A multi-unmanned ship-borne radar node resource and waveform joint scheduling method and system for sea surface mobile target tracking

Abstract

The application provides a multi-unmanned ship-borne radar node resource and waveform joint scheduling method and system for sea surface mobile target tracking, solves the technical problem that the existing ship-borne radar resource optimization method does not combine the transmission waveform to optimize the resource and cannot consider the tracking accuracy and resource utilization rate. It includes obtaining echo information of the target, predicting and updating the target state, calculating the Fisher information matrix of the target, and screening the generated target set to be updated; calculating the equivalent position posterior Cramer-Lo lower bound after the Fisher information matrix, constructing a double target cost function; solving the measurement error covariance matrix corresponding to the optimal transmission waveform, updating the Fisher information matrix; globally optimizing the double target cost function, outputting the optimal radar node and transmission power allocation matrix, after detection and measurement update, feeding back the posterior state to the next detection period, completing the double closed loop tracking. The application can be widely applied to the field of radar tracking technology.

Description

Technical Field

[0001] This application belongs to the field of radar tracking technology, and more specifically, it relates to a method and system for joint scheduling of multi-unmanned surface-mounted radar node resources and waveforms for tracking mobile targets on the sea surface. Background Technology

[0002] In recent years, unmanned surface vessels (USVs) have shown broad application prospects in civilian and marine engineering fields. USV swarms rely on intelligent methods to plan, coordinate, and manage complex marine unmanned systems, enabling target tracking and escort, and are therefore widely used in practical scenarios such as maritime search and rescue and marine resource protection. Compared to land-based radar, USV-borne radar is mostly used in scenarios such as sea surface patrol, requiring the ability to operate autonomously on the sea surface for extended periods; however, currently, USV-borne radar generally suffers from short endurance.

[0003] Current research largely focuses on resource management nodes in radar systems, such as node selection and power allocation, discussing how to optimize the allocation of limited system resources to maximize network resource utilization while maintaining tracking performance. However, existing resource allocation methods do not consider the impact of transmitted waveforms on tracking performance, failing to achieve a balance between tracking accuracy and resource utilization, resulting in either poor tracking accuracy or low resource utilization. Therefore, a new resource scheduling method is urgently needed to address these issues. Summary of the Invention

[0004] The purpose of this application is to provide a method and system for joint scheduling of resources and waveforms of multiple unmanned surface radar nodes for tracking mobile targets on the sea surface, so as to solve the technical problem that the existing surface radar resource optimization methods do not combine the transmitted waveform to optimize resources, and cannot take into account both tracking accuracy and resource utilization.

[0005] To achieve the above objectives, the first embodiment of this application provides a method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface, including the following steps: Acquire the echo information of the target, predict and update the target state, calculate the Fisher information matrix of the target, adaptively optimize the revisit time interval, and filter to generate a set of targets to be updated; Calculate the equivalent location posterior Cramerlow lower bound based on the Fisher information matrix, and construct a bi-objective cost function; For each target in the target set to be updated, solve for the measurement error covariance matrix corresponding to the optimal transmission waveform, and update the Fisher information matrix. The cost function of the two targets is jointly optimized globally to output the optimal radar node and transmit power allocation matrix. After detection and measurement updates, the posterior state is fed back to the next detection cycle to complete the dual closed-loop tracking.

[0006] Preferably, the process of adaptively optimizing the revisit time interval includes: quantizing the target's Fisher information matrix into the target prediction error; if the target prediction error in the current frame reaches or exceeds the preset target expected accuracy, the target is marked as the object of measurement update in this period and included in the target set to be updated; otherwise, the radar remains silent in this frame period and does not perform active illumination and measurement update.

[0007] Preferably, the process of predicting and updating the target state includes: obtaining the posterior state of the target at the previous moment, using Kalman filtering or particle filtering to deduce the prior state of the target at the current moment, sequentially updating and predicting the target state, and calculating the Fisher information matrix of the target under time-domain progression.

[0008] Preferably, the process of solving the measurement error covariance matrix corresponding to the optimal transmitted waveform and updating the Fisher information matrix includes: constructing a two-dimensional discrete waveform library containing Gaussian pulse length and frequency width; making predictions in the two-dimensional discrete waveform library based on the prior state of the target; traversing to find the optimal waveform parameter combination that minimizes the expected measurement prediction error; substituting the measurement error covariance matrix corresponding to the optimal transmitted waveform in the optimal waveform parameter combination into the calculation process of the measurement Fisher information matrix; and updating the Fisher information matrix.

