Radar resource scheduling method for detecting multiple targets by fixed-track mobile platform

Abstract

The invention discloses a radar resource scheduling method for detecting multiple targets by a fixed-track mobile platform. The method comprises the following steps: step 1, constructing a target motion model, a mobile platform radar motion model and an observation model in a fixed-track scene; step 2, establishing an objective function and constraint conditions; 3, performing global search by using a heritage algorithm to generate an initial resource allocation scheme; step 4, taking the initial resource allocation scheme as an initial value, and carrying out local refinement optimization through a sequential quadratic programming algorithm to improve the precision; step 5, carrying out dynamic state updating and loop optimization, and generating an updated target state estimation and posterior covariance matrix; step 6, carrying out loop iteration optimization, and carrying out the step 3 and the step 4 on the result of the step 5 to obtain the target state estimation and posterior covariance matrix. And generating optimal power and residence time. Simulation results show that compared with a single algorithm, the multi-target tracking precision is remarkably improved, and an efficient solution is provided for multi-target detection of the mobile platform radar in a complex environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of mobile platform radar resource scheduling, and specifically provides a radar resource scheduling method for a fixed-track mobile platform to detect multiple targets, solving the joint optimization problem of power and dwell time in a fixed-track scenario. Background Art

[0002] In recent years, mobile radars have become increasingly widely used in military reconnaissance and multi-target collaborative tracking. By acquiring real-time information such as target position and velocity, they have become core equipment for high-precision tracking. However, mobile radars are limited by platform payload, transmit power has a thermal dissipation threshold, and beam dwell time is constrained by the demands of multiple concurrent tasks. This has led to an increasing conflict between resource constraints and the need for dynamic scheduling. Optimizing the power and dwell time in fixed-track scenarios to meet the high-precision requirements of multi-target tracking has become a key issue that needs to be addressed.

[0003] Existing research on radar resource scheduling primarily focuses on fixed and mobile platforms. While resource scheduling methods for fixed-platform radars, such as power clustering and dynamic site selection, improve tracking efficiency through joint optimization, they are difficult to directly apply to mobile platform scenarios because they fail to consider the mobility characteristics and fixed track constraints of mobile platforms. For mobile platforms, traditional single algorithms (such as genetic algorithms or sequential quadratic programming) face significant challenges: While swarm intelligence-based genetic algorithms (GAs) possess global search capabilities, they suffer from low convergence efficiency under the coupled constraints of power and dwell time; gradient-based algorithms (such as sequential quadratic programming (SQP)) rely on high-quality initial solutions and are prone to falling into local optimality, resulting in insufficient resource allocation accuracy in complex scenarios.

[0004] Multi-target tracking by mobile radar platforms places higher demands on real-time resource scheduling. Existing adaptive scheduling methods focus on trajectory planning and joint resource optimization, but overlook the coordinated scheduling of power and dwell time in fixed-track scenarios. In battlefield environments characterized by high-speed target motion and complex, ever-changing environments, the limitations of single algorithms are further magnified. A hybrid strategy combining global exploration and local optimization is urgently needed to meet the operational needs of mobile platforms within mission constraints. Summary of the Invention

[0005] The purpose of the present invention is to propose a radar resource scheduling method for detecting multiple targets on a fixed-track mobile platform, so as to solve the technical problems faced by existing fixed-track mobile platform radars in multi-target tracking, such as the transmission power thermal dissipation threshold, the beam dwell time multi-task concurrency constraints, and the low global search efficiency or insufficient local optimization capability of traditional single algorithms in resource scheduling, which lead to poor multi-target tracking accuracy and resource allocation consistency.

