Signal parameter optimal allocation estimation method for clutter environment
By constructing a multi-sensor joint detection model and improving the utility function, and combining graph neural networks to optimize signal allocation, virtual suspicious areas are dynamically generated. This solves the problems of accuracy and robustness in signal detection and parameter estimation under cluttered environments, and enables priority identification and efficient computation of high-threat signals.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-23
- Publication Date
- 2026-03-31
AI Technical Summary
In cluttered environments, existing signal detection and parameter estimation methods suffer from problems such as unreasonable utility function design, low efficiency in solving optimization models, and lack of intelligent allocation methods. These issues lead to inaccurate signal category judgment, large estimation bias, and difficulty in adapting to complex high-dimensional feature spaces.
A multi-signal joint detection and parameter estimation model under multi-sensor clutter environment is constructed. An improved utility function is designed. One-to-one matching is performed by adding virtual targets. A constrained optimization model is established using SAA-AFROC curves. Signal allocation is optimized by combining graph neural networks. Virtual suspicious areas are dynamically generated. The optimal estimation rule is derived. The optimal detection rule is solved by using the Lagrangian function.
It significantly improves the accuracy and robustness of signal detection and parameter estimation, prioritizes the identification of high-threat signals, dynamically adapts to complex clutter environments, reduces false alarm rates, and improves computational efficiency.
Smart Images
Figure CN121763232A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of signal processing and multi-target tracking technology, specifically referring to a method for optimal allocation estimation of signal parameters in clutter environments. Background Technology
[0002] In the problem of joint detection and parameter estimation of multiple signals, especially in cluttered environments, the performance of traditional methods is limited by issues such as the unknown number of signals and the uncertainty of measurement sources. Existing methods, such as the FROC / AFROC performance evaluation framework based on random finite sets for multi-target tracking algorithms, are theoretically sound, but still suffer from the following problems in practical applications: unreasonable utility function design: traditional utility functions are prone to estimation bias when the signal category is not accurately determined; low efficiency of optimization model solution: traditional methods, such as the Hungarian algorithm, can solve for the optimal allocation, but the computational complexity is high in high-dimensional scenarios; lack of intelligent allocation methods: existing methods do not fully utilize the deep information of the measurement data and are difficult to adapt to complex cluttered environments.
[0003] Existing computer-aided detection systems often separate detection and parameter estimation into two independent steps, which can easily lead to error accumulation. Although there are studies on joint detection and estimation, their objective functions do not fully meet application requirements, and traditional optimization methods are inefficient in solving complex high-dimensional feature spaces. Their simple allocation methods are also difficult to achieve the required accuracy and robustness. Therefore, this paper proposes an optimal allocation estimation method for signal parameters in clutter environments. Summary of the Invention
[0004] The purpose of this invention is to provide a method for estimating the optimal allocation of signal parameters in cluttered environments, so as to solve the problems mentioned in the background art.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for optimal allocation estimation of signal parameters in clutter environments, comprising the following steps:
[0006] S1. Construct a multi-signal joint detection and parameter estimation model under multi-sensor clutter environment;
[0007] S2. Based on the idea of optimal allocation, an improved utility function is designed. By adding a virtual target, the allocation problem is transformed, and a one-to-one matching between the real signal and the estimated value is performed.
[0008] S3. Establish a constrained optimization model using the SAA-AFROC curve as the performance standard, and calculate the multi-sensor measurement likelihood function under the assumptions of no signal and the existence of real signal to provide data for the model;
[0009] S4. Derive the optimal estimation rule based on the improved utility function, then substitute it into the model, and obtain the optimal detection rule through model transformation and Lagrange function solution.
[0010] S5. Set simulation parameters and verify the detection and estimation performance of the proposed method by comparing multiple performance curves and analyzing the influence of parameters.