[0009] Preferably, before calculating the equivalent position posterior Cramero lower bound based on the Fisher information matrix, a decision variable matrix needs to be formed using the radar network node scheduling state and power configuration matrix. When a matrix element in the decision variable matrix is ​​0, it indicates that the radar node has not been assigned a target to track; when a matrix element is between 0 and 1, it indicates that the radar node has been activated and assigned a target to track; when a matrix element is 1, it indicates that the radar node is tracking the target at maximum power.

[0010] Preferably, the process of global joint optimization includes: the adaptive particle swarm optimization algorithm based on KL divergence performs a global search on the decision variable matrix; at the beginning of each iteration, the feature position distribution of the entire particle swarm in the multidimensional solution space is abstracted into an empirical probability density function; and the diversity of the current population is quantified by calculating KL divergence. When the KL divergence decreases abnormally, the inertial weight of the particles is adaptively increased through exponential function feedback to help the particles escape the local optimum trap. At the same time, the population genes are disrupted through genetic recombination to conduct a secondary exploration of the solution space and output the optimal radar node and transmit power allocation matrix.

[0011] Preferably, after calculating the equivalent position posterior Cramero lower bound based on the Fisher information matrix, the tracking performance cost function and the system power cost function are constructed respectively, and the weighted sum is used to obtain the dual-objective cost function; The formula for the bi-objective cost function is: ; In the formula, For empirical preference weighting coefficients, To track the performance cost function, This is the system power cost function.

[0012] Preferably, the tracking error quantification index of a single target position is calculated based on the posterior Cramerlow lower bound of the equivalent position, and the tracking performance cost function is constructed based on the accumulation of the one-sided penalty function, as shown in the formula: ; In the formula, To track the performance cost function, The number of targets. For the decision variable matrix, This is a quantitative indicator for single-target position tracking error. For the first The expected tracking accuracy of each target.

[0013] Preferably, the system power cost function is constructed by summing the normalized transmit power of all radar nodes, as shown in the formula: ; In the formula, Let be the system power cost function. The number of targets. For radar nodes, In order to be in Time of the first The radar node for the first Normalized power weights for each objective.

[0014] The second embodiment of this application provides a multi-unmanned surface vessel-borne radar node resource and waveform joint scheduling system for tracking maneuvering targets on the sea surface, including: The adaptive tracking and scheduling module is used to acquire the echo information of the target, predict and update the target state, calculate the Fisher information matrix of the target, adaptively optimize the revisit time interval, and filter and generate a set of targets to be updated. The cost function construction optimization module is used to calculate the equivalent position posterior Cramerlow lower bound based on the Fisher information matrix and construct the bi-objective cost function. The node resource optimization module solves for the measurement error covariance matrix corresponding to the optimal transmission waveform for the target in the target set to be updated, and updates the Fisher information matrix. The closed-loop tracking module is used to perform global joint optimization of the cost function of the two targets, output the optimal radar node and transmit power allocation matrix, and after detection and measurement updates, feed back the posterior state to the next detection cycle to complete the dual closed-loop tracking.

[0015] The beneficial effects of this application are as follows: This application provides a method and system for joint scheduling of resources and waveforms for multiple unmanned surface vessel-borne radar nodes in tracking maneuvering targets on the sea surface. First, it acquires the echo information of the target, predicts and updates the target state, calculates the Fisher information matrix of the target, adaptively optimizes the revisit time interval, and generates a set of targets to be updated. The measurement update frequency is dynamically adjusted according to the target state, avoiding redundant resource consumption caused by fixed-period detection of all targets, effectively reducing the overall system energy consumption. Next, based on the Fisher information matrix, the equivalent position posterior Cramer-Rao lower bound is calculated, and a dual-target cost function is constructed, integrating tracking accuracy and system resource consumption into a unified optimization framework, quantifying the balance between tracking performance and resource utilization as the decision-making basis. Then, for the targets in the set of targets to be updated, the measurement error covariance matrix corresponding to the optimal transmitted waveform is solved, and the Fisher information matrix is ​​updated. This jointly optimizes the transmitted waveform design and resource allocation, using the optimal waveform to reduce the theoretical lower bound of single measurement error, further improving tracking accuracy and expanding the optimization space of resource scheduling. Finally, by performing global joint optimization of the cost function for both targets, the optimal radar node and transmit power allocation matrix is ​​output. After detection and measurement updates, the posterior state is fed back to the next detection cycle to complete dual closed-loop tracking. This minimizes system resource consumption while ensuring the desired tracking accuracy, improves the working endurance of the unmanned surface vessel radar network, and achieves adaptive control of transmit waveform and radar node resources.

