A method for detecting and tracking weak multi-target targets in complex maneuvers under range ambiguity

Abstract

This invention pertains to sensor data processing methods, specifically a method for detecting and tracking complex maneuvering weak multi-target targets under ranging ambiguity. The method addresses the prominent challenges of target motion model mismatch and the coupling of target maneuvering and distance measurement ambiguity when detecting and tracking complex maneuvering weak targets. It achieves coarse detection of weak multi-target targets through sparse representation for noise reduction. Furthermore, by introducing target maneuvering variables into the target state under a δ-GLMB filter, constructing a pulse interval incremental tracking model, and designing a multi-target ambiguity likelihood function, it achieves precise tracking of complex maneuvering weak multi-target targets under ranging ambiguity. This overcomes the limitations of existing PHD filtering methods and has strong engineering application value and promising prospects for widespread application.

Description

Technical Field

[0001] This invention pertains to sensor data processing methods, specifically to a method for detecting and tracking weak multi-targets in complex maneuvers under ranging ambiguity. Background Technology

[0002] Detection and tracking of maneuvering, weak targets is a prominent challenge in target detection. Low signal-to-noise ratios lead to low detection probabilities, making targets easily lost, and multi-target correlation is complex. Lowering the detection threshold to improve the probability results in a surge in false alarm rates, causing an exponential increase in the complexity of correlation algorithms. Probabilistic hypothesis density (PHD) filtering based on random finite sets is widely used in multi-target tracking due to its advantages, such as eliminating the need for data correlation, significantly reducing computational complexity, and adapting to dense clutter environments.

[0003] In existing technologies, PHD filtering-based methods have certain advantages in multi-target tracking in low signal-to-noise ratio, dense clutter environments. However, when sensors detect and track weak, maneuvering targets, the limitations of this method become apparent: firstly, it relies on a pre-defined target motion model, which is difficult to match with the complex maneuvering trajectories of weak targets, easily causing model mismatch and leading to decreased tracking accuracy; secondly, to obtain the maximum detection range, sensors typically employ a high pulse repetition frequency operating mode, resulting in fuzzy distance measurements, which, coupled with target maneuvering, further exacerbates the difficulty of detecting and tracking weak, multi-target targets. These are the shortcomings of existing technologies.

[0004] In view of this, it is very necessary to provide a method and system for detecting and tracking weak multi-targets in complex maneuvers under ranging ambiguity, so as to solve the above-mentioned defects in the prior art. Summary of the Invention

[0005] The purpose of this invention is to address the two major technical shortcomings of existing PHD filtering techniques in handling complex and weak multi-target detection, namely, the mismatch between the actual target motion model and the coupling of target maneuverability and distance measurement ambiguity. This invention provides a method and system for detecting and tracking complex and weak multi-targets under range measurement ambiguity, thereby solving the aforementioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for detecting and tracking weak multi-target targets under complex maneuvers with ranging ambiguity includes the following steps: Step S1, the initialization step of the δ-GLMB filter, in which: Initialize the δ-GLMB filter and particles based on prior information; Construct a pulse interval increment tracking model based on the Markov criterion; Step S2, the step of acquiring multi-target fuzzy measurements, in which: Acquire raw 3D fuzzy measurement data; Amplitude calculations are performed on the original sensor 3D fuzzy measurement data to generate a distance-Doppler-azimuth 3D energy distribution map; Step S3, the weak multi-target coarse detection step, in which: The range-Doppler-azimuth three-dimensional energy distribution map is decomposed into sub-measurements. A sparse matrix and an observation matrix are constructed based on the characteristics of the sensor's transmitted signals, and the sub-measurements are sparsely represented. The subspace tracking algorithm is used to extract coarse target measurement data; Step S4, the step of maneuvering multi-target fine tracking, in which: Based on the particle's state vector from the previous moment and the pulse interval increment tracking model, predict the particle's state vector at the current moment. Generate a new set of particles for searching new targets; Construct a multi-target fuzzy measurement likelihood function, and based on the coarsely detected target measurement data, update the weights of all particles at the current time under the δ-GLMB filtering framework; The particle set is resampled, and cluster analysis is used to extract the precise estimated state of each target; Step S5, the steps for starting and associating a track, in which: The intuitive track initiation method is used to accurately estimate the state of each target and initiate the track. The nearest neighbor method is used to accurately estimate the state of each target and then associate the track. Generate multi-target trajectory information and output precise tracking results for maneuvering weak multi-target targets; Step S6, the step of closing the loop for weak target detection and tracking, in which: Repeat steps S2 to S5 until the sensor is turned off.

[0007] Preferably, step S1 specifically includes: Step S11, initialize the variables required for the δ-GLMB filter: the number of particles required to initialize a single target is... The number of particles searching for new targets is The total number of fuzzy measurement data extracted at time k is The total number of targets estimated at time k is The total number of particles used in the δ-GLMB filter at time k is ,in ,initialization , ; Step S12, initialize the state vector of the particle: for any particle index Randomly select pulse interval increments from the set of pulse interval increments. Target location information is generated uniformly from the possible location space of the target. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. Randomly select pulse intervals from the set of possible target pulse intervals. The initial state vector of the particle is: The initial weights of the particles are: ; Step S13: Construct a pulse interval increment tracking model based on the Markov criterion, with the following transition matrix: .

[0008] Preferably, step S2 specifically includes: Step S21: Using three pulse repetition frequencies alternately, the original three-dimensional fuzzy measurement of the target at time k is obtained. , is represented as: , in, Indicates the k-th time. Fuzzy distance measurement of a target This represents the Doppler measurement of the m-th target at time k. This represents the azimuth angle measurement of the m-th target at time k. This represents the number of measurements detected at time k.

[0009] Step S22, process sequentially From the original 3D fuzzy measurement data, all original 3D fuzzy measurement data falling within the influence range of the current target are selected and projected onto a 3D discretized mesh to generate a range-Doppler-azimuth 3D energy distribution map of the current target. : , in, Indicates the number of fuzzy distance measurement units. Indicates the number of Doppler measurement units. Indicates the number of azimuth measurement units. This indicates that at time k, in the distance-Doppler-azimuth three-dimensional energy map, it is located in the cell. The measured value of the complex signal strength at the location.