[0011] Preferably, in step S1, a joint detection and parameter estimation task with an unknown number of signals is performed using multiple sensors. Two hypotheses are defined to correspond to scenarios with no signal and scenarios with a real signal, respectively. Let y = [y1, y2, ..., y K [ ] represents the observation data from K sensors, where y K Let be the observation vector of the k-th sensor. Under the no-signal assumption, all measurements originate from clutter. The number of clutter particles follows a known probability distribution, and the location of the clutter particles also follows a preset probability distribution. The multi-sensor measurement likelihood function under the no-signal assumption is:
[0012]
[0013] In the formula, p(y|nosignal) represents the conditional probability density function of the observed data y under the no-signal assumption, which is the probability of observing data y in a no-signal scenario, and y represents the multi-sensor observation data vector. From the product operator representing the product of the likelihood functions of all K sensors, k=1 to K, ∫ c The operator p(y) represents the integral operator over clutter measurement c, pter(c) represents the probability density function of the clutter measurement, describing the probability distribution of the occurrence of clutter measurement c, and p(y) represents the probability density function of the clutter measurement c. k |c) Given the clutter measurement c and the observation data y of the k-th sensor. k The conditional probability density function;
[0014] Under the assumption of a real signal, the measurements include measurements derived from the real signal and clutter measurements. The probability distribution characteristics of the clutter are consistent with the no-signal assumption. Measurements derived from the real signal are generated through a mapping relationship. The likelihood function of multi-sensor measurements under the assumption of a real signal is:
[0015] p(y|signal)=∑ E P(E)·p(y|E),
[0016] In the formula, p(y|signal) represents the conditional probability density function of the observed data y under the assumption of a real signal, which is the probability of observing data y in the scenario where a real signal exists. P(E) represents the probability of the joint event E occurring, which is the probability of the specific event occurring under the given assumption. E represents the combination of the real signal and clutter observed by different sensors. p(y|E) represents the conditional probability density function of the observed data y given the joint event E, and the noise of each sensor is independent of each other, while also remaining independent of the real signal and clutter.
[0017] Preferably, in step S1, the unknown signal parameters and their estimated values are distinguished. The unknown signal parameters include the number of real signals and the location information of each real signal. The estimated values of the unknown signal parameters include the estimated number of signals and the location information of each estimated signal. For high-threat signals, such as high-speed approaching or highly maneuverable signals, their threat level attributes are marked in the parameter record.
[0018] Preferably, in step S2, the specific process of designing the decision-oriented utility function is as follows: the utility function is constructed as a function simulating a reward system, providing cumulative positive incentives for correct detection and accurate estimation behaviors, treating a single detection task as an investment, and correct decisions as corresponding benefits; through a task-sensitive scoring method, combined with signal threat level attributes, the scoring weights are set, and the threat level-weighted utility function is implemented as follows:
[0019]
[0020] In the formula, Let represent the utility function value, and s represent the set of actual signal locations. Indicates the estimated signal location combination, α i β represents the matching weight of the i-th signal. i Let σ represent the estimated weight of the i-th signal, σ represent the position estimation accuracy coefficient, and α represent the position estimation accuracy coefficient. i Represented as α i =1+θ i ·(T i -T min ), θ i T represents the threat level coefficient. i The threat level of the i-th signal is represented by the value of the i-th signal. For high-threat signals, even if there is a slight deviation in the location estimation, a higher score is still given, so that the utility function has a clear physical meaning and economic interpretation, and can reflect the decision value of signals with different threat levels.
[0021] Preferably, in step S2, the specific process of constructing the optimal signal allocation method based on the graph neural network is as follows: The real target location and the suspicious region output by the model are used as two types of nodes in a bipartite graph to construct a bipartite graph model, transforming the matching problem between the real target and the suspicious region into an optimal bipartite graph matching problem; the bipartite graph is processed by the graph neural network algorithm, and by learning the feature associations between the real target and the suspicious region, such as positional similarity and signal strength correlation, the optimal matching scheme of the bipartite graph is solved. The graph neural network bipartite graph matching cost function is:
[0022]
[0023] In the formula, C ij w represents the matching cost between the real signal i and the estimated signal j.p w represents positional similarity. s The semantic similarity weight is represented by N(), which represents the neighborhood set of a node. The optimal matching scheme ensures a one-to-one correspondence, that is, a real target is matched with at most one suspicious region, and a suspicious region is assigned at most one real target. The detection confidence and parameter estimation value are positively reinforced when a suspicious region is successfully matched.
[0024] Preferably, in step S2, the specific process of dynamically generating virtual suspicious regions is as follows: Real-time analysis of the quantity matching relationship and matching competition between real targets and suspicious regions; when the number of suspicious reports is unequal to the number of real signals, or when multiple highly similar suspicious regions exist near a real target causing matching competition, the virtual suspicious region generation process is initiated; the generation of virtual suspicious regions aims to fill gaps in the matching cost matrix and optimize the overall matching cost. Virtual suspicious regions are dynamically generated in areas lacking suspicious targets and not interfering with the matching of real targets, used to absorb excess false positive suspicious reports or alleviate matching competition. The virtual suspicious region generation optimization model is as follows:
[0025]
[0026] In the formula, v represents the location of the virtual suspicious area, and γ j Let η represent the attraction coefficient of the j-th estimated signal. j This represents the competition suppression coefficient of the j-th estimated signal. This represents the competition inhibition term. for Quantitative estimation of the competition intensity between signals, rather than using fixed or random position settings, ensures the balance and accuracy of the allocation process.