[0016] In summary, this application significantly reduces the resource consumption of multi-surface unmanned surface vessel radar tracking systems while ensuring tracking accuracy requirements, and can significantly improve the radar system's operational endurance. Simultaneously, it effectively integrates radar transmission waveform design, allowing for more flexible selection of transmission waveforms to optimize tracking performance and further enhance tracking accuracy. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A control block diagram of a multi-unmanned surface vessel-borne radar node resource and waveform joint scheduling method for tracking maneuvering targets on the sea surface provided in an embodiment of this application; Figure 2 A flowchart of an optimization algorithm for resource regulation and optimization problems using the KL-APSO adaptive particle swarm optimization algorithm based on KL divergence, provided as an embodiment of this application; Figure 3This is a topology diagram of a distributed detection system provided in an embodiment of this application; Figure 4 A comprehensive analysis diagram of resource allocation for a multi-radar system provided in an embodiment of this application; Figure 5 A comparison chart of the target tracking accuracy performance of this application and other algorithms is provided for one embodiment of this application; Figure 6 A heatmap comparison of resource allocation between this application and other algorithms is provided for one embodiment of this application; Figure 7 A comparison chart of resource utilization between this application and other algorithm systems is provided for one embodiment of this application; Figure 8 This is a schematic diagram illustrating the selection of waveform parameters for each radar node according to an embodiment of this application. Detailed Implementation

[0019] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0020] This application provides a method and system for joint scheduling of multi-unmanned surface vessel-borne radar node resources and waveforms for tracking maneuvering targets on the sea surface, and proposes a dual-closed-loop collaborative scheduling framework. First, a distributed tracking model incorporating target motion state and radar measurement state is constructed. Based on the target state prediction error, the target measurement revisit time interval is dynamically evaluated and adaptively calculated to eliminate redundant detection frequencies. Second, a dual-target optimization model based on a one-sided penalty function is established, using the deviation between the posterior Cramer-Rao lower bound (PCRLB) of the target tracking equivalent position and the desired accuracy as a penalty term to precisely balance tracking accuracy and system radar node resource loss. At the optimization solution level, this application introduces an adaptive particle swarm optimization algorithm (KL-APSO) based on KL divergence to globally optimize node allocation and power weights. KL divergence is used to measure the homogeneity of the population in real time and dynamically adjust the inertia weight and crossover mutation probability, fundamentally overcoming early convergence defects. Furthermore, this application introduces an adaptive waveform agility inner-loop strategy based on the minimum prediction error criterion, building upon node resource scheduling. By traversing a two-dimensional waveform library to find the minimum measurement error, it achieves dual closed-loop collaborative optimization of radar node resources and waveforms. Simulation results demonstrate that this application can significantly reduce system resource consumption and greatly improve the stealth and continuous operation capability of unmanned surface vessel radar networks in complex sea environments, while meeting the preset target tracking accuracy.

[0021] Please see Figure 1The first embodiment of this application provides a method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface, comprising: S1: Obtain the echo information of the target, predict and update the target state, calculate the Fisher information matrix of the target, adaptively optimize the revisit time interval, and filter to generate a set of targets to be updated.

[0022] In the context of A network of unmanned surface-to-water radar nodes, within the sea area including In application scenarios involving non-cooperative maneuvering targets on the sea surface, the echo information of the target is collected by a distributed multi-unmanned surface vessel radar network to obtain the posterior state of the target at the previous moment. Kalman filtering or particle filtering is used to deduce the prior state of the target at the current moment. The target state is then sequentially updated and predicted, and finally the Fisher Information Matrix (FIM) of the target under time-domain propagation is calculated. The target prediction error is obtained by quantification using the Fisher information matrix.

[0023] In order to reduce radar redundancy detection from the time dimension and save system resources, this application performs dynamic adaptive optimization of the measurement update revisit time interval for each target. Based on the comparison between the target prediction error and the target's expected accuracy, the measurement update revisit time interval for each target is adaptively optimized to filter and generate a set of targets to be updated.

[0024] Specifically, the system's basic frame interval is preset to maximize the revisit time interval as the optimization objective. While lengthening the revisit time interval, the target prediction error is controlled to approach but not exceed the product threshold of a preset safety threshold and the target's expected accuracy. As the revisit time interval increases, the target prediction error continues to accumulate. When the target prediction error in the current frame reaches or exceeds the product threshold, the target is forcibly marked as an object that must be measured and updated in this cycle and included in the target set to be updated. For targets with prediction errors far below the product threshold, the radar remains silent in this frame cycle and does not perform active illumination or measurement updates, thereby completing the full target time domain screening and generating the target set to be updated in this cycle.