[0006] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A radar resource scheduling method for detecting multiple targets using a fixed-track mobile platform specifically comprises the following steps:

[0008] Step 1: Build a multi-target tracking system model in a fixed track scenario, including the following three models:

[0009] (1) Target motion model: Assume that the target moves in a uniform linear motion, and the state vector in, and Respectively represent the horizontal and vertical coordinate positions of the target q at time k, and They represent the speed of the target q in the X-axis and Y-axis directions at time k respectively;

[0010] State transition equation The state transfer matrix F is:

[0011]

[0012] Where ΔT represents the time interval;

[0013] W q Represents zero-mean Gaussian white noise, and its process noise covariance matrix Q q,k-1 for:

[0014]

[0015] (2) Mobile platform radar motion model: The mobile platform radar moves along a fixed track at a uniform speed in a straight line, and its position update equation is:

[0016]

[0017] Where, and They represent the positions of the radar at time k and time k-1 respectively, v x and v y Represents the speed of the radar in the X-axis and Y-axis directions respectively;

[0018] (3) Observation model: the observation vector Z of the target q at time k q,k =h(X q,k )+V q,k ;

[0019] Where, the measurement function is:

[0020]

[0021] V q,kis Gaussian measurement noise, and its covariance matrix is ​​R q,k It is related to the signal-to-noise ratio SNR and is expressed as:

[0022]

[0023] Among them, σ r,q,k is the distance error of target q at time k, σ θ,q,k is the angle error of target q at time k, expressed as where c, β, λ, and γ are the speed of light, effective beam bandwidth, emission wavelength, and antenna aperture, respectively; the signal-to-noise ratio (SNR) is expressed as Where T q,k is the residence time of target q at time k, P q,k is the transmission power of target q at time k, T r is the pulse repetition period, G t is the transmitting antenna gain, G r is the receiving antenna gain, σ RCS is the radar cross section of target q, G RP , T0 and F r are the processing gain, noise temperature and noise figure of the radar receiver respectively, k B is the Boltzmann constant, B is the bandwidth of the radar receiver matched filter, r q,k is the distance between target q and radar at time k, is the azimuth of target q from the radar at time k;

[0024] Step 2: Establish a constrained optimization model

[0025] Objective function: The optimization goal is to minimize the weighted sum of each target BCRLB trace. The BCRLB matrix trace is The Bayesian information matrix Prior information matrix Measurement Information Matrix Among them, H q,k is h(X q,k ) is represented by:

[0026]

[0027] So the objective function can finally be expressed as: Among them, Q is the target number, ω q is the target weight;

[0028] The constraints are:

[0029]

[0030] Among them, Tmax and T min are the upper and lower limits of the dwell time for each beam, P max and P min are the upper and lower limits of each beam’s transmit power, T total and P total are the total beam dwell time and total power, respectively, and are the total resource constraints;

[0031] Step 3: Use the legacy algorithm GA to perform global search and generate the initial resource allocation plan:

[0032] Initialize the GA population, set the population size, and use real number coding to encode the transmission power P q,k and residence time T q,k Encoding, each individual is a 2Q-dimensional vector, where the first Q dimension corresponds to power and the second Q dimension corresponds to residence time; the initial individual is randomly generated within the constraint range to ensure that P is satisfied min ≤P q,k ≤P max 、T min ≤T q,k ≤T max , total resource constraints Taking the objective function in step 2 as the fitness function, the initial resource allocation scheme [P (0) q,k ,T (0) q,k ] to ensure the global search for the potential optimal solution;

[0033] Step 4: Using the initial resource allocation plan generated in step 3 as the initial value, perform local refinement optimization to improve accuracy using the sequential quadratic programming algorithm (SQP):

[0034] Using the preliminary solution output by GA as the initial value, a quadratic programming subproblem including the objective function gradient and Hessian matrix is ​​constructed, specifically:

[0035]

[0036] stA(x+d)≤b,lb≤x+b≤ub

[0037] Where x = [P 1,k ,T 1,k ,...,P Q,k ,T Q,k ] T is the optimization variable vector, d is the search direction; H is the Hessian matrix of the objective function, is the objective function gradient; A(x+d)≤b is a linear constraint, lb and ub are the upper and lower bound constraints of the variables;

[0038] By iteratively solving the quadratic programming subproblem, the local convergence property of SQP is used to solve the solution generated by GA [P (0) q,k ,T (0) q,k ] to make fine adjustments and obtain the optimal solution that meets the constraints [P * q,k ,T * q,k ], as the optimal resource allocation scheme;

[0039] Step 5: Dynamic state update and loop optimization, specifically using the extended Kalman filter (EKF) to process the observation results after the optimal resource allocation solution output in step 4 is executed to generate an updated target state estimate. and the posterior covariance matrix Σ q,k ;

[0040] Step 6: Loop iterative optimization: for each time k=2,...,T total , T total is the total number of time steps, using the target state estimate outputted in step 5 of the previous moment (k-1) and the posterior covariance matrix Σ q,k-1 Through steps 3 and 4, the optimal power and residence time [P * q,k ,T * q,k ], meeting the dual constraints of power and residence time; and outputting and storing the results.

