Track fusion method of incremental updating Gaussian mixture model and multi-state transition filtering

Abstract

The invention discloses a track fusion method for incremental updating of a Gaussian mixture model and multi-state transition filtering, and relates to the technical field of track fusion, and the method comprises the steps: carrying out the preprocessing of observation information of a radar and electronic reconnaissance equipment; obtaining a feature vector of the observation information and performing target category identification to obtain a target category label set; generating an initial track of the observation subset by using a multi-correlation gate and a cost function; identifying track pairs with potential interaction and / or conflicts from the initial track set to form a target track set without intersection and / or interference; based on a plurality of preset state transition models, using the track quality score set and the sensor weight set to obtain a track fusion result; on the premise of considering the real-time performance and the precision, the cross track and the high maneuvering target are efficiently processed based on the range and performance difference of multiple sensors, and key filtering and associated parameters are adaptively adjusted according to the change of the environment and the sensor state, so that the continuous and accurate tracking of the target track information is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of track fusion, and more specifically, to a track fusion method based on an incrementally updated Gaussian mixture model and multi-state transition filtering. Background Art

[0002] In the field of multi-target tracking and situation awareness, in order to obtain accurate target information from various heterogeneous sensors such as radar, optoelectronics, acoustics, and even electronic reconnaissance, the prior art often first performs time synchronization and preliminary calibration to ensure the comparability of the measurement results of different types of sensors under the same reference time axis. This process generally uses a unified clock or an external reference signal to correct the time and frequency of the output data of each device, and reduces the measurement deviation between sensors by means of amplitude compensation, phase correction, etc. when necessary.

[0003] After the preliminary alignment is completed, the traditional scheme will perform threshold determination on the observed values in the data stream of each sensor, and select the points that exceed the detection threshold or have a large signal significance as candidate targets. At the same time, key attributes such as the speed, direction, and distance of the target will also be extracted and encapsulated into the target information in a unified format for subsequent association and fusion processes to call. Subsequently, for the candidate target data output by multiple sensors, the prior art mostly uses fixed or adaptive "range gates" or "angle gates" methods to determine which observation points may correspond to the same target; in terms of association algorithms, common practices include both "nearest neighbor association" and more complex schemes such as "multiple hypothesis tracking" to find a better data matching combination when the number of candidate points is large.

[0004] At the filtering and prediction level, if the target motion is approximately linear or has low maneuverability, the Kalman filter and its improved methods can maintain stable accuracy in short-term prediction; if the target undergoes nonlinear or even large turns, extended Kalman filter, unscented Kalman filter or particle filter are required to update the target state, thereby improving the robustness and accuracy of tracking. Finally, the data of each sensor are usually combined by weighted average or interpolation strategy at the fusion stage, and multi-source heterogeneous observations are integrated through a certain measurement importance to output the final trajectory, and the target category is discriminated or its identity is revised when necessary to provide input for subsequent real-time monitoring and high-level decision-making.

[0005] The prior art of the above track fusion has at least the following problems:

[0006] 1. Data differences and nonlinear calibration problems between multi-source heterogeneous sensors; Due to different application environments and equipment characteristics, various types of sensors often have large differences in range, measurement resolution, noise characteristics and even data update frequency. Most existing technologies can only complete preliminary alignment by linear frequency correction or amplitude and phase compensation, but it is difficult to obtain high-precision mapping in scenarios with complex error distribution and nonlinear distortion of observed signals. If certain differences in resolution or stability are ignored during sensor fusion, it often leads to obvious jitter or inconsistency in the target trajectory. Especially when electronic reconnaissance equipment and heterogeneous sources such as radar are measuring simultaneously, how to make full use of the measurement dimensions that each is good at and fuse different noise characteristics is still a technical bottleneck faced by existing solutions.

[0007] 2. Bottlenecks in data association and real-time processing in high-density target environments: When there are a large number of targets in the observation scene at the same time (for example, when the number reaches dozens or even hundreds), the traditional threshold judgment and multiple hypothesis association algorithms often have a sharp increase in computational complexity, and may even be difficult to complete high-precision data matching in a short period of time; coupled with the fact that the movement trajectories of multiple targets are close to each other or frequently cross each other, simple nearest neighbor or fixed shape gates are often prone to association errors or missed detections in large-scale environments. In addition, in the subsequent filtering and prediction stages, if the algorithm fails to update the interaction between targets in real time and dynamically adjust the filtering parameters, it may also cause significant deviations in the final fusion trajectory, thereby reducing the system's monitoring efficiency for high-density target clusters.