[0025] In a containing In an unmanned surface vessel radar network consisting of nodes, there exist ROI (Return of Interest) sea areas. A non-cooperative maneuvering target, the radar node set is denoted as . The target set is denoted as Assume the coordinates of each radar node in the reference two-dimensional Cartesian coordinate system are known. In the [missing information]... At the nth discrete sampling time, the th The state vector of each target ( Momentary Goal coordinates , Momentary Goal speed of movement (Updated according to Markov evolution laws. Assume the state equation of a maneuvering target on the sea surface is expressed as:) ; In the formula, for Momentary Goal The state vector, For the previous sample Momentary Goal The state vector, For the system Momentary Goal The state transition matrix, The time step between two consecutive tracking samples, i.e., the revisit time interval. The representation is the process noise covariance matrix.

[0026] Unmanned surface vessel radar node For the target The original observation equations obtained from the probe can be abstracted into a nonlinear measurement function, as shown in the formula: ; In the formula, For radar exist Detect targets at all times The obtained measured echo values, Represents a nonlinear mapping function. This is an additive measurement noise vector.

[0027] S2: Determine the decision variables, calculate the equivalent position posterior Cramero lower bound based on the Fisher information matrix, construct the tracking performance cost function and the system power cost function respectively, and obtain the bi-objective cost function by weighting.

[0028] Using radar network node scheduling status and power configuration matrix as decision variables, a dual-objective cost function is constructed that comprehensively considers target tracking accuracy constraints and system resource consumption. Specifically, the equivalent posterior Cramer-Rao lower bound of the position is used as the evaluation index for target tracking accuracy, and a one-sided penalty function is used to characterize the penalty cost when the tracking accuracy does not meet the expected requirements.

[0029] Specifically, the radar network node scheduling state and power configuration matrix are used as optimization decision variables, and a decision variable matrix is ​​defined. The formula is: ; Matrix elements ,exist Time of the first The radar node for the first The normalized power weights of each target, which also characterize the active scheduling state of radar nodes: represent Real-time radar node Unassigned tracking target , represent Real-time radar node Activated and involved in the target The tracking task Represents the radar node Track the target with maximum power .

[0030] To establish a quantifiable evaluation benchmark for optimization algorithms, this application uses the posterior Cramero lower bound (PCRLB) to characterize the theoretical extreme lower bound of the mean square error of unbiased estimation for target tracking. Based on the additivity of the Fisher information matrix (FIM) under independent observation conditions, the current... Momentary Goal Global joint FIM matrix It can be obtained by weighted summation of its prior FIM information and the FIM measurements of all radar nodes tracking the target: ; In the formula, for Momentary Goal The Fisher information matrix is ​​derived from the globally optimized Fisher information matrix from the previous time step. It was predicted that... for Time of the first Radar No. 1 targets Resource weight, The Fisher information matrix for the measurement data is represented as: ; In the formula, For the present Jacobian matrix at time, for Time of the first Radar No. 1 targets The inverse of the corresponding measurement noise covariance matrix.

[0031] To extract the target spatial positioning accuracy, a matrix is ​​extracted using the position term. Transform the global Fisher information matrix and solve for the equivalent positional posterior Cramer-Rao lower bound (PCRLB), the formula is as follows: ; In the formula, Here is the position error covariance matrix. Extract the matrix for the position item. Extract the transpose of the matrix for the positional terms. for Momentary Goal The global joint FIM matrix.

[0032] The trace of the position error covariance matrix is ​​taken as the quantitative index of single-target position tracking error. The formula is: ; The equivalent position's posterior Cramerlow lower bound is the theoretical evaluation index for the accuracy of the unbiased target estimation.

[0033] Construct a tracking performance cost function based on a one-sided penalty function, and pre-define the first... The expected tracking accuracy of each target is (QoS metrics), only Furthermore, a normalization penalty term is introduced when the tracking accuracy fails to meet the preset requirements; when Furthermore, when the tracking accuracy meets expectations, the penalty term is set to zero. The formula for constructing the tracking performance cost function using a one-sided penalty function is as follows: ; In the formula, To track the performance cost function, This is a quantitative indicator for single-target position tracking error.

[0034] A system power cost function is constructed synchronously, using the sum of the normalized allocated power of all active radar nodes in the network to characterize the overall resource consumption of the system. The formula is as follows: ; In the formula, This is the system power cost function.