[0027] Preferably, in S3, the constrained optimization model is constructed as follows: based on the utility function designed in S2, the average posterior estimated utility is defined, and the signal detection score is obtained by combining the decision function and the measurement probability distribution; the constraint condition is set that the probability of at least one false positive event occurring in a no-signal scenario does not exceed a preset threshold; the constrained optimization model aims to maximize the signal detection score while satisfying the above-mentioned false positive probability constraint, and the constrained optimization model is as follows:
[0028]
[0029] In the formula, τ represents the decision threshold, δ(τ,y) represents the decision function, α represents the false positive probability threshold, and ∫ y This represents the summation of all possible observations, and the integration operator over the observation data y.
[0030] Preferably, in step S3, the calculation of the multi-sensor measurement likelihood function is divided into two scenarios: In the absence of signal, the multi-sensor measurement likelihood function is obtained by multiplying the probability distribution of the number of clutter and the probability density of the clutter position of each sensor; In the presence of real signal, based on the law of total probability, the feasible joint events are divided by combining the joint probability data association algorithm, the occurrence probability of each feasible joint event and the measurement likelihood function under the corresponding conditions are calculated, and finally the multi-sensor measurement likelihood function is obtained by summing.
[0031] Preferably, in S4, the derivation process of the optimal estimation rule is as follows: Determine the core indicators of the estimation parameters, including the estimation accuracy of the correlation between the number of signals, their location, and the threat level; clarify the correlation between these core indicators and the actual signal parameters and the decision function; with the goal of maximizing the average posterior estimation utility based on the S2 utility function, combine the measurement probability distribution and the prior probability distribution of the signal parameters to derive the optimal estimation rule, which is implemented as follows:
[0032]
[0033] In the formula, Let M represent the set of optimal estimated signal locations, where M represents the optimal location of all estimated signals, and w represents the number of signals. i Let v represent the prior weight of the i-th signal. i This represents the likelihood weight of the i-th signal. This represents the prior probability distribution of the estimated signal.
[0034] Preferably, in step S4, the process of solving the optimal detection rule includes: substituting the derived optimal estimation rule into the constrained optimization model and defining a constant term to simplify the model expression; transforming the original constrained optimization model into a more easily solvable form through equivalent transformation; introducing relaxation factors and Lagrange multipliers to construct a generalized Lagrange multiplier; searching for parameter values that satisfy the preset error accuracy through the bisection method, and finally solving to obtain the optimal detection rule.
[0035] Preferably, the implementation of S5 includes:
[0036] The first step is to set the simulation parameters, including the number of sensors, sensor noise characteristic parameters, probability distribution parameters of clutter number and location, range of real signal number, location probability distribution parameters and threat level classification criteria, signal detection probability, maximum tolerance distance, and number of Monte Carlo experiment runs.
[0037] The second step is to design a comparison scheme and select different numbers of sensors and different utility functions, such as the traditional utility function without threat weights and the allocation algorithm of fixed virtual nodes, as comparison algorithms.
[0038] The third step is to generate multiple performance curves, including SAA-AFROC curves, ROC curves, RMSE curves, and average curves for signal number estimation, and to separately label the decision performance data of high-threat signals in the curve analysis.
[0039] The fourth step is to conduct parameter impact analysis, fix other parameters, and adjust key parameters such as maximum tolerance distance, false positive event probability threshold, and virtual suspicious area generation frequency, and observe the changing trend of performance curves under different parameter values;
[0040] The fifth step is to verify the performance of the method. By comparing the performance curves of the proposed method with those of the comparative algorithm, and combining the results of parameter influence analysis, we can determine the advantages of the proposed method in terms of detection accuracy and parameter estimation precision for signals of different threat levels.
[0041] Compared with the prior art, the beneficial effects of the present invention are:
[0042] 1. This invention addresses the technical challenges of high false alarm rates, low matching accuracy, and poor adaptability to dynamic signals in signal detection and parameter estimation in complex clutter environments. It proposes a joint detection and parameter estimation method based on multi-sensor collaboration, threat level weighting, and graph neural network optimization. By constructing a multi-sensor joint detection model and combining it with a dynamic virtual target generation and constraint optimization framework, it overcomes the shortcomings of traditional methods in handling unknown signal numbers, strong clutter interference, and prioritizing high-threat signals. This not only significantly improves the accuracy and robustness of detection and estimation but also achieves priority identification and decision optimization for high-threat signals by introducing threat level attributes and an economic utility function.
[0043] 2. This invention improves the utility function by designing an optimal allocation concept. By adding virtual targets, the signal matching problem is transformed into a one-to-one optimization problem, effectively solving the matching error problem of traditional allocation algorithms when the number of signals is uncertain. The threat level-weighted utility function proposed in this step combines the signal threat attribute with the detection benefit, enabling high-threat signals to obtain higher scores even when estimation bias exists, thereby improving the detection priority of key signals. In addition, the bipartite graph matching method based on graph neural networks learns the association between signal position and semantic features and dynamically optimizes the matching cost function, significantly improving matching accuracy and computational efficiency. The dynamic generation strategy of virtual suspicious regions further alleviates the matching competition problem.