[0008] Based on the above problems, how to efficiently complete federal or centralized fusion in the complex measurement data of "multi-source heterogeneous sensors" and at the same time maintain the accuracy and real-time of association matching under "high-density targets" has become an important research challenge in current multi-target tracking research. Summary of the invention

[0009] The purpose of the present invention is to provide a track fusion method of incrementally updating Gaussian mixture model and multi-state transfer filtering, which can efficiently process cross-tracks and highly maneuverable targets based on the range and performance differences of multiple sensors while taking into account both real-time performance and accuracy, and adaptively adjust key filtering and associated parameters according to changes in the environment and sensor states to achieve continuous and accurate tracking of target track information.

[0010] The above technical objectives of the present invention are achieved through the following technical solutions:

[0011] The present application provides a track fusion method of incrementally updating a Gaussian mixture model and multi-state transfer filtering, including the following specific steps:

[0012] Synchronize the observation information collected by the radar and the electronic reconnaissance equipment at the same moment and perform format conversion, and complete the missing data and / or filter the abnormal data for the observation sequence obtained after time synchronization and format conversion to obtain a multi-source observation sequence;

[0013] Obtain the feature vectors of the observation information at each time step in the multi-source observation sequence, and use the preset initialized improved incremental DP-GMM model to identify the target category for the feature vectors at each time step, and obtain a target category label set representing the target category and its allocation information of each feature vector in the multi-source observation sequence;

[0014] Based on the target category label set, form an observation subset through the observation information of the same target category in the multi-source observation sequence, use the preset multiple association gates and cost functions to generate the initial tracks of each observation subset, and obtain an initial track set containing the initial tracks of each observation subset;

[0015] Screen and determine the track pairs with potential interaction and / or conflict from the initial track set, and merge and / or eliminate each track pair by defining a global cost function related to track association to form a target track set after removing crossing and / or interference;

[0016] Obtain the observation records of multiple sensors on the same time series as the multi-source observation sequence, calculate the reliability weights of each sensor and the quality scores of each track in the target track set, and obtain a track quality score set containing the quality scores of each track and a sensor weight set containing each reliability weight;

[0017] Based on the preset multiple state transition models, use the track quality score set and the sensor weight set to obtain a track fusion result, and the track fusion result includes a track state and a track covariance matrix.

[0018] On the basis of the above technical solutions, the present invention can also be improved as follows.

[0019] Further, the above-mentioned obtaining the track fusion result by using the track quality score set and the sensor weight set based on the preset multiple state transition models is specifically as follows:

[0020] Obtain the Sigma point set of multiple state transition models, and obtain the state prediction and covariance prediction of the Sigma point set;

[0021] Use the track quality score set to calculate the model probability values of each target motion model at each moment;

[0022] Based on the sensor weight set, calculate and obtain the comprehensive measurement vectors of each sensor;

[0023] Based on state prediction and covariance prediction, the track fusion result is obtained by using the comprehensive measurement vector and the model probability value.

[0024] Furthermore, the above-mentioned missing data completion is realized through an interpolation function, and the interpolation function is specifically:

[0025]

[0026] In the formula, F i (t) is the interpolation function for completing the missing data, t is the interpolation time, (x i (t k+1 ) - x i (t k )) represents the observation increment of the sensor at adjacent times, (t k+1 - t k ) represents the interpolation interval length. For t not within any valid observation interval, set F i (t) to 0 and mark it as invalid, and ignore this part of the data.

[0027] Furthermore, the above-mentioned target class recognition for the feature vector of each time step is specifically:

[0028]

[0029] In the formula, p(z n = k|x n , α, x 1:n-1 ) represents the assignment probability that the feature vector is the target class k, π k represents the weight of the current k-th mixture component, p(x n |θ k ) represents the likelihood of the k-th component corresponding Gaussian distribution for x n , θ k represents the parameter set of the mixture component k including the mean μ k , covariance ∑ k , α represents the concentration parameter of the Dirichlet process, x 1:n-1 represents the prior data, and K represents the number of mixture components existing in the current model.