[0010] Preferably, in the range-Doppler-azimuth three-dimensional energy distribution map generated in step S22, the element located in the cell... Complex signal strength measurement at the location : The value is determined by the unit. Whether it is affected by the echo of the current target can be divided into two cases: , in, It is Gaussian white noise. Let the energy diffusion kernel function be the target echo. Let be the state vector of the m-th target at time k. Let k be the fuzzy distance parameter at time k. Let m be the complex amplitude of the m-th target. , A cell in the distance-Doppler-azimuth energy map representing the current target. The situation affected by the target echo.

[0011] Preferably, step S3 specifically includes: Step S31, initialize the target total number ; The range-Doppler-azimuth three-dimensional energy distribution map is decomposed along the azimuth dimension. For any unit in the azimuth dimension, the index... Generating sub-measures: ; The distance-Doppler-azimuth three-dimensional energy distribution map is decomposed into Height measurement.

[0012] Step S32: Construct a sparse matrix based on the characteristics of the sensor's transmitted signal. and observation matrix ; Step S33, for the index of any unit in the azimuth dimension Sub-measurement Convert to column vectors in column-major order And perform sparse representation on it to obtain sparse vectors; Step S34: Construct the target coarse detection threshold : , in, SNR is the target signal-to-noise ratio, which is an intermediate variable. If the maximum value in the sparse vector is less than the target coarse detection threshold This indicates that the current sub-quantum measurement If no target is detected, return to step S2; if the maximum value in the projected vector is greater than or equal to the target coarse detection threshold. This indicates that the sub-quantity measurement The target was detected, and step S35 was executed; Step S35, target total number Increase by 1, that is ; The subspace pursuit algorithm is used to find the solution that minimizes the following expression. : ; turn up Find the index of the maximum value in the range and calculate the fuzzy distance measurement of the target corresponding to that index. and Doppler measurement ; Indexed by sub-measurement azimuth dimension Calculate azimuth measurement ; By combining fuzzy distance measurements, Doppler measurements, and azimuth measurements, effective fuzzy target measurement data can be extracted from noisy fuzzy measurement data. This serves as the output of coarse target measurement data.

[0013] Total number of targets Assign to ,Right now At this time, if If no target is detected by coarse detection at the current moment, return to step S2 to obtain the original 3D fuzzy measurement data for the next moment; if Then the coarse detection target measurement data Form a set ,Right now .

[0014] Preferably, step S4 specifically includes: Step S41, Particle set prediction: If the total number of particles at time k-1 in the previous moment If the value is 0, then proceed directly to step S42 to generate a particle set for searching for a new target; If the total number of particles at time k-1 in the previous moment If not zero, then for any particle index Based on the pulse interval increment at time k-1 Pulse Interval Incremental Transfer Matrix And pulse interval increment tracking model, predicting particles Increment of pulse interval at time k And then according to Increment of pulse interval at time ,particle And the target state transition equation, further predicting the current time step. Particle state vector: .

[0015] Step S42, generate a new set of particles for searching new targets: Randomly select pulse interval increments from the set of pulse interval increments. Target location information is randomly generated from the possible location space of the target according to a uniform distribution. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. Randomly select pulse intervals from the set of possible target pulse intervals. ; Generate the state vector of the newborn particle and particle weight ; State vector and weight Combined elements Formation of new particles; The set of all newly formed particles, as the set of newly formed particles .

[0016] Step S43, Particle weight calculation: Constructing a multi-objective fuzzy measurement likelihood function : , in, The probability of target detection. For measurement error, This is new information, used to describe the fuzzy measurement at the current moment. With prediction of fuzzy measurement The differences between them can avoid the problem that the multi-assumption method requires multiple assumptions for distance measurement, which may lead to too many measurements and too much computation. Based on multi-objective fuzzy measurement likelihood function The weights of all particles at time k are calculated using coarse target measurement data and the δ-GLMB filter update equation. , .

[0017] Step S44, Target Number Estimation and Particle Resampling: Calculate the sum of weights for all particles, and round the sum to obtain a precise estimate of the target number. ; like If no target is detected, proceed directly to step S6; if Then, the total number of particles required at the current moment is assigned as the product of the precise estimate of the target number and the number of particles required for a single target, i.e. and for particle sets Resampling is performed to obtain a new set of particles. .

[0018] Step S45, Target State Extraction: Cluster analysis is used to divide the particle set Divided into Each class; The center of each class That is, the first A precise estimate of the target state, ,in, Indicates the first The position of the target at time k. Indicates the first The velocity of the target at time k. Indicates the first The turning rate of a target at time k. Indicates the first A precise estimate of the number of pulse intervals for a target at time k.

[0019] Furthermore, the present invention also provides a complex maneuvering weak multi-target detection and tracking system under ranging ambiguity, comprising: The δ-GLMB filter initialization module contains: Initialize the δ-GLMB filter and particles based on prior information; Construct a pulse interval increment tracking model based on the Markov criterion; The multi-target fuzzy measurement acquisition module includes: Acquire raw 3D fuzzy measurement data; Amplitude calculations are performed on the original three-dimensional fuzzy measurement data to generate a distance-Doppler-azimuth three-dimensional energy distribution map; The weak multi-target coarse detection module includes: The range-Doppler-azimuth three-dimensional energy distribution map is decomposed into sub-measurements. Based on the characteristics of the sensor's transmitted signals, a sparse matrix and an observation matrix are constructed, and the sub-measurements are sparsely represented. The subspace tracking algorithm is used to extract coarse target measurement data; The maneuvering multi-target precision tracking module contains: Based on the particle's state vector from the previous moment and the pulse interval increment tracking model, predict the particle's state vector at the current moment. Generate a new set of particles for searching new targets; Construct a multi-target fuzzy measurement likelihood function, and based on the coarsely detected target measurement data, update the weights of all particles at the current time under the δ-GLMB filtering framework; The particle set is resampled, and cluster analysis is used to extract the precise estimated state of each target; The track initiation and track association module contains: The intuitive track initiation method is used to accurately estimate the state of each target and initiate the track. The nearest neighbor method is used to accurately estimate the state of each target and then associate the track. Generate multi-target trajectory information and output precise tracking results for maneuvering weak multi-target targets; The weak target detection and tracking closed-loop module includes: Repeat the work performed by the multi-target fuzzy measurement acquisition module, the track initiation module, and the track association module until shutdown.