[0041] Compared with the prior art, the present invention has the following significant advantages:

[0042] (1) The present invention constructs a dynamic work task model that includes parameters such as beam dwell time and task priority, which can integrate multi-dimensional information such as radar working background (such as threat level), target number and characteristics (such as speed and distance) in real time.

[0043] (2) This paper innovatively proposes a GA-SQP collaborative strategy, which combines the global search capability of the genetic algorithm (GA) with the local fine optimization advantages of sequential quadratic programming (SQP). GA explores potential optimal solutions in a wide solution space through selection, crossover, and mutation operations, avoiding falling into local minima; SQP uses the GA output as the initial value and uses gradient information to quickly converge to a high-precision solution, thus compensating for the shortcomings of GA in local optimization.

[0044] (3) The present invention effectively resolves the contradiction between limited radar resources and dynamic scheduling requirements, and provides an efficient resource scheduling solution for multi-target collaborative detection in complex battlefield environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the target motion trajectory, mobile platform radar motion trajectory and predicted trajectory.

[0046] Figure 2 This is the BCRLB lower bound graph obtained by comparing the GA-SQP collaborative algorithm with the fixed platform radar as a benchmark, and using GA, SQP and SA for comparison respectively.

[0047] Figure 3 This is the resource scheduling result using the GA-SQP collaborative algorithm.

[0048] The present invention is further explained below with reference to the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0049] The radar resource scheduling method for detecting multiple targets by a fixed-track mobile platform provided by the present invention specifically includes the following steps:

[0050] Step 1: Build a multi-target tracking system model in a fixed track scenario, including the following three models:

[0051] (1) Target motion model: Assume that the target moves in a uniform linear motion, and the state vector in, and Respectively represent the horizontal and vertical coordinate positions of the target q at time k, and They represent the speed of the target q in the X-axis and Y-axis directions at time k respectively.

[0052] State transfer equation X q,k =FX q,k-1 +W q , where the state transfer matrix F is:

[0053]

[0054] Where ΔT represents the time interval;

[0055] W q Represents zero-mean Gaussian white noise, and its process noise covariance matrix Q q,k-1 for:

[0056]

[0057] (2) Mobile platform radar motion model: The mobile platform radar moves along a fixed track at a uniform speed in a straight line, and its position update equation is:

[0058]

[0059] Where, and They represent the positions of the radar at time k and time (k-1), respectively, v x and v y Represents the speed of the radar in the X-axis and Y-axis directions respectively.

[0060] (3) Observation model: the observation vector Z of the target q at time k q,k =h(X q,k )+V q,k ;

[0061] Where, the measurement function is:

[0062]

[0063] V q,k is Gaussian measurement noise, and its covariance matrix is ​​R q,k It is related to the signal-to-noise ratio (SNR) and can be expressed as:

[0064]

[0065] Among them, σ r,q,k is the distance error of target q at time k, σ θ,q,k is the angle error of target q at time k, expressed as where c, β, λ, and γ are the speed of light, effective beam bandwidth, emission wavelength, and antenna aperture, respectively; the signal-to-noise ratio (SNR) is expressed as Where T q,k is the residence time of target q at time k, P q,k is the transmission power of target q at time k, T r is the pulse repetition period, G t is the transmitting antenna gain, G r is the receiving antenna gain, σ RCS is the radar cross section (RCS) of target q, G RP , T0 and F r are the processing gain, noise temperature and noise figure of the radar receiver respectively, k B is the Boltzmann constant, B is the bandwidth of the radar receiver matched filter, r q,k is the distance between target q and radar at time k, is the azimuth of target q from the radar at time k.