[0030] Furthermore, the above-mentioned calculation is performed on each observation point in each observation subset by using a preset multiple association gate, and the calculation results of the multiple association gates are weighted and fused, and the comprehensive gating decision criterion with a preset threshold is specifically:

[0031]

[0032] Among them, (x, y) represents the rectangular coordinates of the observation point in one of the observation subsets, (r, θ) represents the polar coordinate form of the observation point; R j(x, y) represents the gating function of the rectangular gate, E j (x, y) represents the gating function of the elliptical gate, S j (r, θ) represents the gating function of the sector gate. A gating function value of 1 indicates that the observation point is within the corresponding gating area, and a value of 0 indicates that the observation point falls outside the gate; represents the center of the corresponding gating function, (Δx j , Δy j ) represents the half-width of the rectangular gate, (a j , b j ) represents the semi-major and semi-minor axes of the elliptical gate, ρ j 、 respectively represent the radial and azimuth ranges of the sector gate, and the subscript j represents the category of the observation subset;

[0033]

[0034] In the formula, G j (x k , y k ) represents the result of weighted fusion of the calculation results of the multiple association gates, w r 、w e 、w s are the weight factors of the rectangular gate, elliptical gate, and sector gate respectively, τ j is the comprehensive gating threshold for category j. If G j (x k , y k ) = 1, then this measurement point is included in the set of observations to be associated for the current category j; if G j (x k , y k ) = 0, then this data point is discarded.

[0035] Furthermore, the initial track in the set of observations to be associated is represented by the following cost function:

[0036]

[0037] In the formula, represents the initial track of target category j, (k, u) represents the index number of adjacent observation point pairs in track T j , (x k , y k ) and (x u , y u ) respectively represent the coordinates of adjacent observation points, t k 、t u represent the corresponding acquisition times; Ω j represents the gating compliance area of category j, and ω(ξ, η) represents the penalty weight for the deviation between the discrete measurement points and the track path.

[0038] Furthermore, the pairs of tracks with potential interaction and / or conflict screened and determined from the initial track set are specifically as follows:

[0039]

[0040] where D(H i ,H j ) = 1 indicates that there is a cross or dense interference in terms of time and space between track H i and track H j . Then, track H i and track H j are a pair of tracks with potential interaction and / or conflict. denotes the indicator function, which takes the value of 1 when the condition in the parentheses holds, and 0 otherwise; the set of moments in track H i is T i , the set of moments in H j is T j , the position of track H i at moment t k is the position of track H j at moment t r is d0 is the selected fixed dynamic distance threshold, and Δt0 represents the time interval threshold.

[0041] Furthermore, the above global cost function is specifically as follows:

[0042]

[0043] where E(σ) is the global cost function, σ represents the current association scheme, and through multiple iterations of E(σ) and adaptive adjustment of the annealing temperature during the simulated annealing process, the track association scheme with the minimum global cost is searched for; represents the set index of all tracks, L(H i |σ) represents the retention and merging status of track H i under scheme σ, W(H i ,H j ) represents the mismatch penalty coefficient of the pair of tracks (H i ,H j ). The value of L(H i |σ) is related to whether track H i is retained or merged. The value of W(H i ,H j ) is dynamically set according to the severity of track crossing. If D(H i ,H j ) = 1, for (H i ,Hj ) Apply a higher penalty to the cases that are still regarded as independent tracks under σ to encourage the merging or filtering of intersecting tracks first;

[0044] Each pair of tracks is merged and / or removed to form a set of target tracks after removing intersections and / or interferences. Specifically: After the optimization algorithm search is completed through the global cost function E(σ), the finally converged association scheme σ* is analyzed, and for the pair of tracks (H i , H j ) in set A, process them according to the merge and retention flags in σ* to generate a set of target tracks.

[0045] Furthermore, the reliability weights of the above-mentioned various sensors are specifically:

[0046]

[0047] Among them, W k represents the reliability weight of sensor k, represents the time-varying noise distribution of sensor k itself, R k represents the effective range of sensor k, s (k) represents the working stability evaluated in a given environment. The integral term in the denominator part is used to measure the cumulative influence of noise on the range, and s (k) Comprehensively corrects the working stability by multiplying with the fraction to ensure that sensors with higher measurement stability contribute higher weights in subsequent fusion.