[0020] Preferably, the δ-GLMB filter initialization module specifically includes: Initialize the variables required for the δ-GLMB filter: the number of particles required to initialize a single target is... The number of particles searching for new targets is The total number of fuzzy measurement data extracted at time k is The total number of targets estimated at time k is The total number of particles used in the δ-GLMB filter at time k is ,in ,initialization , ; Initialize the state vector of the particle: for any particle index Randomly select pulse interval increments from the set of pulse interval increments. Target location information is generated uniformly from the possible location space of the target. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. The number of pulse intervals is randomly selected from the set of possible pulse intervals for the target. The initial state vector of the particle is: The initial weights of the particles are: ; A pulse interval increment tracking model is constructed based on the Markov criterion, and its transition matrix is: .

[0021] Preferably, the multi-target fuzzy measurement acquisition module specifically includes: By employing three pulse repetition frequencies alternating, the original three-dimensional fuzzy measurement of the target at time k is obtained. , is represented as: , in, Indicates the k-th time. Fuzzy distance measurement of a target This represents the Doppler measurement of the m-th target at time k. This represents the azimuth angle measurement of the m-th target at time k. This represents the number of measurements detected at time k.

[0022] Process in sequence From the original 3D fuzzy measurement data, all original 3D fuzzy measurement data falling within the influence range of the current target are selected and projected onto a 3D discretized mesh to generate a range-Doppler-azimuth 3D energy distribution map of the current target. : , in, Indicates the number of fuzzy distance measurement units. Indicates the number of Doppler measurement units. Indicates the number of azimuth measurement units. This indicates that at time k, in the distance-Doppler-azimuth three-dimensional energy map, it is located in the cell. The measured value of the complex signal strength at the location.

[0023] Preferably, in the range-Doppler-azimuth three-dimensional energy distribution map of the multi-target fuzzy measurement acquisition module, the element located in the cell... Complex signal strength measurement at the location : The value is determined by the unit. Whether it is affected by the echo of the current target can be divided into two cases: , in, It is Gaussian white noise. Let the energy diffusion kernel function be the target echo. Let be the state vector of the m-th target at time k. Let be the fuzzy distance parameter at time k. Let m be the complex amplitude of the m-th target. , A cell in the distance-Doppler-azimuth energy map representing the current target. The situation affected by the target echo.

[0024] Preferably, the weak multi-target coarse detection module specifically includes: Initialize the total number of targets ; The range-Doppler-azimuth three-dimensional energy distribution map is decomposed along the azimuth dimension. For any unit in the azimuth dimension, the index... Generating sub-measures: ; The distance-Doppler-azimuth three-dimensional energy distribution map is decomposed into Height measurement.

[0025] Based on the characteristics of the sensor's transmitted signals, a sparse matrix is ​​constructed. and observation matrix ; For any unit in the azimuth dimension, the index Sub-measurement Convert to column vectors in column-major order And perform sparse representation on the column vector to obtain a sparse vector; Construct a coarse detection threshold for the target : , in, SNR is the target signal-to-noise ratio, which is an intermediate variable. If the maximum value in the sparse vector is less than the target coarse detection threshold This indicates that the current sub-quantum measurement If no target is detected, return to the multi-target fuzzy measurement acquisition module; if the maximum value in the projected vector is greater than or equal to the target coarse detection threshold. This indicates that the sub-quantity measurement If a target is detected, the total number of targets will be... Increase by 1, that is ; The subspace pursuit algorithm is used to find the solution that minimizes the following expression. : ; turn up Find the index of the maximum value in the range and calculate the fuzzy distance measurement of the target corresponding to that index. and Doppler measurement ; Indexed by sub-measurement azimuth dimension Calculate azimuth measurement ; By combining fuzzy distance measurements, Doppler measurements, and azimuth measurements, effective fuzzy target measurement data can be extracted from noisy fuzzy measurement data. This serves as the output of coarse target measurement data.

[0026] Total number of targets Assign to ,Right now At this time, if If no target is detected by coarse detection at the current moment, the system returns to the multi-target fuzzy measurement acquisition module to obtain the original 3D fuzzy measurement data for the next moment; if Then the coarse detection target measurement data Form a set ,Right now .

[0027] As a preferred embodiment, the maneuvering multi-target fine tracking module specifically includes: a particle set prediction submodule, a new particle set generation submodule for searching new targets, a particle weight calculation submodule, a target number estimation and particle resampling submodule, and a target state extraction submodule. The particle set prediction submodule specifically includes: If the total number of particles at time k-1 in the previous moment If the value is 0, then directly proceed to the module for generating a new set of particles to search for a new target, and generate a set of particles to search for a new target; If the total number of particles at time k-1 in the previous moment If not zero, then for any particle index Based on the pulse interval increment at time k-1 Pulse Interval Incremental Transfer Matrix And pulse interval increment tracking model, predicting particles Increment of pulse interval at time k And then according to Increment of pulse interval at time ,particle And the target state transition equation, further predicting the current time step. Particle state vector: .

[0028] The module for generating a new set of particles to search for new targets specifically includes: Randomly select pulse interval increments from the set of pulse interval increments. Target location information is randomly generated from the possible location space of the target according to a uniform distribution. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. Randomly select pulse intervals from the set of possible target pulse intervals. ; Generate the state vector of the newborn particle and particle weight ; State vector and weight Combined elements Formation of new particles; The set of all newly formed particles, as the set of newly formed particles .

[0029] The aforementioned particle weight calculation submodule specifically includes: Constructing a multi-objective fuzzy measurement likelihood function : , in, The probability of target detection. For measurement error, This is new information, used to describe the fuzzy measurement at the current moment. With prediction of fuzzy measurement The differences between them can avoid the problem that the multi-assumption method requires multiple assumptions for distance measurement, which may lead to too many measurements and too much computation. Based on multi-objective fuzzy measurement likelihood function The weights of all particles at time k are calculated using coarse target measurement data and the δ-GLMB filter update equation. , .

[0030] The target number estimation and particle resampling submodule specifically includes: Calculate the sum of weights for all particles, and round the sum to obtain a precise estimate of the target number. ; like If no target is detected, the weak target detection and tracking closed-loop module will be executed directly; if Then, the total number of particles required at the current moment is assigned as the product of the precise estimate of the target number and the number of particles required for a single target, i.e. and for particle sets Resampling is performed to obtain a new set of particles. .