[0066] Step 2: Establish a constrained optimization model

[0067] Objective function: The optimization goal is to minimize the weighted sum of each target BCRLB trace. The BCRLB matrix trace is The Bayesian information matrix Prior information matrix Measurement Information Matrix Among them, H q,k is h(X q,k ) is represented by:

[0068]

[0069] So the objective function can finally be expressed as: Among them, Q is the target number, ω q is the target weight;

[0070] The constraints are:

[0071]

[0072] Among them, T max and T min are the upper and lower limits of the dwell time for each beam, P max and P min are the upper and lower limits of each beam’s transmit power, T total and P total are the total beam dwell time and total power respectively, and is the total resource constraint.

[0073] Step 3: Use the Genesis Algorithm (GA) to perform a global search and generate an initial resource allocation plan:

[0074] Initialize the GA population, set the population size N = 100, and use real number coding to encode the transmission power P q,k and residence time T q,k Encoding, each individual is a 2Q-dimensional vector, where the first Q dimension corresponds to power and the second Q dimension corresponds to residence time; the initial individual is randomly generated within the constraint range to ensure that P is satisfied min ≤P q,k ≤P max 、T min ≤T q,k ≤T max , total resource constraints Taking the objective function in step 2 as the fitness function, the initial resource allocation scheme [P (0) q,k ,T (0) q,k] to ensure the global search for the potential optimal solution.

[0075] Step 4: Using the initial resource allocation plan generated in step 3 as the initial value, perform local refinement optimization to improve accuracy using the Sequential Quadratic Programming (SQP) algorithm:

[0076] Using the preliminary solution output by GA (i.e., the initial resource allocation plan generated in step 3) as the initial value, a quadratic programming subproblem including the objective function gradient and the Hessian matrix is ​​constructed. Specifically,

[0077]

[0078] stA(x+d)≤b,lb≤x+b≤ub

[0079] Where x = [P 1,k ,T 1,k ,...,P Q,k ,T Q,k ] T is the optimization variable vector, d is the search direction; H is the Hessian matrix of the objective function, is the objective function gradient; A(x+d)≤b is a linear constraint (such as total resource constraint lb and ub are the upper and lower bounds of the variables (such as T min ≤T q,k ≤T max ).

[0080] By iteratively solving the quadratic programming subproblem, the local convergence property of SQP is used to solve the solution generated by GA [P (0) q,k ,T (0) q,k ] to make fine adjustments and obtain the optimal solution that meets the constraints [P * q,k ,T * q,k ], as the optimal resource allocation scheme, to improve the quality and accuracy of understanding.

[0081] Step 5: Dynamic state update and loop optimization. Specifically, the Extended Kalman Filter (EKF) is used to process the observation results after the optimal resource allocation solution output in Step 4 is executed. The specific process is as follows:

[0082] Prediction step: Calculate the prior state estimate based on the target motion model constructed in step 1 in is the state estimate of the target q at time (k-1), F is the state transfer matrix in step 1; the prior covariance matrix is ​​updated Σ q,k|k-1 =FΣ q,k-1 FT +Q q,k-1 , where Σ q,k|k-1 is the state covariance matrix of the target q at the (k-1) moment, Q q,k-1 The process noise covariance matrix defined in step 1 is used to quantify the uncertainty of the target motion;

[0083] Update step (measurement update): Use the k-time observation value Z q,k (Observation model in step 1) Corrected state estimate in is the predicted observation value, K k is the Kalman gain, which can be expressed as Among them, R q,k is the measurement noise covariance matrix, reflecting the observation noise level; Σ q,k|k-1 is the prior covariance matrix at time k, and based on the state estimate at time (k-1), the uncertainty of the state at time k is predicted; then the posterior state estimate is updated: The prior state estimate is corrected by the residual between the observed value and the predicted value to obtain a more accurate posterior state estimate; finally, the posterior covariance matrix is ​​obtained based on the prior covariance matrix: Σ q,k =(IK k H q,k )Σ q,k|k-1 , where I is the identity matrix and the updated posterior covariance matrix Σ q,k It reflects the reduction of uncertainty in the state estimation at time k.