[0048] Furthermore, the quality scores of each track in the above-mentioned set of target tracks are specifically:

[0049]

[0050] In the formula, represents the quality score of track , e dist (t) represents the ranging error, e ang (t) represents the angle measurement error, e hist (t) represents the difference between the track and the historical track, w d , w a , w h respectively represent the weights of the ranging, angle measurement, and historical difference terms, and t0 and t n respectively represent the start and end times of the track.

[0051] Furthermore, the above-mentioned Sigma point set is specifically:

[0052]

[0053] In the formula, Denote the set of Sigma points at time t, x j (t) represents the state estimate, P j (t) is the covariance estimate, n represents the dimension, Denote the column vector obtained by taking the p-th column or the (p - n)-th column of the symmetric decomposition matrix of (n + λ)P j (t);

[0054] State prediction and covariance prediction, specifically:

[0055]

[0056] In the formula, Denote the state prediction, Denote the covariance prediction, is the i-th Sigma point in the set of Sigma points, W i (m) is the weight of each Sigma point, Q is the prior process noise covariance matrix, n represents the total number of points in the set of Sigma points.

[0057] Furthermore, calculating the model probability values of each target motion model at each time using the set of track quality scores is specifically as follows:

[0058]

[0059] In the formula, μ j (t + 1) represents the model probability value of model M j at time t + 1, Denote the track 's quality score, κ j (t) is the coefficient calculated according to the matching degree between the actual observation and model M j , p represents the total number of target motion models.

[0060] Furthermore, calculating the comprehensive measurement vector of each sensor based on the set of sensor weights is specifically as follows:

[0061]

[0062] In the formula, z h (t) represents the comprehensive measurement vector of sensor k, W k represents the weight of sensor k, z k (t) is the measurement vector of sensor k, K is the total number of sensors.

[0063] Furthermore, the above track state is specifically:

[0064]

[0065] Wherein:

[0066]

[0067] In the formula, is the track state, μ j (t) represents the model probability value of model M j at time t, κ j (t) is the coefficient calculated according to the matching degree between the actual observation and model M j , represents the quality score of the track , p represents the total number of target motion models, represents state prediction, K t represents the Kalman gain, z h (t) represents the comprehensive measurement vector of sensor k, H is the prior observation matrix, represents covariance prediction, R is the prior measurement noise covariance.

[0068] Furthermore, the above track covariance matrix is specifically:

[0069]

[0070] Wherein:

[0071]

[0072] In the formula, P(t + 1) represents the track covariance matrix, is the track state, μ j (t) represents the model probability value of model M j at time t, κ j (t) is the coefficient calculated according to the matching degree between the actual observation and model M j , represents the quality score of the track , p represents the total number of target motion models, represents state prediction, K t represents the Kalman gain, z h (t) represents the comprehensive measurement vector of sensor k, H is the prior observation matrix, represents covariance prediction, R is the prior measurement noise covariance, I represents a positive definite matrix, that is, a matrix with diagonal elements of 1 and the rest of 0.

[0073] In the second aspect, the present application provides a track fusion system for incremental update Gaussian mixture model and multi-state transition filtering, which is applied to the track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to any one of claims 1 - 15, including:

[0074] A data processing module for performing time synchronization and format conversion on the observation information collected by a radar and an electronic reconnaissance device at the same moment, and performing missing data completion and / or abnormal data filtering on the observation sequence obtained through time synchronization and format conversion to obtain a multi-source observation sequence;

[0075] A target classification module for obtaining the feature vectors of the observation information at each time step in the multi-source observation sequence, and using a preset initialized improved incremental DP-GMM model to perform target category recognition on the feature vectors at each time step to obtain a target category label set representing the target categories and their allocation information of the feature vectors in the multi-source observation sequence;

[0076] An initial track generation module for forming an observation subset based on the observation information of the same target category in the multi-source observation sequence based on the target category label set, and using a preset multiple association gate and cost function to generate the initial tracks of each observation subset, and obtaining an initial track set containing the initial tracks of each observation subset;

[0077] A track association optimization module for screening and determining track pairs with potential interaction and / or conflict from the initial track set, and merging and / or eliminating each track pair by defining a global cost function related to track association to form a target track set after removing intersections and / or interferences;

[0078] A track quality analysis module for obtaining the observation records of multiple sensors on the same time series as the multi-source observation sequence, calculating the reliability weights of each sensor and the quality scores of each track in the target track set, and obtaining a track quality score set containing the quality scores of each track and a sensor weight set containing each reliability weight;

[0079] A fused track output module for obtaining a track fusion result based on a preset multiple state transition models, using the track quality score set and the sensor weight set, where the track fusion result includes a track state and a trajectory covariance matrix.