[0031] The target state extraction submodule specifically includes: Cluster analysis is used to divide the particle set Divided into Each class; The center of each class That is, the first A precise estimate of the target state, ,in, Indicates the first The position of the target at time k. Indicates the first The velocity of the target at time k. Indicates the first The turning rate of a target at time k. Indicates the first A precise estimate of the number of pulse intervals for a target at time k.

[0032] The beneficial effects of this invention are as follows: It achieves coarse detection of weak multi-target targets through a sparse representation method, reconstructing and extracting weak target signals from strong noise and clutter backgrounds, enabling preliminary estimation of the target's existence, number, and state. This significantly reduces the data dimensionality and false alarm rate in subsequent processing, overcoming the problem of PHD filtering failure in traditional methods under low detection probabilities. Furthermore, by introducing the target's angular velocity variable into the target state under the δ-GLMB filter, it can directly describe the target's complex maneuvers, avoiding the problem of mismatch in the preset model. Finally, by introducing the pulse interval number variable into the target state... A pulse interval incremental tracking model is constructed, transforming the range unambiguity problem into an estimation problem of the dynamic changes in the pulse interval number, which is solved synchronously during the filtering process. Specifically, by generating a range-Doppler-azimuth three-dimensional energy distribution map, the original ambiguous measurement data is organized into three-dimensional structured information. Through sparse representation, weak target measurement information is extracted from a strong noise background, providing more robust input information for target tracking. An improved δ-GLMB filter enables the tracking of multiple weak targets in situations where range ambiguity and target maneuvering coexist, avoiding the coupling problem between range measurement ambiguity and target maneuvering. Overall, the method of this invention not only effectively reduces false alarms but also achieves precise tracking of complex maneuvering weak multi-target targets under range ambiguity conditions, overcoming the limitations of existing PHD filtering methods.

[0033] Therefore, it is evident that the present invention has outstanding substantive features and significant progress compared with the prior art, and the beneficial effects of its implementation are also obvious. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0035] Figure 1 This is a flowchart of the method for detecting and tracking weak multi-targets under complex maneuvers with ranging ambiguity provided by the present invention.

[0036] Figure 2 These are the actual flight paths of the three maneuvering targets provided by this invention.

[0037] Figure 3 This is a measurement at a certain moment provided by the present invention.

[0038] Figure 4 This is the coarse detection result of weak multi-target detection at a certain moment provided by the present invention.

[0039] Figure 5 This invention provides a precise estimation effect on the number of targets.

[0040] Figure 6 This invention provides a sophisticated tracking effect for complex maneuvers and weak multi-target targets.

[0041] Figure 7 This is a schematic diagram of the principle of the complex maneuvering weak multi-target detection and tracking system under ranging ambiguity provided by the present invention.

[0042] Among them, 1-δ-GLMB filter initialization module, 2-multi-target fuzzy measurement acquisition module, 3-weak multi-target coarse detection module, 4-maneuvering multi-target fine tracking module, 5-track initiation and track association module, and 6-weak target detection and tracking closed-loop module. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following implementation methods.

[0044] Example 1: like Figure 1 As shown in the figure, this embodiment provides a method for detecting and tracking weak multi-targets in complex maneuvers under ranging ambiguity, such as... Figure 2 The example shown demonstrates the detection and tracking of three complex maneuvering moving targets in a multi-target tracking scenario. The target signal-to-noise ratio is 6dB. Figure 3 As shown, the target is submerged in noise, falling into the category of weak targets, and distance measurement is also ambiguous. The method includes the following steps: Step S1, the initialization step of the δ-GLMB filter, in which: Initialize the δ-GLMB filter and particles based on prior information; Construct a pulse interval increment tracking model based on the Markov criterion; Step S1 specifically includes: Step S11, initialize the variables required for the δ-GLMB filter: the number of particles required to initialize a single target is... The number of particles searching for new targets is The total number of fuzzy measurement data extracted at time k is The total number of targets estimated at time k is The total number of particles used in the δ-GLMB filter at time k is ,in ,initialization , ; Step S12, initialize the state vector of the particle: for any particle index Randomly select pulse interval increments from the set of pulse interval increments. Target location information is generated uniformly from the possible location space of the target. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. The number of pulse intervals is randomly selected from the set of possible pulse intervals for the target. The initial state vector of the particle is: The initial weights of the particles are: ; It should be noted that this invention describes complex target maneuvers by adding the target's angular velocity variable to the state vector; describes the unambiguous interval of the target distance by adding the pulse interval number variable; and describes the change in the target's pulse interval number by adding the pulse interval number increment. Step S13: Construct a pulse interval increment tracking model based on the Markov criterion, with the following transition matrix:

[0045] It should be noted that the construction of the pulse interval number incremental tracking model can transform the problem of resolving distance ambiguity into the problem of estimating the number of pulse intervals during the δ-GLMB filtering process.

[0046] Step S2, the step of acquiring multi-target fuzzy measurements, in which: Acquire raw 3D fuzzy measurement data; Amplitude calculations are performed on the original three-dimensional fuzzy measurement data to generate a distance-Doppler-azimuth three-dimensional energy distribution map; Step S2 specifically includes: Step S21: The sensor uses three pulse repetition frequencies to work alternately to acquire the original three-dimensional fuzzy measurement of the target at time k. , is represented as: , in, Indicates the k-th time. Fuzzy distance measurement of a target This represents the Doppler measurement of the m-th target at time k. This represents the azimuth angle measurement of the m-th target at time k. This represents the number of measurements detected at time k.

[0047] Step S22, to obtain Each original 3D fuzzy measurement data point is associated with a specific target, assuming that the influence range of a single target is a circular region with a radius of 2 units centered at its location. Based on this assumption, the data is processed sequentially. From the original 3D fuzzy measurement data, all original 3D fuzzy measurement data falling within the influence range of the current target are selected and projected onto a 3D discretized mesh to generate a range-Doppler-azimuth 3D energy distribution map of the current target. : , in, Indicates the number of fuzzy distance measurement units. Indicates the number of Doppler measurement units. Indicates the number of azimuth measurement units. This indicates that at time k, in the distance-Doppler-azimuth three-dimensional energy map, it is located in the cell. The measured value of the complex signal strength at the location.