[0044] 3. This invention provides reliable data support for the model through multi-sensor likelihood function calculation under the assumptions of no signal and presence of signal. This step achieves a balance between detection performance and false alarm rate by defining the average posterior estimation utility and signal detection score, combined with false positive probability constraints. This modeling approach breaks through the limitations of traditional methods that rely solely on a single performance index, enabling the model to dynamically adjust the detection threshold according to actual needs. At the same time, by dividing joint events through a joint probability data association algorithm, the robustness and decision accuracy of the model in high clutter environments are significantly improved.
[0045] 4. This invention derives the optimal estimation rule through the utility function and solves the optimal detection rule by combining the Lagrange function. With the goal of maximizing the average posterior estimation utility, it combines the prior probability distribution of the signal with the probability distribution of the measurement, effectively suppressing the influence of clutter interference on the estimation results. By introducing a relaxation factor and bisection optimization, it significantly improves the computational efficiency and convergence stability. Attached Figure Description
[0046] Figure 1 The present invention provides the operational flow of a method for optimal allocation estimation of signal parameters in clutter environments. Figure 1 ;
[0047] Figure 2 The present invention provides the operational flow of a method for optimal allocation estimation of signal parameters in clutter environments. Figure 2 ;
[0048] Figure 3 The present invention provides the operational flow of a method for optimal allocation estimation of signal parameters in clutter environments. Figure 3 ;
[0049] Figure 4 The present invention provides the operational flow of a method for optimal allocation estimation of signal parameters in clutter environments. Figure 4 ;
[0050] Figure 5 This is a schematic diagram comparing the position estimation RMSE of the optimal signal parameter allocation estimation method for clutter environments according to the present invention.
[0051] Figure 6 This is a schematic diagram comparing signal detection scores for an optimal signal parameter allocation estimation method for clutter environments according to the present invention.
[0052] Figure 7 This is a schematic diagram illustrating the average estimated number of true signals for an optimal signal parameter allocation estimation method in a clutter environment according to the present invention.
[0053] Figure 8This is a schematic diagram of signal detection scores with different R values for a signal parameter optimal allocation estimation method for clutter environments according to the present invention.
[0054] Figure 9 This diagram illustrates the number of true signals with different average R values for the optimal allocation estimation method of signal parameters in clutter environments according to the present invention. Detailed Implementation
[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0056] Example
[0057] Please see Figures 1-9 As shown, the present invention provides a technical solution comprising the following steps:
[0058] S1. Construct a multi-signal joint detection and parameter estimation model under multi-sensor clutter environment;
[0059] S2. Based on the idea of optimal allocation, an improved utility function is designed. By adding a virtual target, the allocation problem is transformed, and a one-to-one matching between the real signal and the estimated value is performed.
[0060] S3. Establish a constrained optimization model using the SAA-AFROC curve as the performance standard, and calculate the multi-sensor measurement likelihood function under the assumptions of no signal and the existence of real signal to provide data for the model;
[0061] S4. Derive the optimal estimation rule based on the improved utility function, then substitute it into the model, and obtain the optimal detection rule through model transformation and Lagrange function solution.
[0062] S5. Set simulation parameters and verify the detection and estimation performance of the proposed method by comparing multiple performance curves and analyzing the influence of parameters.
[0063] Preferably, in step S1, a joint detection and parameter estimation task with an unknown number of signals is performed using multiple sensors. Two hypotheses are defined to correspond to scenarios with no signal and scenarios with a real signal, respectively. Let y = [y1, y2, ..., y K [ ] represents the observation data from K sensors, where y K Let be the observation vector of the k-th sensor. Under the no-signal assumption, all measurements originate from clutter. The number of clutter particles follows a known probability distribution, and the location of the clutter particles also follows a preset probability distribution. The multi-sensor measurement likelihood function under the no-signal assumption is:
[0064]
[0065] In the formula, p(y|nosignal) represents the conditional probability density function of the observed data y under the no-signal assumption, which is the probability of observing data y in a no-signal scenario, and y represents the multi-sensor observation data vector. From the product operator representing the product of the likelihood functions of all K sensors, k=1 to K, ∫ c The operator p(y) represents the integral operator over clutter measurement c, pter(c) represents the probability density function of the clutter measurement, describing the probability distribution of the occurrence of clutter measurement c, and p(y) represents the probability density function of the clutter measurement c. k |c) Given the clutter measurement c and the observation data y of the k-th sensor. k The conditional probability density function;
[0066] Under the assumption of a real signal, the measurements include measurements derived from the real signal and clutter measurements. The probability distribution characteristics of the clutter are consistent with the no-signal assumption. Measurements derived from the real signal are generated through a mapping relationship. The likelihood function of multi-sensor measurements under the assumption of a real signal is:
[0067] p(y|signal)=∑ E P(E)·p(y|E),
[0068] In the formula, p(y|signal) represents the conditional probability density function of the observed data y under the assumption of a real signal, which is the probability of observing data y in the scenario where a real signal exists. P(E) represents the probability of the joint event E occurring, which is the probability of the specific event occurring under the given assumption. E represents the combination of the real signal and clutter observed by different sensors. p(y|E) represents the conditional probability density function of the observed data y given the joint event E, and the noise of each sensor is independent of each other, while also remaining independent of the real signal and clutter.