[0035] Ultimately, the system uses experience preference weighting coefficients. The tracking performance cost function With system power cost function A linear weighted combination is performed to form a global bi-objective cost function that takes into account both target tracking accuracy constraints and system resource consumption. The formula is as follows: ; In the formula, For empirical preference weighting coefficients, To track the performance cost function, This is the system power cost function.

[0036] S3: For each target in the target set to be updated, find the measurement error covariance matrix corresponding to the optimal transmission waveform and update the Fisher information matrix.

[0037] For each target in the target set to be updated, each unmanned surface vessel (USV) radar node performs a traversal optimization based on the minimum prediction error criterion within a pre-defined waveform parameter library to determine the optimal combination of waveform parameters that minimizes the expected measurement error covariance. The measurement error covariance matrix mapped by this optimal waveform parameter combination is then updated to the local Fisher information matrix of the corresponding node. The pre-defined waveform parameter library is a two-dimensional discrete grid library containing two dimensions: Gaussian pulse length and Gaussian pulse frequency width. The traversal optimization criterion is to find the parameters corresponding to the grid node that minimize the trace of the equivalent measurement error covariance matrix.

[0038] Specifically, before performing macro-level network resource allocation optimization, each distributed local radar node first initiates an inner-layer waveform optimization closed loop. A two-dimensional discrete waveform library containing Gaussian pulse length and frequency width is constructed locally on each node. Each radar node uses the target's prior state to make predictions within the constructed two-dimensional discrete waveform library, traversing to find the optimal waveform parameter combination that minimizes the expected measurement prediction error. Subsequently, the measurement error covariance matrix corresponding to this optimal waveform is substituted into the node's calculations to update the local Fisher information matrix (FIM). This closed-loop mechanism, through waveform-level optimization, significantly improves the theoretical accuracy limit of a single measurement, providing room for further reducing compression power in the outer loop.

[0039] In an optional embodiment, an adaptive revisit time for the target set to be updated is performed. Optimization. Maximize the time span between two detections while ensuring that the predicted PCRLB does not exceed the preset expected accuracy.

[0040] ; ; In the formula, For the first The radar node for the first The optimal adaptive revisit time obtained by solving the objective is... This is the candidate revisit time interval between two consecutive radar detections of the same target. For the first The radar node for the first The target at the revisit interval The Fisher Information Matrix (FIM) in the prediction domain. The PCRLB error matrix for the critical states of the target after screening. For accuracy redundancy coefficient, For the first The maximum permissible tracking error threshold is preset for each target. To optimize the constraints, This is for matrix trace operations.

[0041] Secondly, a waveform library for LFM (Linear Frequency Modulation) transmitted waveforms is established, with optional parameters including... Gaussian pulse length and Gaussian pulse frequency width. Each node first uses prior information about the target state to iterate and optimize the waveform parameters, and then uses the minimum error covariance criterion to determine the transmission waveform parameters with optimal performance.

[0042] Finally, substituting the error covariance matrix corresponding to the optimal transmission waveform into the measurement FIM matrix calculation significantly reduces measurement noise and provides more space for resource scheduling optimization.

[0043] S4: An adaptive particle swarm optimization algorithm based on KL divergence is used to perform global joint optimization of the cost function of the two targets, and output the optimal radar node and transmit power allocation matrix that meets the constraints. After detection and measurement updates, the posterior state estimation results are fed back to the next detection cycle to complete the dual closed-loop tracking.

[0044] The local Fisher information matrix, which integrates the optimal waveform parameters, is substituted into the aggregation calculation of the global Fisher information matrix. The KL-APSO adaptive particle swarm optimization algorithm is used to perform global joint optimization of the dual-objective cost function, and outputs the optimal radar node selection and transmit power allocation matrix that satisfies the constraints.

[0045] The KL divergence-based adaptive particle swarm optimization algorithm (KL-APSO) is used to optimize the decision variable matrix. A global search is performed. At the beginning of each iteration, KL-APSO abstracts the characteristic position distribution of the entire particle swarm in the multidimensional solution space into an empirical probability density function, and measures the diversity of the current population by calculating the KL divergence. When the KL divergence decreases abnormally, indicating that the system is rapidly collapsing towards a local extremum, the algorithm adaptively increases the inertia weight of the particles through exponential function feedback to help the particles escape the local optimum trap; at the same time, it scrambles the population's genes through genetic recombination to conduct a secondary exploration of the solution space. Finally, the optimal resource scheduling scheme is output.

[0046] Specifically, please refer to Figure 3 The adaptive particle swarm optimization algorithm based on KL divergence includes: randomly initializing a preset number of particles in a multidimensional decision space, mapping the position vector of each particle to a generation of resource allocation decision matrix, and performing legality judgment and boundary penalty based on node physical constraints.