[0048] In the distance-Doppler-azimuth three-dimensional energy distribution map generated in step S22, the element located in the cell Complex signal strength measurement at the location : The value is determined by the unit. Whether or not the echo from the current target is received can be divided into two cases: , in, It is Gaussian white noise. Let the energy diffusion kernel function be the target echo. Let be the state vector of the m-th target at time k. Let k be the fuzzy distance parameter at time k. Let m be the complex amplitude of the m-th target. The calculation method is as follows: , in, For complex phase factor, For phase.

[0049] A cell in the distance-Doppler-azimuth energy map representing the current target. The specific calculation method for the influence of target echo is as follows: , in, For the first The distance corresponding to each distance unit For the first Doppler corresponding to each Doppler unit For the first The azimuth angle corresponding to each azimuth angle unit. The variance parameter is the distance dimension. The variance parameter along the Doppler dimension. The variance parameter is the azimuth dimension. Let be the loss constant in the distance dimension. Let be the loss constant in the Doppler dimension. This is the loss constant in the azimuth dimension.

[0050] Step S3, the weak multi-target coarse detection step, in which: The range-Doppler-azimuth three-dimensional energy distribution map is decomposed into sub-measurements. Based on the characteristics of the sensor's transmitted signals, a sparse matrix and an observation matrix are constructed, and the sub-measurements are sparsely represented. Subspace tracking algorithms are used to extract coarse target measurement data, such as Figure 4 As shown; Step S3 specifically includes: Step S31, initialize the target total number ; The range-Doppler-azimuth three-dimensional energy distribution map is decomposed along the azimuth dimension. For any unit in the azimuth dimension, the index... Generating sub-measures: ; The distance-Doppler-azimuth three-dimensional energy distribution map is decomposed into Height measurement.

[0051] Step S32: Construct a sparse matrix based on the characteristics of the sensor's transmitted signal. and observation matrix ; Step S33, for the index of any unit in the azimuth dimension Sub-measurement Convert to column vectors in column-major order And perform sparse representation on the column vector to obtain a sparse vector.

[0052] Step S34: Construct the target coarse detection threshold : , in, SNR is the target signal-to-noise ratio, which is an intermediate variable. If the maximum value in the sparse vector is less than the target coarse detection threshold This indicates that the current sub-quantum measurement If no target is detected, return to step S2; if the maximum value in the projected vector is greater than or equal to the target coarse detection threshold. This indicates that the sub-quantity measurement The target was detected, and step S35 was executed; Step S35, target total number Increase by 1, that is ; The subspace pursuit algorithm is used to find the solution that minimizes the following expression. : ; turn up Find the index of the maximum value in the range and calculate the fuzzy distance measurement of the target corresponding to that index. and Doppler measurement ; Indexed by sub-measurement azimuth dimension Calculate azimuth measurement ; By combining fuzzy distance measurements, Doppler measurements, and azimuth measurements, effective fuzzy target measurement data can be extracted from noisy fuzzy measurement data. This serves as the output of coarse target measurement data.

[0053] Total number of targets Assign to ,Right now At this time, if If no target is detected by coarse detection at the current moment, return to step S2 to obtain the original 3D fuzzy measurement data for the next moment; if Then the coarse detection target measurement data Form a set ,Right now .

[0054] Step S4, the step of maneuvering multi-target fine tracking, in which: Based on the particle's state vector from the previous moment and the pulse interval increment tracking model, predict the particle's state vector at the current moment. Generate a new set of particles for searching new targets; Construct a multi-target fuzzy measurement likelihood function, and based on the coarsely detected target measurement data, update the weights of all particles at the current time under the δ-GLMB filtering framework; The particle set is resampled, and cluster analysis is used to extract the precise estimated state of each target; Step S4 specifically includes: Step S41, Particle set prediction: If the total number of particles at time k-1 in the previous moment If the value is 0, then proceed directly to step S42 to generate a particle set for searching for a new target; If the total number of particles at time k-1 in the previous moment If not zero, then for any particle index Based on the pulse interval increment at time k-1 Pulse Interval Incremental Transfer Matrix And pulse interval increment tracking model, predicting particles Increment of pulse interval at time k And then according to Increment of pulse interval at time ,particle And the target state transition equation, further predicting the current time step. Particle state vector: .

[0055] Step S42, generate a new set of particles for searching new targets: Randomly select pulse interval increments from the set of pulse interval increments. Target location information is randomly generated from the possible location space of the target according to a uniform distribution. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. Randomly select pulse intervals from the set of possible target pulse intervals. ; Generate the state vector of the newborn particle and particle weight ; State vector and weight Combined elements Formation of new particles; The set of all newly formed particles, as the set of newly formed particles .

[0056] Step S43, Particle weight calculation: Constructing a multi-objective fuzzy measurement likelihood function : , in, The probability of target detection. For sensor measurement error, This is new information, used to describe the fuzzy measurement at the current moment. With prediction of fuzzy measurement The differences between them can avoid the problem that the multi-assumption method requires multiple assumptions for distance measurement, which may lead to too many measurements and too much computation. Based on multi-objective fuzzy measurement likelihood function The weights of all particles at time k are calculated using coarse target measurement data and the δ-GLMB filter update equation. , .

[0057] Step S44, Target Number Estimation and Particle Resampling: Calculate the sum of weights for all particles, and round the sum to obtain a precise estimate of the target number. ; like If no target is detected, proceed directly to step S6; if Then, the total number of particles required at the current moment is assigned as the product of the precise estimate of the target number and the number of particles required for a single target, i.e. and for particle sets Resampling is performed to obtain a new set of particles. .

[0058] Step S45, Target State Extraction: Cluster analysis is used to divide the particle set Divided into Each class; The center of each class That is, the first A precise estimate of the target state, ,in, Indicates the first The position of the target at time k. Indicates the first The velocity of the target at time k. Indicates the first The turning rate of a target at time k. Indicates the first A precise estimate of the number of pulse intervals for a target at time k.

[0059] After the steps of maneuvering multi-target fine tracking, the result is as follows: Figure 5 As shown, the asterisk "*" represents the actual number of targets, and the circle "o" represents the estimated number of targets. Target loss occurred only a few times, successfully achieving effective detection and tracking of complex, maneuvering, and weak targets. The multi-target precision tracking effect is as follows: Figure 6 As shown.