[0080] In a third aspect, the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the method according to any one of the first aspect is implemented.

[0081] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute the method according to any one of the first aspect.

[0082] Compared with the prior art, the present invention has at least the following beneficial effects:

[0083] 1. Adaptive iterative processing and linkage monitoring: Based on the sensor network and real-time monitoring module deployed by the system, when the external electromagnetic environment is perceived to be significantly deteriorating (for example, the emergence of a new interference source) or the target's maneuvering characteristics change suddenly, it automatically triggers the re-processing of the new observation data and the original trajectory data.

[0084] This process runs through the basic processes of data preprocessing, target classification, initial track generation and track association, and re-estimates the key filter parameters and sensor reliability in the core algorithm link of sensor weight calculation and unscented Kalman filter fusion; the iterative processing mode based on this linkage monitoring avoids the lag and insufficient coverage caused by traditional static periodic refresh, and can update the track status in time when the target undergoes large-scale maneuvers or external interference suddenly increases, ensuring that the overall track management accuracy and continuity remain at a high level.

[0085] 2. Multi-model probability adaptive correction based on track quality drive: In the model probability update link of the multi-model unscented Kalman filter, factors from track quality assessment are integrated to form a probability adaptive solution driven by track quality.

[0086] In the multi-model unscented Kalman filter in the fusion stage, different possible motion models of the target (uniform speed, nonlinear steering, high maneuverability acceleration) are predicted and measured and updated separately. In order to improve the adaptability to highly dynamic targets, the present invention constructs a track quality score in the model probability update formula, dynamically highlighting the guiding role of historical tracks with higher reliability in model selection. Specifically, each candidate track is quantitatively evaluated by the track quality scoring module, and enters the model probability correction formula in the form of a weight during the filter update process, assisting the filter in allocating resources between multiple models in real time. Since the track quality and model probability are recalculated after each observation fusion, this means that the present technical solution can identify the sudden turning or violent acceleration state of the target in a short time, reduce the estimation offset of traditional single model filtering under high maneuverability, and avoid excessive reliance on a single model assumption.

[0087] 3. Weight Integration Calculation of Multi-source Sensors for Dynamic Noise Environments: Integrate and quantify the noise characteristics and stability of multi-source observation sequences in segments, and introduce a combination of offline (sensor performance indicators) and online (real-time observation deviation statistics) methods to dynamically correct the weights of each sensor. In the calculation of sensor weights, the present invention constructs an integration factor by performing time-varying sampling on the original signal or filter residuals, and using the noise mean, variance, and observation deviation degree accumulated over a period of time. Combining with the reference performance of the sensor (such as effective range, measurement sensitivity) to form a comprehensive quantization index to determine the weight of the sensor in the current period. For sensors with a sudden increase in noise, the integration factor will increase rapidly, and the weight will decrease accordingly, thereby weakening its influence on the final fusion result; for sensors that have always maintained a high degree of stability, the weight will be continuously maintained at a high level. Based on this "multi-period integration + adaptive adjustment" strategy, this solution realizes robust suppression of sensors with instantaneous high noise or temporary failures, and can more effectively eliminate random or pulsed interference compared to fixed weighting or single-measurement scenario fusion, ensuring high-precision track tracking and maintenance in multi-target scenarios. Description of the Drawings

[0088] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0089] Figure 1 It is the overall flowchart in the embodiments of the present invention;

[0090] Figure 2 It is the preprocessing flowchart in the embodiments of the present invention;

[0091] Figure 3 It is the flowchart for target classification of multi-source observation sequences based on the online incremental Dirichlet process Gaussian mixture model in the embodiments of the present invention;

[0092] Figure 4 It is the flowchart for generating an initial track by applying a multiple association gate strategy based on the target classification result in the embodiments of the present invention;

[0093] Figure 5 It is the flowchart for further associating the initial track by constructing dynamic constraints and taking the simulated annealing algorithm as an example of an optimization algorithm in the embodiments of the present invention;

[0094] Figure 6 It is the flowchart for analyzing the track quality of the associated output track and calculating the sensor reliability weight in the embodiments of the present invention;

[0095] Figure 7 It is the flowchart for track fusion based on the multi-model unscented Kalman filter in the embodiments of the present invention;

[0096] Figure 8 It is the flowchart of the track fusion method in the embodiment of the present invention;

[0097] Figure 9 It is the connection schematic diagram of the track fusion system in the embodiment of the present invention. Specific embodiments

[0098] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Components of the embodiments of the present invention usually described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations.