[0047] Within the multidimensional decision space, the number of random initializations is... A swarm of particles. Each particle contains two vectors: position and velocity. The position vector represents... Mapped to the first Resource allocation matrix of generation particles Each dimension corresponds to a resource allocation coefficient for a specific target for a radar node. The particle velocity represents the search step size and direction.

[0048] The initial particle positions are validated against constraints to ensure that each radar node meets the requirements. And each target Cooperative radar numbers .

[0049] For particles that do not meet the constraints, a penalty factor is introduced to correct their fitness value, guiding the particles back to the feasible solution space.

[0050] During the algorithm iteration process, the empirical distribution probability function of the population particles in the feature distribution space is calculated, and the relative entropy between it and the ideal uniform distribution probability density is calculated using KL divergence, so as to quantify the diversity and homogeneity of the population in real time.

[0051] At the beginning of each iteration, KL divergence is used to feedback the degree of population homogeneity. The formula is: ; In the formula, For discrete interval variables within the particle characteristic distribution space, For the first Sub-particles In the characteristic interval The empirical probability function of the distribution. It represents the uniform probability density under ideal conditions.

[0052] When particle swarms exhibit individual differences due to excessive convergence When the value decreases, it indicates that the population particles tend to aggregate, and the system may be at risk of falling into local extrema.

[0053] Based on the real-time calculated KL divergence index, the inertial weight of each generation of particles is dynamically adjusted through a negative correlation index feedback mechanism. When the KL divergence decreases, indicating that the population is over-converged, the inertial weight is adaptively increased to enhance the global search domain.

[0054] The algorithm dynamically adjusts the inertial weights of particles based on feedback from diversity measurements and the exponential function. To obtain individual weights with feedback. The formula is: ; ; In the formula, , These represent the maximum and minimum values ​​of the weights, respectively. Larger weights are beneficial for global exploration, while smaller weights are beneficial for exploring detailed regions. To adjust the non-negative penalty coefficient for adaptive response sensitivity, KL scattering, This is the weighting compensation coefficient. In order, particles Fitness of the population, minimum fitness of the population, and average fitness of the population.

[0055] When diversity is insufficient and fitness improvement stagnates, the denominator becomes smaller. This increases the particle's global search capability, enhancing its ability to escape local optima.

[0056] Particles are determined based on dynamic weights and their optimal individual positions. With the global optimal position of the population The state evolution is performed using the following formula: ; ; In the formula, For the first The search velocity vector of the particle. For the first The search position vector of the particle. , These refer to the acceleration factor, which controls the speed at which a particle approaches its own experience and the collective experience. , Both refer to random sampling weights, defined as follows: A random variable with a random distribution.

[0057] An adaptive crossover and mutation probability model with a negative exponential decay relationship to KL divergence is established, which automatically triggers genetic operators to reshape the population's gene locus distribution when the population is in danger of local extrema.

[0058] To further avoid getting trapped in local optima, establish a... Adaptive crossover probability of negative correlation and mutation probability The formula is: ; ; In the formula, This is the preset maximum crossover probability upper limit. This is the preset maximum mutation probability upper limit. All are exponential decay control factors.

[0059] When population diversity decreases, the algorithm automatically triggers crossover and random mutation to forcibly recombine the population distribution for secondary exploration.

[0060] The particle's position and velocity are updated based on dynamically updated inertia weights and individual and global optimal experiences, and the process is repeated until the maximum number of iterations is met. Alternatively, if the fitness requirement is met, the globally optimal position vector can be extracted and inversely mapped to the final radar network power allocation matrix, as shown in the formula: ; In the formula, For radar network power allocation matrix, This is the globally optimal position vector.

[0061] The multi-unmanned surface vessel radar network schedules designated radar nodes to detect and measure targets according to predetermined parameters based on the output optimal radar node and transmit power allocation matrix, as well as the optimal waveform parameter combination. It then feeds back the posterior state estimation results to the next detection cycle, thus completing dual closed-loop tracking.

[0062] Specifically, the multi-unmanned surface vessel radar fusion center distributes the calculated optimal joint allocation matrix and optimal waveform parameters to each node. Each node then precisely controls the output power ratio of its transmitter and modulates the corresponding Gaussian linear frequency modulated waveform. After obtaining the latest posterior state, it iteratively transmits it to the next time slice, completing a dual closed loop of waveform and resource management.