[0084] Through the above process, step 5 generates the updated target state estimate and the posterior covariance matrix Σ q,k , which are the input parameters for the target motion model, mobile platform radar motion model, and observation model in steps 3-4 at the next time step (k+1), driving the next cycle of resource allocation iteration. Specifically, the state information (such as target uncertainty) generated in step 5 is used to update the parameters of the target motion model and observation model in steps 3 (GA global search) and 4 (SQP local optimization), ensuring that resource allocation adapts to dynamic target changes.

[0085] Step 6: Loop iterative optimization: for each time k=2,...,T total (T total is the total number of time steps), perform iterative optimization according to the following process:

[0086] (1) Resource allocation and status update

[0087] Use the target state estimate output from step 5 at the previous moment (k-1) and the posterior covariance matrix Σ q,k-1Through step 3 (GA global search) and step 4 (SQP local optimization), the optimal power and residence time [P * q,k ,T * q,k ], satisfying the dual constraints of power and dwell time;

[0088] Radar Press P * q,k With T * q,k After executing resource allocation, obtain the observation value Z at time k q,k , generate the target state estimate at time k through step 5 and the posterior covariance matrix Σ q,k .

[0089] (2) Result output and storage

[0090] Save the target state estimate at time k Forming a sequence Save the optimal resource allocation at time k

[0091] When k = T total When , the complete state estimation sequence of multi-target tracking results is output And output the optimal resource allocation set at each moment

[0092] Preferably, the Bayesian information matrix J q,k The calculation is as follows:

[0093] Where Cov(X q,k|k-1 )=FΣ q,k-1 F T +Q q,k-1 , where Σ q,k|k-1 is the state covariance matrix of the target q at the (k-1) moment, Q q,k-1 is the process noise covariance matrix of the target q at time (k-1) (see step 1); the measurement information matrix The covariance matrix R q,k Related to the signal-to-noise ratio SNR, Where, T q,k is the residence time of target q at time k, P q,k is the transmission power of target q at time k, T r is the pulse repetition period, G t is the transmit antenna gain, G r is the receiving antenna gain, σ RCS is the radar cross section (RCS) of target q, G RP , T0 and F rare the processing gain, noise temperature and noise figure of the radar receiver, k B is the Boltzmann constant, B is the bandwidth of the radar receiver matched filter, r q,k is the distance of target q from the radar at time k.

[0094] Example

[0095] The radar resource scheduling for detecting multiple targets by a fixed-track mobile platform provided in this embodiment specifically includes the following steps:

[0096] Step 1: Build a multi-target tracking system model

[0097] (1) Target motion model:

[0098] The state vector of target q at time k is The transfer matrix F describes the uniform motion, and the covariance matrix Q of the process noise q Dynamically changes with time interval ΔT (e.g. when ΔT = 1s, the noise intensity σ q =10.

[0099] (2) Mobile platform motion model:

[0100] The initial position is (0,0)m, the initial speed is (300,100)m / s, and the position is updated to

[0101] (3) Observation model:

[0102] The covariance matrix R of the measurement noise q,k , which can be expressed as:

[0103]

[0104] Among them, σ r,q,k is the distance error of target q at time k, which can be expressed as σ θ,q,k is the angle error of target q at time k, which can be expressed as Where c, β, λ and γ are the speed of light, effective beam bandwidth, emission wavelength and antenna aperture, respectively, and the signal-to-noise ratio SNR and the allocated power P q,k , residence time T q,k Positive correlation.

[0105] Step 2: Establish a constrained optimization model

[0106] Objective function:

[0107] Weighted sum minimization The weight (threat level) is set to ω = [1, 1, 1].

[0108] Constraints:

[0109] Single target dwell time 0.005s≤T q,k ≤0.02s, total beam dwell time ≤0.025s; single target power 100W≤P q,k ≤800W, total power ≤1000W.

[0110] Step 3: Perform GA-SQP collaborative optimization

[0111] GA parameters:

[0112] The population size is 50, the number of iterations is 100, the crossover probability is 0.8, the mutation probability is 0.1, and the initial solution evenly distributes resources, such as T q,1 =0.025 / 3s, P q,1 =1000 / 3W.