[0069] Preferably, in step S1, the unknown signal parameters and their estimated values are distinguished. The unknown signal parameters include the number of real signals and the location information of each real signal. The estimated values of the unknown signal parameters include the estimated number of signals and the location information of each estimated signal. For high-threat signals, such as high-speed approaching or highly maneuverable signals, their threat level attributes are marked in the parameter record.
[0070] Preferably, in step S2, the specific process of designing the decision-oriented utility function is as follows: the utility function is constructed as a function simulating a reward system, providing cumulative positive incentives for correct detection and accurate estimation behaviors, treating a single detection task as an investment, and correct decisions as corresponding benefits; through a task-sensitive scoring method, combined with signal threat level attributes, the scoring weights are set, and the threat level-weighted utility function is implemented as follows:
[0071]
[0072] In the formula, Let represent the utility function value, and s represent the set of actual signal locations. Indicates the estimated signal location combination, α i β represents the matching weight of the i-th signal. i Let σ represent the estimated weight of the i-th signal, σ represent the position estimation accuracy coefficient, and α represent the position estimation accuracy coefficient. i Represented as α i =1+θ i ·(T i -T min ), θ i T represents the threat level coefficient. i The threat level of the i-th signal is represented by the value of the i-th signal. For high-threat signals, even if there is a slight deviation in the location estimation, a higher score is still given, so that the utility function has a clear physical meaning and economic interpretation, and can reflect the decision value of signals with different threat levels.
[0073] Preferably, in S2, the specific process of constructing the optimal signal allocation method based on the graph neural network is as follows: taking the real target location and the suspicious area output by the model as two types of nodes in the bipartite graph, constructing a bipartite graph model, and transforming the matching problem between the real target and the suspicious area into the optimal matching problem of the bipartite graph.
[0074] The bipartite graph is processed using a graph neural network algorithm. By learning the feature associations between the real target and the suspicious region, such as location similarity and signal strength correlation, the optimal matching scheme of the bipartite graph is found. The cost function of graph neural network bipartite graph matching is:
[0075]
[0076] In the formula, C ij w represents the matching cost between the real signal i and the estimated signal j. p w represents positional similarity. s The semantic similarity weight is represented by N(), which represents the neighborhood set of a node. The optimal matching scheme ensures a one-to-one correspondence, that is, a real target is matched with at most one suspicious region, and a suspicious region is assigned at most one real target. The detection confidence and parameter estimation value are positively reinforced when a suspicious region is successfully matched.
[0077] Preferably, in S2, the specific process of dynamically generating virtual suspicious areas is as follows: real-time analysis of the matching relationship between the number of real targets and suspicious areas and the matching competition situation. When there is a discrepancy between the number of suspicious reports and the number of real signals, or when there are multiple highly similar suspicious areas near a real target, resulting in matching competition.
[0078] Initiate the virtual suspicious area generation process. The generation of virtual suspicious areas aims to fill gaps in the matching cost matrix and optimize overall matching costs. Virtual suspicious areas are dynamically generated in regions lacking suspicious targets and not interfering with real target matching. This is used to absorb excess false positive suspicious reports or alleviate matching competition. The virtual suspicious area generation optimization model is as follows:
[0079]
[0080] In the formula, v represents the location of the virtual suspicious area, and γ j Let η represent the attraction coefficient of the j-th estimated signal. j This represents the competition suppression coefficient of the j-th estimated signal. This represents the competition inhibition term. for Quantitative estimation of the competition intensity between signals, rather than using fixed or random position settings, ensures the balance and accuracy of the allocation process.