[0063] The second embodiment of this application provides a multi-unmanned surface vessel-borne radar node resource and waveform joint scheduling system for tracking maneuvering targets on the sea surface, including: Multi-unmanned surface vessel radar network detection module: used to detect non-cooperative targets on the sea surface based on a distributed unmanned surface vessel platform, and to obtain raw measurement information such as the target's range, azimuth angle and Doppler frequency shift; State prediction and temporal filtering module: It is connected to the multi-unmanned surface vessel radar network detection module to estimate and predict the spatiotemporal state of the target using Kalman filter-type algorithms, calculate the Fisher information matrix of the target, and adaptively generate the set of targets to be updated based on the error threshold. Waveform optimization configuration module: used to perform pre-calculation of transmission parameters at local nodes, extract the combination of Gaussian pulse length and frequency width that minimizes the expected measurement prediction error from the built-in two-dimensional waveform library, and output the equivalent local measurement error information matrix of fused waveform features to the subsequent stage; Node resource optimization module: It is used to receive the optimized local measurement error information matrix of each node, stack them to generate a global Fisher information matrix and a posterior Cramer-Rao lower bound; and execute the adaptive particle swarm optimization algorithm based on KL divergence to solve and optimize the bi-objective cost function that combines the one-sided penalty function. Resource scheduling and waveform execution module: Based on the optimal joint allocation matrix output by the edge collaborative joint solution module, it issues control commands to the multi-unmanned surface vessel radar network detection module, and dynamically configures the activation status, relative transmit power, and corresponding matching underlying radio frequency waveform parameters of each unmanned surface vessel radar node.

[0064] Example 1: Simulation experiment verification.

[0065] The system state is a combination of A multi-unmanned surface-to-surface radar network, consisting of several surface-to-surface radar nodes, detects and tracks a single maneuvering target within the area of ​​interest (ROI). The target's initial position is located at... ,speed The three shipborne radar nodes are located at... , and The actual trajectory of the target in two-dimensional space is as follows Figure 3 As shown.

[0066] Waveform library selection of Gaussian pulse length range: Gaussian pulse frequency width range Carrier frequency selection .

[0067] Resource optimization relative weight coefficients are set as follows: In this application's algorithm, the total number of PSO particles is set to 50, the total number of evolutionary iterations is set to 100, the upper bound of the inertial weight is set to 0.8, the lower bound of the inertial weight is set to 0.4, the upper bound of the crossover probability is set to 0.6, the lower bound of the crossover probability is set to 0.2, the upper bound of the mutation probability is set to 0.2, and the lower bound of the mutation probability is set to 0.05. Typical values ​​widely used in existing practical radar tracking scenarios are adopted. As the expected PCRLB value.

[0068] Based on the algorithm of this application, and using the existing KHPSO-JNSPA algorithm for comparison, the results of resource allocation, tracking accuracy comparison, and radar system resource consumption comparison are as follows: Figure 4 , 5 As shown in Figures 6 and 7, the waveform selection during the tracking process is as follows: Figure 8 As shown.

[0069] Table 1 shows a comparison of the two PCRLB algorithms, and Table 2 shows a comparison of system resource utilization.

[0070] Table 1: Comparison of PCRLB between the two algorithms

[0071] Table 2: Comparison of resource utilization rates of the two algorithm systems

[0072] As shown in Table 1, the tracking accuracy of the algorithm in this application is better than that of the benchmark algorithm (the smaller the PCRLB value, the higher the theoretical tracking accuracy). As shown in Table 2, the resource consumption of the algorithm in this application is reduced by about 34.7% compared with the benchmark algorithm. It can be seen that, while ensuring the desired tracking accuracy (19.58m < 20m), the algorithm in this application achieves lower system resource consumption (0.175 < 0.268) compared with the benchmark algorithm. This shows that the algorithm in this application can balance tracking accuracy and resource utilization, and achieve a lower resource consumption rate while ensuring the tracking accuracy requirement, thus significantly improving the working endurance of the radar system.

[0073] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0074] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface, characterized in that, Includes the following steps: Acquire the echo information of the target, predict and update the target state, calculate the Fisher information matrix of the target, adaptively optimize the revisit time interval, and filter to generate a set of targets to be updated; Calculate the equivalent positional posterior Cramerlow lower bound based on the Fisher information matrix, and construct a bi-objective cost function; For each target in the set of targets to be updated, the measurement error covariance matrix corresponding to the optimal transmission waveform is solved, and the Fisher information matrix is ​​updated. The dual-target cost function is globally jointly optimized to output the optimal radar node and transmit power allocation matrix. After detection and measurement updates, the posterior state is fed back to the next detection cycle to complete dual closed-loop tracking. After calculating the equivalent position posterior Cramero lower bound based on the Fisher information matrix, the tracking performance cost function and the system power cost function are constructed respectively, and the weighted sum is used to obtain the dual-objective cost function. The formula for the bi-objective cost function is: ； In the formula, For empirical preference weighting coefficients, To track the performance cost function, The system power cost function; The tracking error quantification index of a single target position is calculated based on the posterior Cramerlow lower bound of the equivalent position. The tracking performance cost function is constructed based on the accumulation of the one-sided penalty function, and the formula is as follows: ； In the formula, To track the performance cost function, The number of targets. For the decision variable matrix, This is a quantitative indicator for single-target position tracking error. For the first The expected tracking accuracy of each target.