[0113] Step 4, SQP optimization:

[0114] Use the GA solution as the initial value and set the convergence tolerance to 1e -6 ,The power and dwell time are adjusted through gradient calculation.,For example, when target 3 is the farthest away, SQP increases its power from the evenly distributed 333W to 700W, and its dwell time from 0.008s to 0.015s.

[0115] Step 5, EKF update:

[0116] After predicting the target position, the noisy observation values ​​(such as distance error ±50m, angle error ±0.5°) are used to correct the state estimate and update the covariance matrix to provide accurate state information for resource allocation at the next moment.

[0117] In order to prove the feasibility and effectiveness of the present invention, the following simulation verification was carried out.

[0118] (1) Scene setting:

[0119] The initial positions of the three targets are (10000, 20000) m, (12000, 20000) m, and (14000, 20000) m, respectively. The speeds are (0, -200) m / s, (0, -300) m / s, and (0, -400) m / s, respectively. The total time is 30 frames with an interval of 1 second. Figure 1 The target's trajectory, the mobile platform's radar trajectory, and the predicted trajectory are shown. Initially, the predicted target trajectory (dashed green line) deviates significantly from the actual trajectory (solid red line). This is due to the initial distance between the target and the radar, resulting in low signal-to-noise ratio and a large error. Over time, the distance between the target and the radar decreases, and the signal-to-noise ratio increases. This allows the algorithm to estimate the target's motion state more accurately, significantly improving the fit between the predicted trajectory and the actual trajectory.

[0120] (2) Accuracy comparison:

[0121] Figure 2 In order to demonstrate the improvement of GA-SQP collaborative algorithm on multi-target tracking performance, this paper fixes the radar at the origin position, that is, uses GA-SQP collaborative algorithm to compare with the fixed platform radar as a benchmark, and uses GA, SQP and SA for comparison respectively. The simulation results are shown in the figure below. Figure 1 Calculations show that the GA-SQP alternating iteration algorithm (purple line) improves multi-target tracking accuracy by 15.23%, 8.12%, 12.74%, and 73.87%, respectively, compared to the GA (red line), SQP (blue line), SA (black line), and the fixed-platform radar baseline algorithm (green line). This is because GA has a strong global search capability, exploring possible optimization directions within a wide solution space, while SQP, with its local optimization advantage, can quickly converge to a more accurate local optimal solution within the potential area found by GA. The two algorithms work together to optimize and complement each other, avoiding the problem of a single algorithm falling into a local optimum, improving tracking accuracy, and effectively verifying the effectiveness of this algorithm.

[0122] (3) Resource Scheduling:

[0123] Figure 3 The results of beam dwell time and power resource allocation for each target are presented, with different colors representing different beam dwell times and powers. In the initial tracking phase, target 1 is closer to the radar and requires fewer resources, so it is allocated a lower dwell time (blue area). Targets 2 and 3 are more challenging to track due to their greater distance from the radar, so they are allocated more dwell time. In the mid-stage, target 3's faster speed reduces its distance from the radar, so resources shift to target 2, which is slower and farther away (dark red area). In the later stages of tracking, target 1's slower speed increases its distance from the radar, resulting in more dwell time allocation. Regarding power allocation, in the early stages of tracking, target 3, being the farthest away, receives the majority of power resources to ensure tracking accuracy. Later in the tracking phase, although the dwell time decreases, the power allocation increases to maintain tracking effectiveness. The power allocation for target 2 generally coordinates with the dwell time scheduling logic, reflecting a resource linkage scheduling strategy. Since target 1 remains close to the radar throughout the entire tracking phase, the tracking power required is relatively low, so the overall power allocation remains low. The entire scheduling process ensures the improvement of the overall tracking accuracy of multiple targets by determining the distance between the target and the radar in real time and dynamically optimizing resource allocation.

[0124] (4) Result analysis

[0125] By comparing the tracking error curves (BCRLB lower bound) of different algorithms, the superiority of the GA-SQP collaborative algorithm in resource scheduling in multi-target tracking is verified, providing a basis for parameter configuration and algorithm implementation for the engineering application of mobile platform radar.