[0099] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0100] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0101] In the description of the embodiments of the present invention, "a plurality" represents at least 2.

[0102] Embodiment 1: This embodiment provides a track fusion method of an incremental update Gaussian mixture model and multi-state transition filtering, as Figure 8 shown, including the following specific steps:

[0103] S1. Perform time synchronization and format conversion on the observation information collected by the radar and the electronic reconnaissance equipment at the same moment, and perform missing data filling and / or abnormal data filtering on the observation sequence obtained after time synchronization and format conversion to obtain a multi-source observation sequence.

[0104] Optionally, the above-mentioned missing data filling is implemented through an interpolation function, and the interpolation function is specifically:

[0105]

[0106] In the formula, F i (t) is the interpolation function for filling missing data, t is the moment to be interpolated, (x i (t k+1 ) - x i (t k)) represents the observation increment of the sensor at adjacent times, (t k+1 -t k ) represents the interpolation interval length. For t not within any valid observation interval, set F i (t) to 0 and mark it as invalid, and ignore this part of the data.

[0107] S2. Obtain the feature vectors of the observation information at each time step in the multi-source observation sequence, and use the preset initialized improved incremental DP-GMM model to identify the target category of the feature vector at each time step, and obtain the target category label set representing the target category and its allocation information of each feature vector in the multi-source observation sequence.

[0108] Optionally, the above-mentioned identification of the target category of the feature vector at each time step is specifically as follows:

[0109]

[0110] In the formula, p(z n =k|x n ,α,x 1:n-1 ) represents the allocation probability that the feature vector is the target category k, π k represents the weight of the current k-th mixture component, p(x n |θ k ) represents the likelihood of the Gaussian distribution corresponding to the k-th component for x n , θ k represents the parameter set of the mixture component k, including the mean μ k , covariance ∑ k , α represents the concentration parameter of the Dirichlet process, x 1:n-1 represents the prior data, and K represents the number of existing mixture components in the current model.

[0111] S3. Based on the target category label set, form an observation subset through the observation information of the same target category in the multi-source observation sequence, use the preset multiple association gates and cost functions to generate the initial tracks of each observation subset, and obtain the initial track set containing the initial tracks of each observation subset.

[0112] Optionally, the above-mentioned use of the preset multiple association gates to calculate each observation point in each observation subset, weight and fuse the calculation results of the multiple association gates, and use the preset threshold comprehensive gating decision criterion is specifically as follows:

[0113]

[0114] Among them, (x, y) represents the rectangular coordinates of the observation point in one of the observation subsets, and (r, θ) represents the polar coordinate form of the observation point; R j(x, y) represents the gating function of a rectangular gate, E j (x, y) represents the gating function of an elliptical gate, S j (r, θ) represents the gating function of a sector gate. A gating function value of 1 indicates that the observation point is within the corresponding gating area, and a value of 0 indicates that the observation point falls outside the gate; represents the center of the gate corresponding to the gating function, (Δx j , Δy j ) represents the half-width of the rectangular gate, (a j , b j ) represents the semi-axis lengths of the elliptical gate, ρ j 、 respectively represent the radial and azimuth ranges of the sector gate. The subscript j represents the category of the observation subset.

[0115] Furthermore, the calculation results of the multiple association gates are weighted and fused. Specifically:

[0116]

[0117] In the formula, G j (x k , y k ) represents the result of weighted fusion of the calculation results of the multiple association gates, w r 、w e 、w s are the weight factors of the rectangular gate, elliptical gate, and sector gate respectively, τ j is the comprehensive gating threshold for category j. If G j (x k , y k ) = 1, then this measurement point is included in the set of observations to be associated for the current category j; if G j (x k , y k ) = 0, then this data point is discarded.

[0118] Optionally, the initial track in the set of observations to be associated is represented by the following cost function:

[0119]

[0120] In the formula, represents the initial track of target category j, (k, u) represents the index numbers of adjacent observation point pairs in track T j , (x k , y k ) and (x u , y u ) represent the coordinates of adjacent observation points respectively, t k 、t u represent the corresponding acquisition times; Ωj The gated coincidence region representing category j, and ω(ξ, η) represents the penalty weight for the deviation between the discrete measurement points and the trajectory path.