2. The method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface as described in claim 1, characterized in that, The process of adaptively optimizing the revisit time interval includes: quantizing the Fisher information matrix of the target into a target prediction error; if the target prediction error in the current frame reaches or exceeds the preset target expected accuracy, the target is marked as the object of measurement update in this period and included in the set of targets to be updated; otherwise, the radar remains silent in this frame period and does not perform active illumination and measurement update.

3. The method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface as described in claim 1, characterized in that, The process of predicting and updating the target state includes: obtaining the posterior state of the target at the previous moment, using Kalman filtering or particle filtering to deduce the prior state of the target at the current moment, sequentially updating and predicting the target state, and calculating the Fisher information matrix of the target under time-domain progression.

4. The method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface as described in claim 3, characterized in that, The process of solving the measurement error covariance matrix corresponding to the optimal transmitted waveform and updating the Fisher information matrix includes: constructing a two-dimensional discrete waveform library containing Gaussian pulse length and frequency width; making predictions in the two-dimensional discrete waveform library based on the prior state of the target; traversing to find the optimal waveform parameter combination that minimizes the expected measurement prediction error; substituting the measurement error covariance matrix corresponding to the optimal transmitted waveform in the optimal waveform parameter combination into the calculation process of the Fisher information matrix; and updating the Fisher information matrix.

5. The method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface as described in claim 1, characterized in that, Before calculating the equivalent position posterior Cramerlow lower bound based on the Fisher information matrix, a decision variable matrix needs to be formed by the radar network node scheduling state and power configuration matrix. When the matrix element in the decision variable matrix is ​​0, it indicates that the radar node has not been assigned to track the target. When the matrix element is between 0 and 1, it indicates that the radar node is activated and assigned to track a target; When the matrix element is 1, it indicates that the radar node is tracking the target at maximum power.

6. The method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface as described in claim 5, characterized in that, The process of global joint optimization includes: using an adaptive particle swarm optimization algorithm based on KL divergence to perform a global search on the decision variable matrix; at the beginning of each iteration, the feature position distribution of the entire particle swarm in the multidimensional solution space is abstracted into an empirical probability density function; and the diversity of the current population is quantified by calculating KL divergence. When the KL divergence decreases abnormally, the inertial weight of the particles is adaptively increased through exponential function feedback to help the particles escape the local optimum trap; at the same time, the population genes are disrupted through genetic recombination to conduct a secondary exploration of the solution space and output the optimal radar node and transmit power allocation matrix.

7. The method for joint scheduling of resources and waveforms of multiple unmanned surface vessel-borne radar nodes for tracking maneuvering targets on the sea surface as described in claim 1, characterized in that, The system power cost function is constructed by summing the normalized transmit power of all radar nodes, and the formula is: ； In the formula, Let be the system power cost function. The number of targets. For radar nodes, In order to be in Time of the first The radar node for the first Normalized power weights for each objective.

8. A multi-unmanned surface vessel-borne radar node resource and waveform joint scheduling system for tracking maneuvering targets on the sea surface, applied to the multi-unmanned surface vessel-borne radar node resource and waveform joint scheduling method for tracking maneuvering targets on the sea surface as described in any one of claims 1-7, characterized in that, include: An adaptive tracking and scheduling module is used to acquire the echo information of the target, predict and update the target state, calculate the Fisher information matrix of the target, adaptively optimize the revisit time interval, and filter and generate a set of targets to be updated. The cost function construction and optimization module is used to calculate the equivalent position posterior Cramerlow lower bound based on the Fisher information matrix and construct a bi-objective cost function. The node resource optimization module solves for the measurement error covariance matrix corresponding to the optimal transmission waveform for the targets in the target set to be updated, and updates the Fisher information matrix. The closed-loop tracking module is used to perform global joint optimization of the cost function of the two targets, output the optimal radar node and transmit power allocation matrix, and after detection and measurement updates, feed back the posterior state to the next detection cycle to complete the dual closed-loop tracking.

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