Claims

1. A radar resource scheduling method for detecting multiple targets using a fixed-track mobile platform, characterized in that: The specific steps include: Step 1: Build a multi-target tracking system model in a fixed track scenario, including the following three models: (1) Target motion model: Assume that the target moves in a uniform linear motion, and the state vector in, and Respectively represent the horizontal and vertical coordinate positions of the target q at time k, and They represent the speed of the target q in the X-axis and Y-axis directions at time k respectively; State transfer equation X q,k =FX q,k-1 +W q , where the state transfer matrix F is: Where ΔT represents the time interval; W q Represents zero-mean Gaussian white noise, and its process noise covariance matrix Q q,k-1 for: (2) Mobile platform radar motion model: The mobile platform radar moves along a fixed track at a uniform speed in a straight line, and its position update equation is: Where, and They represent the positions of the radar at time k and time k-1 respectively, v x and v y Represents the speed of the radar in the X-axis and Y-axis directions respectively; (3) Observation model: the observation vector Z of the target q at time k q,k =h(X q,k )+V q,k ; Where, the measurement function is: V q,k is Gaussian measurement noise, and its covariance matrix is ​​R q,k It is related to the signal-to-noise ratio SNR and is expressed as: Among them, σ r,q,k is the distance error of target q at time k, σ θ,q,k is the angle error of target q at time k, expressed as where c, β, λ, and γ are the speed of light, effective beam bandwidth, emission wavelength, and antenna aperture, respectively; the signal-to-noise ratio (SNR) is expressed as Where T q,k is the residence time of target q at time k, P q,k is the transmission power of target q at time k, T r is the pulse repetition period, G t is the transmitting antenna gain, G r is the receiving antenna gain, σ RCS is the radar cross section of target q, G RP , T0 and F r are the processing gain, noise temperature and noise figure of the radar receiver respectively, k B is the Boltzmann constant, B is the bandwidth of the radar receiver matched filter, r q,k is the distance between target q and radar at time k, is the azimuth of target q from the radar at time k; Step 2: Establish a constrained optimization model Objective function: The optimization goal is to minimize the weighted sum of each target BCRLB trace. The BCRLB matrix trace is The Bayesian information matrix Prior information matrix Measurement Information Matrix Among them, H q,k is h(X q,k ) is represented by: So the objective function can finally be expressed as: Among them, Q is the target number, ω q is the target weight; The constraints are: Among them, T max and T min are the upper and lower limits of the dwell time for each beam, P max and P min are the upper and lower limits of each beam’s transmit power, T total and P total are the total beam dwell time and total power, respectively, and are the total resource constraints; Step 3: Use the legacy algorithm GA to perform global search and generate the initial resource allocation plan: Initialize the GA population, set the population size, and use real number coding to encode the transmission power P q,k and residence time T q,k Encoding, each individual is a 2Q-dimensional vector, where the first Q dimension corresponds to power and the second Q dimension corresponds to residence time; the initial individual is randomly generated within the constraint range to ensure that P is satisfied min ≤P q,k ≤P max 、T min ≤T q,k ≤T max , total resource constraints Taking the objective function in step 2 as the fitness function, the initial resource allocation scheme [P (0) q,k ,T (0) q,k ] to ensure the global search for the potential optimal solution; Step 4: Using the initial resource allocation plan generated in step 3 as the initial value, perform local refinement optimization to improve accuracy using the sequential quadratic programming algorithm (SQP): Using the preliminary solution output by GA as the initial value, a quadratic programming subproblem including the objective function gradient and Hessian matrix is ​​constructed, specifically: stA(x+d)≤b,lb≤x+b≤ub Where x = [P 1,k ,T 1,k ,...,P Q,k ,T Q,k ] T is the optimization variable vector, d is the search direction; H is the Hessian matrix of the objective function, is the objective function gradient; A(x+d)≤b is a linear constraint, lb and ub are the upper and lower bound constraints of the variables; By iteratively solving the quadratic programming subproblem, the local convergence property of SQP is used to solve the solution generated by GA [P (0) q,k ,T (0) q,k ] to make fine adjustments and obtain the optimal solution that meets the constraints [P * q,k ,T * q,k ], as the optimal resource allocation scheme; Step 5: Dynamic state update and loop optimization, specifically using the extended Kalman filter (EKF) to process the observation results after the optimal resource allocation solution output in step 4 is executed to generate an updated target state estimate. and the posterior covariance matrix Σ q,k ; Step 6: Loop iterative optimization: for each time k=2,...,T total , T total is the total number of time steps, using the target state estimate outputted in step 5 of the previous moment (k-1) and the posterior covariance matrix Σ q,k-1 Through steps 3 and 4, the optimal power and residence time at time k are generated [P * q,k ,T * q,k ], meeting the dual constraints of power and residence time; and outputting and storing the results.

