve the minimization problem by bisection method and get:

[0075]

[0076] in, λ t-1 is the Lagrange multiplier;

[0077] Then the dual problem is solved by the projected subgradient algorithm: First, the minimum pulse width that makes the signal-to-noise ratio greater than or equal to 13dB is selected Re-order Determine the data rate; calculate the following task utility difference for each target:

[0078]

[0079] Sort the targets according to the task utility difference from small to large, and set the resource of target i with the smallest utility difference each time as f i =0 until the total resource constraint is met; finally a set of feasible solutions to the original discrete variable optimization problem is obtained.

[0080] Furthermore, the dual problem is solved by the projected subgradient algorithm in step 3.2 as follows:

[0081] Input: λ0>0, ε>0, update step size {γ t} t＞0 , the maximum number of iterations t max ;λ0 is the initial Lagrange multiplier, ε is the accuracy;

[0082] Output: [(y1), (y2), …, (y N )] T ;

[0083] Step 1): Solve the minimization problem for each target by bisection method and obtain the solution (y i ) (t) ;

[0084] Step 2): Calculate the negative subgradient from the calculation result of step 1):

[0085]

[0086] Step 3): Update the Lagrange multiplier λ t :=max(0,λ t-1 +γ t Grad t ), and input the result into step 1);

[0087] Termination: until -η<Grad t <0 or t≥t max or t+1 =λ t .

[0088] Furthermore, the minimization problem solved by the dichotomy method is specifically as follows:

[0089] Input: total resources η, updated Lagrange multiplier λ t ,matrix Orthogonal Decomposition Matrix The weight α corresponding to the utility function i , objective function ψ(·), intermediate function

[0090] in,

[0091] Output: Solution result (y i ) (t) ;

[0092] Step a: Calculation like (y i ) (t) =0;

[0093] Step b: Calculation like Further calculation as well as like Then (y i ) (t) =0; if Then (y i ) (t) =η; in other cases, the binary search is performed on the interval [0, η] to obtain (y i ) (t) ;

[0094] Step c: and like Then (y i ) (t) =0; in other cases, the binary search is performed on the interval [0, η] to obtain (y i ) (t) .

[0095] The beneficial effects of the present invention are:

[0096] The present invention generalizes the radar pulse data rate allocation model based on quality of service QoS to a more general and flexible model, in which the task utility function can be selected from a set of monotonically increasing convex functions, and the construction of the objective function is not limited to using a specific filter to approximate the Bayesian Cramér-Rao lower bound (BCRLB). Therefore, a more efficient nonlinear Bayesian filter can be used. Secondly, the discrete variables are relaxed into variables in a continuous interval, and the quasi-convexity of the non-convex radar pulse data rate scheduling problem based on the quality of service framework is explored, and its objective function is composed of the weighted sum of a set of separable quasi-convex functions. Then, the strong duality between the original non-convex problem and its dual problem after relaxation is derived. Finally, given an arbitrary approximation to BCRLB, a dual projection subgradient power distribution (DPSPA) algorithm is proposed to deal with the dual problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 The present invention is a flow chart of a joint radar pulse data rate scheduling method based on multi-target tracking.

[0098] Figure 2 This is the result of different tracking accuracies being fed back to the tracking data rate adjustment when the target flies away from the radar station in the implementation example of the present invention.

[0099] Figure 3 This is the result of different tracking accuracies being fed back to the tracking data rate adjustment when the target flies close to the radar station in the implementation example of the present invention.

[0100] Figure 4 It is the total amount of resources consumed by the radar station in tracking the target in the implementation example of the present invention. DETAILED DESCRIPTION

[0101] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Figure 1 As shown, a flow chart of a radar pulse data rate scheduling method based on multi-target tracking of the present invention, the method steps are specifically as follows:

[0102] A joint radar pulse data rate scheduling method based on multi-target tracking, the method comprising the steps of:

[0103] Step 1: Determine the topological structure of radar and target and the managed resource variables;

[0104] A radar system located at (x, y) tracks N targets widely distributed in the monitoring area. At the kth tracking moment, the state vector of target i is In order to maintain target tracking, at each tracking moment, the radar beam needs to emit a certain amount of pulses to the target to obtain target information. At the same time, in order to ensure the real-time data processing capability of the radar system and the efficiency of communication bandwidth utilization, the data rate needs to be dynamically adjusted. Therefore, the present invention controls the pulse accumulation time and data rate of the radar system, that is, the managed resource variables are: 1. The accumulated time of the pulses emitted by the radar system to target i at each moment 2. Data rate

[0105] In this embodiment, a radar system located at (0, 0) is considered to be used to monitor the target. The motion model of the target is CV (constant velocity). The monitoring area is divided into two areas: 0-600km and 600km away from the radar according to the distance from the radar. The corresponding accuracy requirements are 100m and 500m respectively.