[0060] Step S5, the steps for starting and associating a track, in which: The intuitive track initiation method is used to accurately estimate the state of each target and initiate the track. The nearest neighbor method is used to accurately estimate the state of each target and then associate the track. Generate multi-target trajectory information and output precise tracking results for maneuvering weak multi-target targets; Step S6, the step of closing the loop for weak target detection and tracking, in which: Repeat steps S2 to S5 until the sensor is turned off.

[0061] Example 2: like Figure 7 As shown in the figure, this embodiment provides a complex maneuvering weak multi-target detection and tracking system under ranging ambiguity, including: δ-GLMB filter initialization module 1, in which: Initialize the δ-GLMB filter and particles based on prior information; Construct a pulse interval increment tracking model based on the Markov criterion; The aforementioned δ-GLMB filter initialization module 1 specifically includes: Initialize the variables required for the δ-GLMB filter: the number of particles required to initialize a single target is... The number of particles searching for new targets is The total number of fuzzy measurement data extracted at time k is The total number of targets estimated at time k is The total number of particles used in the δ-GLMB filter at time k is ,in ,initialization , ; Initialize the state vector of the particle: for any particle index Randomly select pulse interval increments from the set of pulse interval increments. Target location information is generated uniformly from the possible location space of the target. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. The number of pulse intervals is randomly selected from the set of possible pulse intervals for the target. The initial state vector of the particle is: The initial weights of the particles are: ; A pulse interval increment tracking model is constructed based on the Markov criterion, and its transition matrix is: .

[0062] Multi-target fuzzy measurement acquisition module 2, in which: Acquire raw 3D fuzzy measurement data; Amplitude calculations are performed on the original three-dimensional fuzzy measurement data to generate a distance-Doppler-azimuth three-dimensional energy distribution map; The multi-target fuzzy measurement acquisition module 2 specifically includes: The sensor operates using three pulse repetition frequencies alternately. The repetition frequency used at the current time k is represented as: , Among them, the function express Divide by The remainder.

[0063] Obtain the target Original 3D fuzzy measurement at time , is represented as: , in, Indicates the k-th time. Fuzzy distance measurement of a target This represents the Doppler measurement of the m-th target at time k. This represents the azimuth angle measurement of the m-th target at time k. This represents the number of measurements detected at time k.

[0064] To obtain The raw 3D fuzzy measurement data of each measurement are associated with each specific target. It is assumed that the influence range of a single target is a circular region with a radius of 2 units, centered at its location. Based on this assumption, the data is processed sequentially. From the original 3D fuzzy measurement data, all original 3D fuzzy measurement data falling within the influence range of the current target are selected and projected onto a 3D discretized mesh to generate a range-Doppler-azimuth 3D energy distribution map of the current target. : , in, Indicates the number of fuzzy distance measurement units. Indicates the number of Doppler measurement units. Indicates the number of azimuth measurement units. This indicates that at time k, in the distance-Doppler-azimuth three-dimensional energy map, it is located in the cell. The measured value of the complex signal strength at the location.

[0065] In the range-Doppler-azimuth three-dimensional energy distribution map of the multi-target fuzzy measurement acquisition module 2, the element located in the cell... Complex signal strength measurement at the location : The value is determined by the unit. Whether it is affected by the echo of the current target can be divided into two cases: , in, It is Gaussian white noise. Let the energy diffusion kernel function be the target echo. Let be the state vector of the m-th target at time k. Let k be the fuzzy distance parameter at time k. Let m be the complex amplitude of the m-th target. The calculation method is as follows: , in, For complex phase factor, For phase.

[0066] A cell in the distance-Doppler-azimuth energy map representing the current target. The specific calculation method for the influence of target echo is as follows: , in, For the first The distance corresponding to each distance unit For the first Doppler corresponding to each Doppler unit For the first The azimuth angle corresponding to each azimuth angle unit. The variance parameter is the distance dimension. The variance parameter along the Doppler dimension. The variance parameter is the azimuth dimension. Let be the loss constant in the distance dimension. Let be the loss constant in the Doppler dimension. This is the loss constant in the azimuth dimension.

[0067] Weak multi-target coarse detection module 3, in which: The range-Doppler-azimuth three-dimensional energy distribution map is decomposed into sub-measurements. Based on the characteristics of the sensor's transmitted signals, a sparse matrix and an observation matrix are constructed, and the sub-measurements are sparsely represented. The subspace tracking algorithm is used to extract coarse target measurement data; The aforementioned weak multi-target coarse detection module 3 specifically includes: Initialize the total number of targets ; The range-Doppler-azimuth three-dimensional energy distribution map is decomposed along the azimuth dimension. For any unit in the azimuth dimension, the index... Generating sub-measures: ; The distance-Doppler-azimuth three-dimensional energy distribution map is decomposed into Height measurement.

[0068] Based on the characteristics of the sensor's transmitted signals, a sparse matrix is ​​constructed. and observation matrix ; For any unit in the azimuth dimension, the index Sub-measurement Convert to column vectors in column-major order And perform sparse representation on the column vector to obtain a sparse vector.

[0069] Construct a coarse detection threshold for the target : , in, SNR is the target signal-to-noise ratio, which is an intermediate variable. If the maximum value in the sparse vector is less than the target coarse detection threshold This indicates that the current sub-quantum measurement If no target is detected, return to the multi-target fuzzy measurement acquisition module 2; if the maximum value in the projected vector is greater than or equal to the target coarse detection threshold. This indicates that the sub-quantity measurement If a target is detected, the total number of targets will be... Increase by 1, that is : The subspace pursuit algorithm is used to find the solution that minimizes the following expression. : ; turn up Find the index of the maximum value in the range and calculate the fuzzy distance measurement of the target corresponding to that index. and Doppler measurement ; Indexed by sub-measurement azimuth dimension Calculate azimuth measurement ; By combining fuzzy distance measurements, Doppler measurements, and azimuth measurements, effective fuzzy target measurement data can be extracted from noisy fuzzy measurement data. This serves as the output of coarse target measurement data.

[0070] Total number of targets Assign to ,Right now At this time, if If no target is detected by coarse detection at the current moment, the system returns to the multi-target fuzzy measurement acquisition module 2 to obtain the raw 3D fuzzy measurement data for the next moment; if Then the coarse detection target measurement data Form a set ,Right now .