2. The radar resource scheduling method for detecting multiple targets by a fixed-track mobile platform according to claim 1, characterized in that: In step 2, the Bayesian information matrix J q,k The calculation is as follows: Where Cov(X q,k|k-1 )=FΣ q,k-1 F T +Q q,k-1 , where Σ q,k|k-1 is the state covariance matrix of the target q at the (k-1) moment, Q q,k-1 is the process noise covariance matrix of target q at time (k-1); the measurement information matrix The covariance matrix R q,k Related to the signal-to-noise ratio SNR, Where, T q,k is the residence time of target q at time k, P q,k is the transmission power of target q at time k, T r is the pulse repetition period, G t is the transmit antenna gain, G r is the receiving antenna gain, σ RCS is the radar cross section of target q, G RP , T0 and F r are the processing gain, noise temperature and noise figure of the radar receiver, k B is the Boltzmann constant, B is the bandwidth of the radar receiver matched filter, r q,k is the distance of target q from the radar at time k.

3. The radar resource scheduling method for detecting multiple targets by a fixed-track mobile platform according to claim 2, characterized in that: Step 5 specifically includes the following operations: Prediction step: Calculate the prior state estimate based on the target motion model constructed in step 1 in is the state estimate of the target q at time (k-1), F is the state transfer matrix in step 1; the prior covariance matrix is ​​updated Σ q,k|k-1 =FΣ q,k-1 F T +Q q,k-1 , where Σ q,k|k-1 is the state covariance matrix of the target q at the (k-1) moment, Q q,k-1 The process noise covariance matrix defined in step 1 is used to quantify the uncertainty of the target motion; Measurement update: using the observation value Z at time k q,k Corrected state estimate in is the predicted observation value, K k is the Kalman gain, which can be expressed as Among them, R q,k is the measurement noise covariance matrix, reflecting the observation noise level; Σ q,k|k-1 is the prior covariance matrix at time k, and based on the state estimate at time (k-1), the uncertainty of the state at time k is predicted; then the posterior state estimate is updated: The prior state estimate is corrected by the residual between the observed value and the predicted value to obtain a more accurate posterior state estimate; finally, the posterior covariance matrix is ​​obtained based on the prior covariance matrix: Σ q,k =(IK k H q,k )Σ q,k|k-1 , where I is the identity matrix and the updated posterior covariance matrix Σ q,k It reflects the reduction of uncertainty in the state estimate at time k; Through the above process, step 5 generates the updated target state estimate and the posterior covariance matrix Σ q,k , which are the input parameters of the target motion model, mobile platform radar motion model and observation model in steps 3 to 4 at the next time (k+1), driving the next cycle of resource allocation iteration.

4. The radar resource scheduling method for detecting multiple targets by a fixed-track mobile platform according to claim 3, characterized in that: Step 6 specifically includes the following operations: (1) Resource allocation and status update Use the target state estimate output from step 5 at the previous moment (k-1) and the posterior covariance matrix Σ q,k-1 Through step 3 (GA global search) and step 4 (SQP local optimization), the optimal power and residence time at time k [P * q,k ,T * q,k ], satisfying the dual constraints of power and dwell time; Radar Press P * q,k With T * q,k After executing resource allocation, obtain the observation value Z at time k q,k , generate the target state estimate at time k through step 5 and the posterior covariance matrix Σ q,k ; (2) Result output and storage Save the target state estimate at time k Forming a sequence Save the optimal resource allocation at time k When k = T total When , the complete state estimation sequence of multi-target tracking results is output And output the optimal resource allocation set at each moment

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