[0106] Step 2: Determine the resource optimization model;

[0107] At time k, the state vector of target i is Its dynamic equation and measurement equation are:

[0108]

[0109] where f k，i (·) is the state transfer function, process noise is zero and has a variance of Gaussian white noise, measured To extract the distance and angle information between the target and the radar system from the echo signal, measure the noise is zero and has a variance of Gaussian white noise;

[0110] Since the Bayesian CR lower bound is used as the lower bound of the mean square error of the estimation error, it is used as an evaluation indicator of tracking performance. The lower bound can be expressed as:

[0111]

[0112] in represents the Fisher information matrix; the BCRLB of the theory requires the true state of the target as well as To find the expectation, we need to use the Monte Carlo sampling approximation; to simplify the calculation, we consider using the approximation To approximate the theoretical BCRLB The trace of the approximate BCRLB matrix is ​​used as a measure of tracking performance, namely

[0113]

[0114] In order to more intuitively obtain the tracking error and the pulse accumulation time used and data rate The decreasing nature of Written in the following form:

[0115]

[0116] in

[0117]

[0118]

[0119] For any nonlinear dynamic system, the tracking performance of each target is measured as can be simplified to the following form:

[0120]

[0121] in and From Unitary decomposition of and From orthogonal decomposition The definition is

[0122] In the limited resource allocation problem under specified tracking accuracy, the specified tracking accuracy of the target, the use of filtering methods, and the approximation method will affect the radar resource allocation, and thus affect the tracking performance of the system. Using the quality of service resource allocation framework, a resource allocation model that meets the radar tracking accuracy requirements is established to optimize the pulse accumulation time and data rate allocated to the target. The specific optimization problem is:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] i=1,2,…,N

[0129] in: is the specified tracking accuracy of the i-th target at time k, and τ represents the pulse accumulation vector of N targets, i.e. d represents the data rate vector of N targets, i.e. The first constraint indicates that the resources consumed by all targets do not exceed the total resources η; the second constraint indicates that the pulse accumulation time allocated to the target must make the signal-to-noise ratio not less than 13dB; the third constraint indicates the optional range of the target's pulse accumulation time; the fourth constraint indicates that the target's data rate is a positive integer; the simplified tracking performance metric Substituting into the objective function:

[0130]

[0131] Since the approximate BCRLB is applicable to commonly used nonlinear Bayesian filtering and the utility function of the task is generalized to a more general monotonically decreasing convex function, the framework of the designed optimization problem can be applied to different tracking task scenarios, and the model has stronger applicability and flexibility.

[0132] Wherein, the approximate BCRLB is calculated by the following formula:

[0133]

[0134]

[0135] Using different nonlinear filter predictions, we can get the following approximations of BCRLB:

[0136] 1) EKF (Extended Kalman Filter) approximation of BCRLB: The EKF estimates of the previous moment and the current moment are recorded as and but:

[0137]

[0138]

[0139]

[0140] in and They are the state transfer functions in And the observation function is The Jacobian matrix at ;

[0141] 2) BCRLB approximated by UKF (Unscented Kalman Filter): The state estimate of UKF at the previous moment is The estimated error covariance matrix is The corresponding sigma point is expressed as The predicted sigma point obtained by the state transfer function is but:

[0142]

[0143]

[0144]

[0145] Step 3: Propose a pulse accumulation time and data rate scheduling strategy for the radar system. First, relax the original optimization problem and discuss the strong duality of the relaxed optimization problem. Then, solve the dual problem according to the optimization theory to obtain the allocation result.

[0146] Step 3.1: Relaxation and strong duality;

[0147] Relax the discrete optimization variables in the original optimization problem into continuous variables with values ​​in a closed interval Right now At the same time, the Lagrange multiplier function is introduced to obtain the optimization problem after relaxing the discrete variables:

[0148]

[0149]

[0150] in λ≥0 is the Lagrange multiplier, and the Lagrangian function of the problem is:

[0151]

[0152] Its dual function is:

[0153]

[0154] The dual problem about the multiplier λ is:

[0155]

[0156] Ignoring the constant term η, we can get through rigorous analysis about is quasi-convex; therefore, the strong duality of the relaxed optimization problem holds, that is, the optimal solution of the problem can be obtained by solving its dual problem;

[0157] Step 3.2: Efficient solution algorithm for resource optimization problem;

[0158] The dual problem is:

[0159]

[0160] First, for each target, we solve the minimization problem by bisection method, and get in Then the dual problem is solved by the projected subgradient algorithm; the optimal solution obtained by the algorithm is a continuous variable, which needs to be further processed to obtain the original discrete variable; first, the minimum pulse width that makes the signal-to-noise ratio greater than or equal to 13dB is selected Re-order Determine the data rate; at this point the resource allocation solution may not satisfy the total resource constraint For each goal, the following task utility difference is calculated:

[0161]

[0162] Sort the targets according to the task utility difference from small to large, and set the resource of target i with the smallest utility difference each time as f i =0 until the total resource constraint is met; finally a set of feasible solutions to the original discrete variable optimization problem is obtained.