[0071] Maneuvering multi-target precision tracking module 4, in which: Based on the particle's state vector from the previous moment and the pulse interval increment tracking model, predict the particle's state vector at the current moment. Generate a new set of particles for searching new targets; Construct a multi-target fuzzy measurement likelihood function, and based on the coarsely detected target measurement data, update the weights of all particles at the current time under the δ-GLMB filtering framework; The particle set is resampled, and cluster analysis is used to extract the precise estimated state of each target; The aforementioned maneuvering multi-target precision tracking module 4 specifically includes: a particle set prediction submodule, a new particle set generation submodule for searching new targets, a particle weight calculation submodule, a target number estimation and particle resampling submodule, and a target state extraction submodule; The particle set prediction submodule specifically includes: If the total number of particles at time k-1 in the previous moment If the value is 0, then directly proceed to the module for generating a new set of particles to search for a new target, and generate a set of particles to search for a new target; If the total number of particles at time k-1 in the previous moment If not zero, then for any particle index Based on the pulse interval increment at time k-1 Pulse Interval Incremental Transfer Matrix And pulse interval increment tracking model, predicting particles Increment of pulse interval at time k And then according to Increment of pulse interval at time ,particle And the target state transition equation, further predicting the current time step. Particle state vector: .

[0072] The module for generating a new set of particles to search for new targets specifically includes: Randomly select pulse interval increments from the set of pulse interval increments. Target location information is randomly generated from the possible location space of the target according to a uniform distribution. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. Randomly select pulse intervals from the set of possible target pulse intervals. ; Generate the state vector of the newborn particle and particle weight ; State vector and weight Combined elements Formation of new particles; The set of all newly formed particles, as the set of newly formed particles .

[0073] The aforementioned particle weight calculation submodule specifically includes: Constructing a multi-objective fuzzy measurement likelihood function : , in, The probability of target detection. For measurement error, This is new information, used to describe the fuzzy measurement at the current moment. With prediction of fuzzy measurement The differences between them can avoid the problem that the multi-assumption method requires multiple assumptions for distance measurement, which may lead to too many measurements and too much computation. Based on multi-objective fuzzy measurement likelihood function The weights of all particles at time k are calculated using coarse target measurement data and the δ-GLMB filter update equation. , .

[0074] The target number estimation and particle resampling submodule specifically includes: Calculate the sum of weights for all particles, and round the sum to obtain a precise estimate of the target number. ; like If no target is detected, it indicates that no target has been detected, and the system directly enters the weak target detection and tracking closed-loop module 6; if Then, the total number of particles required at the current moment is assigned as the product of the precise estimate of the target number and the number of particles required for a single target, i.e. and for particle sets Resampling is performed to obtain a new set of particles. .

[0075] The target state extraction submodule specifically includes: Cluster analysis is used to divide the particle set Divided into Each class; The center of each class That is, the first A precise estimate of the target state, ,in, Indicates the first The position of the target at time k. Indicates the first The velocity of the target at time k. Indicates the first The turning rate of a target at time k. Indicates the first A precise estimate of the number of pulse intervals for a target at time k.

[0076] Module 5, which includes the track initiation and track association functions, contains: The intuitive track initiation method is used to accurately estimate the state of each target and initiate the track. The nearest neighbor method is used to accurately estimate the state of each target and then associate the track. Generate multi-target trajectory information and output precise tracking results for maneuvering weak multi-target targets; The weak target detection and tracking closed-loop module 6 contains: Repeat the work of the multi-target fuzzy measurement acquisition module to the track initiation and track association modules until the sensor is powered off.