[0081] Preferably, in S3, the constrained optimization model is constructed as follows: based on the utility function designed in S2, the average posterior estimated utility is defined, and the signal detection score is obtained by combining the decision function and the measurement probability distribution; the constraint condition is set that the probability of at least one false positive event occurring in a no-signal scenario does not exceed a preset threshold; the constrained optimization model aims to maximize the signal detection score while satisfying the above-mentioned false positive probability constraint, and the constrained optimization model is as follows:
[0082]
[0083] In the formula, τ represents the decision threshold, δ(τ,y) represents the decision function, α represents the false positive probability threshold, and ∫ y This represents the summation of all possible observations, and the integration operator over the observation data y.
[0084] Preferably, in step S3, the calculation method of the multi-sensor measurement likelihood function is divided into two scenarios: in the no-signal scenario, the multi-sensor measurement likelihood function is obtained by combining the probability distribution of the number of clutter and the probability density of the clutter position of each sensor through multiplication.
[0085] In scenarios with real signals, based on the law of total probability and combined with the joint probability data association algorithm, feasible joint events are divided, the occurrence probability of each feasible joint event and the measurement likelihood function under the corresponding conditions are calculated, and finally the multi-sensor measurement likelihood function is obtained by summing.
[0086] Preferably, in S4, the derivation process of the optimal estimation rule is as follows: determine the core indicators of the estimation parameters, including the estimation accuracy of the correlation between the number of signals, location and threat level, and clarify the correlation between the core indicators and the real signal parameters and decision functions.
[0087] With the objective of maximizing the average posterior estimation utility based on the S2 utility function, the optimal estimation rule is derived by combining the measurement probability distribution and the prior probability distribution of the signal parameters, and is implemented as follows:
[0088]
[0089] In the formula, Let M represent the set of optimal estimated signal locations, where M represents the optimal location of all estimated signals, and w represents the number of signals. i Let v represent the prior weight of the i-th signal. i This represents the likelihood weight of the i-th signal. This represents the prior probability distribution of the estimated signal.
[0090] Preferably, in step S4, the process of solving the optimal detection rule includes: substituting the derived optimal estimation rule into the constrained optimization model and defining a constant term to simplify the model expression; transforming the original constrained optimization model into a more easily solvable form through equivalent transformation; introducing relaxation factors and Lagrange multipliers to construct a generalized Lagrange multiplier; searching for parameter values that satisfy the preset error accuracy through the bisection method, and finally solving to obtain the optimal detection rule.
[0091] Preferably, the implementation of S5 includes:
[0092] The first step is to set the simulation parameters, including the number of sensors, sensor noise characteristic parameters, probability distribution parameters of clutter number and location, range of real signal number, location probability distribution parameters and threat level classification criteria, signal detection probability, maximum tolerance distance, and number of Monte Carlo experiment runs.
[0093] The second step is to design a comparison scheme and select different numbers of sensors and different utility functions, such as the traditional utility function without threat weights and the allocation algorithm of fixed virtual nodes, as comparison algorithms.
[0094] The third step is to generate multiple performance curves, including SAA-AFROC curves, ROC curves, RMSE curves, and average curves for signal number estimation, and to separately label the decision performance data of high-threat signals in the curve analysis.
[0095] The fourth step is to conduct parameter impact analysis, fix other parameters, and adjust key parameters such as maximum tolerance distance, false positive event probability threshold, and virtual suspicious area generation frequency, and observe the changing trend of performance curves under different parameter values;
[0096] The fifth step is to verify the performance of the method. By comparing the performance curves of the proposed method with those of the comparative algorithm, and combining the results of parameter influence analysis, we can determine the advantages of the proposed method in terms of detection accuracy and parameter estimation precision for signals of different threat levels.
[0097] Working principle: By constructing a multi-sensor collaborative joint detection and parameter estimation model, two hypothetical scenarios are defined: no signal and presence of real signal. A mathematical model is established based on the probability distribution of clutter number and location. At the same time, the unknown parameters and estimated values of real signals are distinguished, and threat level attributes are marked for high-threat signals such as high-speed maneuvers, enabling the system to prioritize the identification of key targets.