[0163] The algorithm flow of the projected subgradient algorithm and the bisection method used in step 3 is as follows:

[0164] Algorithm 1: Solving the dual problem by projected subgradient method

[0165]

[0166] Algorithm 2: Solving the minimization problem by bisection

[0167]

[0168]

[0169] in

[0170] Figure 2 and Figure 3 The following figure shows the result of the tracking data rate adjustment based on the feedback of different tracking accuracies. The horizontal axis is the tracking time, and the vertical axis is the tracking data rate of the radar to the target. The blue and orange colors are the tracking data rates under different tracking accuracy requirements. It can be seen that the tracking data rate will suddenly change when the target enters the area with different tracking accuracy requirements, and the data rate will decrease or alternate up and down after stabilization. Figure 4 The horizontal axis is the tracking time, and the vertical axis is the total amount of resources consumed by tracking the target. The present invention allocates data rate and pulse accumulation time. It can be understood that data rate and pulse time are resources, and duty cycle refers to the proportion of resources consumed by the target to all resources. When radar resources are not saturated, the resource consumption of the radar presents a "wave" type. Figure 2 and Figure 3The result presented is that when the radar allocates more resources to track the target at the current moment, the target tracking accuracy is improved, then at the next moment, under the current high tracking accuracy, the target's demand for resources is reduced, that is, a shorter pulse width or a lower tracking data rate can achieve the specified tracking accuracy, thus presenting an alternating up and down resource consumption curve.

Claims

1. A joint radar pulse data rate scheduling method based on multi-target tracking, characterized in that: The following steps are involved: Step 1: Determine the topological structure of radar and target and the managed resource variables; Suppose a radar system located at coordinates (x, y) tracks N targets distributed in the monitoring area. At the kth tracking moment, the state vector of target i is At each tracking moment, the radar beam transmits a set amount of pulses to the target to obtain target information and accumulates the pulses of the radar system for a certain period of time. and data rate As a managed resource variable; Step 2: Determine the resource allocation model; Determine the state vector The dynamic equation and measurement equation of the radar are proposed. The Bayesian CR lower bound is used as the evaluation index of the tracking performance. The approximate Bayesian CR lower bound is introduced to derive the tracking performance metric. The resource allocation model that meets the radar tracking accuracy requirements is established, and the allocated pulse accumulation time and data rate are optimized. Step 3: Propose a pulse accumulation time and data rate scheduling strategy for the radar system. First, relax the original optimization problem and discuss the strong duality of the relaxed optimization problem. Then, solve the dual problem according to the optimization theory to obtain the allocation result.

2. The joint radar pulse data rate scheduling method based on multi-target tracking according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: Determine the state vector of target i at the kth tracking moment Dynamic equation and measurement equation: Among them, f k，i (·) is the state transfer function, process noise is zero and has a variance of Gaussian white noise, To extract the distance and angle information between the target and the radar system from the echo signal, measure the noise is zero and has a variance of Gaussian white noise; is the observation vector; Step 2.2: The Bayesian CR lower bound, which is used as the lower bound of the mean square error of the estimation error, is used as the evaluation indicator of the tracking performance, expressed as: in, represents the Fisher information matrix; is the state estimation vector of the i-th target at the k-th moment; It means taking the expectation of the following random variable; Step 2.3: Use the approximate Bayesian CR lower bound To approximate the theoretical Bayesian CR lower bound, the trace of the approximate Bayesian CR lower bound matrix is ​​used as the tracking performance metric, that is, Where Tr means finding the trace of the matrix; := means defining as a symbol; To obtain the tracking error and the pulse accumulation time more intuitively and data rate The decreasing nature of the relationship between Written in the following form: in, represents the estimated performance index calculated from prior information and historical data, taking into account the information of past time steps; It is related to the pulse accumulation time and data rate, reflecting the influence of pulse accumulation time and data rate on estimation accuracy; specifically: in, Describe the impact of state transitions on estimation errors; and Quantify the coupling effect between state transfer equations and observation noise; Describes the impact of the observation equation on the current state estimate; is the approximate Bayesian CR lower bound at the k-1th tracking moment; For any nonlinear dynamic system, the tracking performance of each target is measured as Simplified to the following form: Among them, the matrix and From Unitary decomposition of and From orthogonal decomposition The definition is For the matrix The element corresponding to the mth row and mth column, n is the dimension of the target state vector; Step 2.4: Using the quality of service resource allocation framework, establish a resource allocation model that meets the radar tracking accuracy requirements and optimize the pulse accumulation time and data rate allocated to the target. The optimization problem is as follows: in: is the specified tracking accuracy of the i-th target at time k, and τ represents the pulse accumulation vector of N targets, i.e. d represents the data rate vector of N targets, i.e. f i is the utility function, α i is the weight corresponding to the utility function, η is the total resources, is the signal-to-noise ratio; The first constraint indicates that the resources consumed by all targets do not exceed the total resources η; the second constraint indicates that the pulse accumulation time allocated to the target must make the signal-to-noise ratio not less than 13dB; the third constraint indicates the optional range of the pulse accumulation time of the target; the fourth constraint indicates that the data rate of the target is a positive integer; Simplify tracking performance metrics Substituting into the objective function:

3. The joint radar pulse data rate scheduling method based on multi-target tracking according to claim 2 is characterized in that: The approximate Bayesian CR lower bound is calculated as follows: In the formula, is the approximate Bayesian CR lower bound at the initial tracking moment; is the state vector of target i at the initial tracking moment; represents the second-order gradient of the function; p(·) is the probability density function; Using different nonlinear filter predictions, we obtain the following approximations of the Bayesian CR lower bound: 1) Bayesian CR lower bound approximated by extended Kalman filter: The state estimation of the previous moment and the current moment is obtained by extended Kalman filtering, which are recorded as and but: in, and They are the state transfer functions in And the observation function is The Jacobian matrix at ; represents the first-order gradient of the function; h k,i (·) is the observation function; 2) Bayesian CR lower bound approximated by unscented Kalman filter: The state estimate of the previous moment obtained by unscented Kalman filtering is The estimated error covariance matrix is The corresponding sigma point is expressed as The predicted sigma point obtained by the state transfer function is but: in, The observation function is The Jacobian matrix at .

4. The method for joint radar pulse data rate scheduling based on multi-target tracking according to claim 2 is characterized in that: The step 3 is as follows: Step 3.1: Relaxation and strong duality; Relax the discrete optimization variables in the optimization problem into continuous variables with values ​​in a closed interval Right now At the same time, the Lagrange multiplier function is introduced to obtain the optimization problem after relaxing the discrete variables: in, λ ≥ 0 is the Lagrange multiplier; The Lagrangian function of the optimization problem is: Its dual function is: The dual problem about the Lagrange multiplier λ is: Ignoring the constant term, since about is quasi-convex; therefore, the strong duality of the relaxed optimization problem holds, that is, the optimal solution of the problem is obtained by solving its dual problem; Step 3.2: Efficient solution algorithm for resource optimization problem; The dual problem is: First, for each target, we solve the minimization problem by bisection method and get: in, λ t-1 is the Lagrange multiplier; Then the dual problem is solved by the projected subgradient algorithm: First, the minimum pulse width that makes the signal-to-noise ratio greater than or equal to 13dB is selected Re-order Determine the data rate; calculate the following task utility difference for each target: Sort the targets according to the task utility difference from small to large, and set the resource of target i with the smallest utility difference each time as Until the total resource constraints are met; finally a set of feasible solutions to the original discrete variable optimization problem is obtained.

5. The method for joint radar pulse data rate scheduling based on multi-target tracking according to claim 4 is characterized in that: The specific solution of the dual problem by the projected subgradient algorithm in step 3.2 is as follows: Input: λ0>0, ε>0, update step size {γ t } t≥0 , the maximum number of iterations t max ;λ0 is the initial Lagrange multiplier, ε is the accuracy; Output: Step 1): Solve the minimization problem for each target by bisection method and obtain the solution (y i ) (t) ; Step 2): Calculate the negative subgradient from the calculation result of step 1): Step 3): Update the Lagrange multiplier λ t :=max(0,λ t-1 +γ t Grad t ), and input the result into step 1); Termination: until -η<Grad t <0 or t≥t max or t+1 =λ t .

6. The method for joint radar pulse data rate scheduling based on multi-target tracking according to claim 5 is characterized in that: The method of solving the minimization problem by the dichotomy method is as follows: Input: total resources η, updated Lagrange multiplier λ t ,matrix Orthogonal Decomposition Matrix The weight α corresponding to the utility function i , objective function ψ(·), intermediate function in, Output: Solution result (y i ) (t) ; Step a: Calculation like (y i ) (t) =0; Step b: Calculation like Further calculation as well as like Then (y i ) (t) =0; like Then (y i ) (t) =η; in other cases, the binary search is performed on the interval [0, η] to obtain (y i ) (t) ; Step c: and like Then (y i ) (t) =0; in other cases, the binary search is performed on the interval [0, η] to obtain (y i ) (t) .

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