[0077] The above-disclosed embodiments are merely preferred embodiments of the present invention, but the present invention is not limited thereto. Any non-creative variations that can be conceived by those skilled in the art, as well as any improvements and modifications made without departing from the principles of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method for detecting and tracking weak multi-targets in complex maneuvers under ranging ambiguity, characterized in that, Includes the following steps: Step S1, the initialization step of the δ-GLMB filter, in which: Initialize the δ-GLMB filter and particles based on prior information; Construct a pulse interval increment tracking model based on the Markov criterion; Step S2, the step of acquiring multi-target fuzzy measurements, in which: Acquire raw 3D fuzzy measurement data; Amplitude calculations are performed on the original three-dimensional fuzzy measurement data to generate a distance-Doppler-azimuth three-dimensional energy distribution map; Step S3, the weak multi-target coarse detection step, in which: The range-Doppler-azimuth three-dimensional energy distribution map is decomposed into sub-measurements. Based on the characteristics of the sensor's transmitted signals, a sparse matrix and an observation matrix are constructed, and the sub-measurements are sparsely represented. The subspace tracking algorithm is used to extract coarse target measurement data; Step S4, the step of maneuvering multi-target fine tracking, in which: Based on the particle's state vector from the previous moment and the pulse interval increment tracking model, predict the particle's state vector at the current moment. Generate a new set of particles for searching new targets; Construct a multi-target fuzzy measurement likelihood function, and based on the coarsely detected target measurement data, update the weights of all particles at the current time under the δ-GLMB filtering framework; The particle set is resampled, and cluster analysis is used to extract the precise estimated state of each target; Step S5, the steps for starting and associating a track, in which: The trajectory is initiated by accurately estimating the state of each target; The state of each target is precisely estimated and then correlated with the flight path. Generate multi-target trajectory information and output precise tracking results for maneuvering weak multi-target targets; Step S6, the step of closing the loop for weak target detection and tracking, in which: Repeat steps S2 to S5 until the sensor is turned off; Step S1 specifically includes: Step S11, initialize the variables required for the δ-GLMB filter: the number of particles required to initialize a single target is... The number of particles searching for new targets is The total number of fuzzy measurement data extracted at time k is The total number of targets estimated at time k is The total number of particles used in the δ-GLMB filter at time k is ,in ,initialization , ; Step S12, initialize the state vector of the particle: for any particle index The initial state vector of the particle is: ;in, The pulse interval increment is randomly selected from the set of pulse interval increments. To generate target location information uniformly from the possible target location space, To generate target velocity information uniformly from the range of possible target velocities, To generate target angular velocity information uniformly from the range of possible target angular velocities, The number of pulse intervals is randomly selected from the set of possible target pulse intervals; the initial weights of the particles are... ; Step S13: Construct an incremental tracking model for pulse intervals based on the Markov criterion; Step S4 specifically includes: Step S41, Particle set prediction: If the total number of particles at time k-1 in the previous moment If the value is 0, then proceed directly to step S42 to generate a particle set for searching for a new target; If the total number of particles at time k-1 in the previous moment If not zero, then for any particle index Based on the pulse interval increment at time k-1 Pulse Interval Incremental Transfer Matrix And pulse interval increment tracking model, predicting particles Increment of pulse interval at time k And then according to Increment of pulse interval at time ,particle And the target state transition equation, further predicting the current time step. Particle state vector: ; Step S42, generate a new set of particles for searching new targets: Randomly select pulse interval increments from the set of pulse interval increments. Target location information is randomly generated from the possible location space of the target according to a uniform distribution. Target velocity information is generated uniformly from the possible velocity range of the target. Target angular velocity information is generated uniformly from the range of possible target angular velocities. Randomly select pulse intervals from the set of possible target pulse intervals. ; Generate the state vector of the newborn particle and particle weight ; State vector and weight Combined elements Formation of new particles; The set of all newly formed particles, as the set of newly formed particles ; Step S43, Particle weight calculation: Constructing a multi-objective fuzzy measurement likelihood function ; Based on multi-objective fuzzy measurement likelihood function The weights of all particles at time k are calculated using coarse target measurement data and the δ-GLMB filter update equation. , ; Step S44, Target Number Estimation and Particle Resampling: Calculate the sum of weights for all particles, and round the sum to obtain a precise estimate of the target number. ; like If no target is detected, proceed directly to step S6; if Then, the total number of particles required at the current moment is assigned as the product of the precise estimate of the target number and the number of particles required for a single target, i.e. and for particle sets Resampling is performed to obtain a new set of particles. ; Step S45, Target State Extraction: Cluster analysis is used to divide the particle set Divided into Each class; The center of each class That is, the first A precise estimate of the target state, ,in, Indicates the first The position of the target at time k. Indicates the first The velocity of the target at time k. Indicates the first The turning rate of a target at time k. Indicates the first A precise estimate of the pulse interval number of a target at time k; The expression for the likelihood function of the multi-objective fuzzy measurement is as follows: ， in, The probability of target detection. For measurement error, For new information, calculate the fuzzy measurement at the current moment. With prediction of fuzzy measurement The difference between them is obtained; Step S5 includes: The intuitive track initiation method is used to accurately estimate the state of each target and initiate the track. The nearest neighbor method is used to accurately estimate the state of each target and then associate the track. Generate multi-target trajectory information and output precise tracking results for maneuvering weak multi-target targets.

2. The method for detecting and tracking weak multi-targets under complex maneuvers with ranging ambiguity according to claim 1, characterized in that, The pulse interval increment tracking model in step S13 has the following transition matrix: 。 3. The method for detecting and tracking weak multi-targets under complex maneuvers with ranging ambiguity according to claim 1, characterized in that, Step S2 specifically includes: Step S21: The sensor uses three pulse repetition frequencies to work alternately to acquire the original three-dimensional fuzzy measurement of the target at time k. , is represented as: ， in, Indicates the k-th time. Fuzzy distance measurement of a target This represents the Doppler measurement of the m-th target at time k. This represents the azimuth angle measurement of the m-th target at time k. This represents the number of measurements detected at time k; Step S22, process sequentially From the original 3D fuzzy measurement data, all original 3D fuzzy measurement data falling within the influence range of the current target are selected and projected onto a 3D discretized mesh to generate a range-Doppler-azimuth 3D energy distribution map of the current target. : ， in, Indicates the number of fuzzy distance measurement units. Indicates the number of Doppler measurement units. Indicates the number of azimuth measurement units. This indicates that at time k, in the distance-Doppler-azimuth three-dimensional energy map, it is located in the cell. The measured value of the complex signal strength at the location.

4. The method for detecting and tracking weak multi-targets under complex maneuvers with ranging ambiguity according to claim 3, characterized in that, Step S3 specifically includes: Step S31, initialize the target total number ; The range-Doppler-azimuth three-dimensional energy distribution map is decomposed along the azimuth dimension. For any unit in the azimuth dimension, the index... Generating sub-measures: ； The distance-Doppler-azimuth three-dimensional energy distribution map is decomposed into Height measurement; Step S32: Construct a sparse matrix based on the characteristics of the sensor's transmitted signal. and observation matrix ; Step S33, sub-measurement Convert to column vectors in column-major order. , The column vector is sparsely represented to obtain a sparse vector. Step S34: Construct the target coarse detection threshold : ， in, SNR is the target signal-to-noise ratio, which is an intermediate variable. If the maximum value in the sparse vector is less than the target coarse detection threshold This indicates that the current sub-quantum measurement If no target is detected, return to step S2; if the maximum value in the projected vector is greater than or equal to the target coarse detection threshold. This indicates that the sub-quantity measurement The target was detected, and step S35 was executed; Step S35, target total number Increase by 1, that is ; The subspace pursuit algorithm is used to find the solution that minimizes the following expression. : ； turn up Find the index of the maximum value in the range and calculate the fuzzy distance measurement of the target corresponding to that index. and Doppler measurement ; Indexed by sub-measurement azimuth dimension Calculate azimuth measurement ; By combining fuzzy distance measurements, Doppler measurements, and azimuth measurements, effective fuzzy target measurement data can be extracted from noisy fuzzy measurement data. This serves as the output of coarse target measurement data.

5. The method for detecting and tracking weak multi-targets under complex maneuvering conditions with ranging ambiguity according to claim 4, characterized in that, Step S3 further includes: After outputting the coarse detection target measurement data, the total number of targets will be... Assign to ,Right now ; like If no target is detected by coarse detection at the current moment, return to step S2 to obtain the original 3D fuzzy measurement data for the next moment; if Then the coarse detection target measurement data Form a set ,Right now .

6. The method for detecting and tracking weak multi-targets under complex maneuvers with ranging ambiguity according to claim 4, characterized in that, The target coarse detection threshold in step S3 In the calculation formula, intermediate variables The target signal-to-noise ratio (SNR) used ranges from 3 to 10 dB.

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