[0098] Based on the idea of optimal allocation, a threat level-weighted utility function is designed, transforming correct detection and accurate estimation into accumulative positive incentives. A bipartite graph model is constructed using a graph neural network, mapping real targets and suspicious regions to two types of nodes. The correlation between positional similarity and signal strength is learned to solve for optimal matching. For signal quantity mismatch or high similarity competition, virtual suspicious regions are dynamically generated to fill matching gaps, ensuring a one-to-one matching relationship. Each real target matches only one suspicious region, and the successfully matched signal receives positive reinforcement in detection confidence and parameter estimation. By calculating the clutter measurement likelihood function under the no-signal assumption and the measurement likelihood function under the signal presence assumption, key data support is provided for the model. The average posterior estimation utility is defined as the detection score, and a false positive probability constraint is set. In the no-signal scenario, the false positive does not exceed a preset threshold, enabling the optimized model to maximize detection performance while strictly controlling the false alarm rate. The improved utility function and constraint optimization are then applied. By combining models, an optimal estimation rule is derived that aims to maximize the average posterior estimation utility. This rule integrates the prior probability distribution of the signal and the measurement probability distribution, clarifying the correlation between the number, location, and threat level of the signal. By substituting into the constraint optimization model and simplifying the expression using model transformation, a generalized Lagrange function is constructed by introducing Lagrange multipliers. Finally, the optimal detection threshold is solved using the bisection method, achieving mathematical precision of the detection rule. The performance of the method is verified through systematic simulation: simulation parameters covering multiple dimensions such as sensor characteristics, clutter distribution, and threat level are set; a comparison scheme is designed; multiple performance curves such as SAA-AFROC and ROC are generated and labeled with high-threat signal-specific data; the influence trend of key parameters such as maximum tolerance distance and false positive threshold on performance is analyzed; finally, through curve comparison and parameter sensitivity analysis, the comprehensive advantages of the proposed method in terms of high-threat signal detection accuracy, parameter estimation precision, and dynamic adaptability are quantitatively verified.
[0099] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their likenesses.
[0100] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.
Claims
1. A method for estimating optimal signal parameter allocation in cluttered environments, characterized in that, Includes the following steps: S1. Construct a multi-signal joint detection and parameter estimation model under multi-sensor clutter environment; S2. Based on the idea of optimal allocation, an improved utility function is designed. By adding a virtual target, the allocation problem is transformed, and a one-to-one matching between the real signal and the estimated value is performed. S3. Establish a constrained optimization model using the SAA-AFROC curve as the performance standard, and calculate the multi-sensor measurement likelihood function under the assumptions of no signal and the existence of real signal to provide data for the model; S4. Derive the optimal estimation rule based on the improved utility function, then substitute it into the model, and obtain the optimal detection rule through model transformation and Lagrange function solution. S5. Set simulation parameters and verify the detection and estimation performance of the proposed method by comparing multiple performance curves and analyzing the influence of parameters.
2. The optimal signal parameter allocation estimation method for clutter environments according to claim 1, characterized in that: S1 involves a joint detection and parameter estimation task with an unknown number of signals processed collaboratively by multiple sensors. Two hypotheses are defined to correspond to scenarios with no signal and scenarios with a real signal, respectively. Let y = [y1, y2, ..., y K [ ] represents the observation data from K sensors, where y K Let be the observation vector of the k-th sensor. Under the no-signal assumption, all measurements originate from clutter. The number of clutter particles follows a known probability distribution, and the location of the clutter particles also follows a preset probability distribution. The multi-sensor measurement likelihood function under the no-signal assumption is: In the formula, p(y|nosignal) represents the conditional probability density function of the observed data y under the no-signal assumption, and y represents the multi-sensor observation data vector. Let ∫ represent the product of the likelihood functions for all K sensors. c This represents the integration operator for the clutter measurement c, pcenter(c) represents the probability density function of the clutter measurement, and p(y) represents the integral of the clutter measurement c. k |c) Given the clutter measurement c and the observation data y of the k-th sensor. k The conditional probability density function; Under the assumption of a real signal, the measurements include measurements derived from the real signal and clutter measurements. The probability distribution characteristics of the clutter are consistent with the no-signal assumption. Measurements derived from the real signal are generated through a mapping relationship. The likelihood function of multi-sensor measurements under the assumption of a real signal is: p(y|signal)=∑ E P(E)·p(y|E), In the formula, p(y|signal) represents the conditional probability density function of the observed data y under the assumption of the existence of a real signal, P(E) represents the probability of the joint event E occurring, E represents the combination of the real signal and clutter observed by different sensors, and p(y|E) represents the conditional probability density function of the observed data y given the joint event E. The noise of each sensor is independent of each other and is also independent of the real signal and clutter.
3. The optimal signal parameter allocation estimation method for clutter environments according to claim 2, characterized in that: In step S1, unknown signal parameters and their estimated values are distinguished. The unknown signal parameters include the number of real signals and the location information of each real signal. The estimated values of the unknown signal parameters include the estimated number of signals and the location information of each estimated signal. For high-threat signals, their threat level attributes are marked in the parameter record.
4. The optimal signal parameter allocation estimation method for clutter environments according to claim 1, characterized in that: In S2, the specific process of designing the decision-oriented utility function is as follows: the utility function is constructed as a function simulating a reward system, providing cumulative positive incentives for correct detection and accurate estimation behaviors, treating a single detection task as an investment, and correct decisions as corresponding benefits; through a task sensitivity scoring method, combined with signal threat level attributes, the scoring weights are set, and the threat level-weighted utility function is implemented as follows: In the formula, Let represent the utility function value, and s represent the set of actual signal locations. Indicates the estimated signal location combination, α i β represents the matching weight of the i-th signal. i Let σ represent the estimated weight of the i-th signal, and let σ represent the position estimation accuracy coefficient.
5. The optimal signal parameter allocation estimation method for clutter environments according to claim 4, characterized in that: In S2, the specific process of constructing the optimal signal allocation method based on graph neural networks is as follows: The real target location and the suspicious region output by the model are used as two types of nodes in a bipartite graph to construct a bipartite graph model, transforming the matching problem between the real target and the suspicious region into an optimal bipartite graph matching problem; the bipartite graph is processed by a graph neural network algorithm, and the optimal matching scheme of the bipartite graph is solved by learning the feature association between the real target and the suspicious region. The graph neural network bipartite graph matching cost function is: In the formula, C ij w represents the matching cost between the real signal i and the estimated signal j. p w represents positional similarity. s The semantic similarity weight is represented by N(), which represents the neighborhood set of a node. The optimal matching scheme ensures a one-to-one correspondence, that is, a real target is matched with at most one suspicious region, and a suspicious region is assigned at most one real target. The detection confidence and parameter estimation value are positively reinforced when a suspicious region is successfully matched.
6. The optimal signal parameter allocation estimation method for clutter environments according to claim 5, characterized in that: In step S2, the specific process of dynamically generating virtual suspicious areas is as follows: Real-time analysis of the quantity matching relationship and matching competition between real targets and suspicious areas; when there is a discrepancy between the number of suspicious reports and the number of real signals, the virtual suspicious area generation process is initiated; the generation of virtual suspicious areas aims to fill gaps in the matching cost matrix and optimize the overall matching cost. Virtual suspicious areas are dynamically generated in areas lacking suspicious targets and not interfering with the matching of real targets, used to absorb excess false positive suspicious reports or alleviate matching competition. The virtual suspicious area generation optimization model is as follows: In the formula, v represents the location of the virtual suspicious area, and γ j Let η represent the attraction coefficient of the j-th estimated signal. j This represents the competition suppression coefficient of the j-th estimated signal. This represents the competition inhibition term. for 7. The optimal signal parameter allocation estimation method for clutter environments according to claim 1, characterized in that: In S3, the constrained optimization model is constructed as follows: based on the utility function designed in S2, the average posterior estimated utility is defined, and the signal detection score is obtained by combining the decision function and the measurement probability distribution; the constraint condition is set that the probability of at least one false positive event occurring in a no-signal scenario does not exceed a preset threshold; the constrained optimization model aims to maximize the signal detection score while satisfying the above false positive probability constraint, and the constrained optimization model is as follows: In the formula, τ represents the decision threshold, δ(τ,y) represents the decision function, α represents the false positive probability threshold, and ∫ y This represents the summation of all possible observations.
8. The optimal signal parameter allocation estimation method for clutter environments according to claim 7, characterized in that: In S3, the calculation of the multi-sensor measurement likelihood function is divided into two scenarios: In the absence of signal, the multi-sensor measurement likelihood function is obtained by multiplying the probability distribution of clutter number and probability density of clutter position of each sensor; In the presence of real signal, based on the total probability formula, the feasible joint events are divided by the joint probability data association algorithm, the occurrence probability of each feasible joint event and the measurement likelihood function under the corresponding conditions are calculated, and finally the multi-sensor measurement likelihood function is obtained by summing.
9. The optimal signal parameter allocation estimation method for clutter environments according to claim 1, characterized in that: In S4, the derivation process of the optimal estimation rule is as follows: determine the core indicators of the estimation parameters, including the estimation accuracy of the correlation between the number of signals, location and threat level, and clarify the correlation between the core indicators and the real signal parameters and decision functions; With the objective of maximizing the average posterior estimation utility based on the S2 utility function, the optimal estimation rule is derived by combining the measurement probability distribution and the prior probability distribution of the signal parameters, and is implemented as follows: In the formula, Let M represent the set of optimal estimated signal locations, where M represents the optimal location of all estimated signals, and w represents the number of signals. i Let v represent the prior weight of the i-th signal. i This represents the likelihood weight of the i-th signal. This represents the prior probability distribution of the estimated signal.
10. The optimal signal parameter allocation estimation method for clutter environments according to claim 9, characterized in that: In S4, the process of solving the optimal detection rule includes: substituting the derived optimal estimation rule into the constrained optimization model and defining a constant term to simplify the model expression; transforming the original constrained optimization model into a more easily solvable form through equivalent transformation; introducing relaxation factors and Lagrange multipliers to construct a generalized Lagrange multiplier; searching for parameter values that satisfy the preset error accuracy through the bisection method, and finally solving to obtain the optimal detection rule.