[0121] S4. Screen and determine the track pairs with potential interaction and / or conflict from the initial track set, and merge and / or eliminate each track pair by defining a global cost function related to track association, so as to form a target track set after removing intersections and / or interferences.

[0122] Optionally, screening and determining the track pairs with potential interaction and / or conflict from the initial track set is specifically as follows:

[0123]

[0124] In the formula, D(H i ,H j ) = 1 indicates that there are intersections or dense interferences in the time and space levels between track H i and track H j . Then, track H i and track H j are track pairs with potential interaction and / or conflict. represents the indicator function, which takes the value of 1 when the condition in the parentheses holds, otherwise it takes 0; the moment set in track H i is T i , and the moment set in H j is T j . The position of track H i at moment t k is The position of track H j at moment t r is d0 is the selected fixed dynamic distance threshold, and Δt0 represents the time interval threshold.

[0125] Optionally, the above global cost function is specifically as follows:

[0126]

[0127] In the formula, E(σ) is the global cost function, σ represents the current association scheme, and by performing multiple iterations on E(σ) and adaptively adjusting the annealing temperature during the simulated annealing process, the track association scheme with the minimum global cost is searched; represents the set index of all tracks, L(H i |σ) represents the retention and merging states of track H i under scheme σ, and W(H i ,H j ) represents the track pair (H i ,Hj )'s mismatch penalty coefficient, L(H i |σ) is related to whether the track H i is to be retained or merged. W(H i , H j ) is dynamically set according to the severity of track crossing. If D(H i , H j ) = 1, a higher penalty is imposed on the case where (H i , H j ) is still regarded as an independent track under σ, so as to encourage the merging or filtering of crossing tracks first.

[0128] Among them, each track pair is merged and / or removed to form a set of target tracks after removing crossings and / or interferences. Specifically: after the optimization algorithm search is completed through the global cost function E(σ), the finally converged association scheme σ* is analyzed, and the track pairs (H i , H j ) in set A are processed according to the merge and retention flags in σ* to generate a set of target tracks.

[0129] S5. Obtain the observation records of multiple sensors on the same time series as the multi-source observation sequence, calculate the reliability weights of each sensor and the quality scores of each track in the set of target tracks, and obtain a track quality score set containing the quality scores of each track and a sensor weight set containing each reliability weight.

[0130] Optionally, the reliability weights of the above-mentioned sensors are specifically:

[0131]

[0132] Among them, W k represents the reliability weight of sensor k, represents the time-varying noise distribution of sensor k itself, R k represents the effective range of sensor k, s (k) represents the working stability evaluated in a given environment. The integral term in the denominator part is used to measure the cumulative influence of noise on the range. s (k) Comprehensively corrects the working stability by multiplying with the fraction to ensure that sensors with higher measurement stability contribute higher weights in subsequent fusion.

[0133] Optionally, the quality scores of each track in the above-mentioned set of target tracks are specifically:

[0134]

[0135] In the formula, represents the track The quality score, e dist (t) represents the ranging error, e ang (t) represents the angle measurement error, e hist (t) represents the difference between the track and the historical track, w d and w a and w h respectively represent the weights of the ranging, angle measurement, and historical difference terms, and t0 and t n respectively represent the start and end times of the track.

[0136] S6. Based on a plurality of preset state transition models, a track fusion result is obtained by using the track quality score set and the sensor weight set. The track fusion result includes the track state and the track covariance matrix.

[0137] Among them, the above-mentioned obtaining the track fusion result by using the track quality score set and the sensor weight set based on a plurality of preset state transition models is specifically as follows:

[0138] S61. Obtain the Sigma point set of a plurality of state transition models, and obtain the state prediction and covariance prediction of the Sigma point set.

[0139] Optionally, the above-mentioned Sigma point set is specifically:

[0140]

[0141] In the formula, represents the Sigma point set at time t, x j (t) represents the state estimate, P j (t) is the covariance estimate, n represents the dimension, represents the column vector obtained by taking the p-th column or the (p - n)-th column of the symmetric decomposition matrix of (n + λ)P j (t).

[0142] Among them, the above-mentioned state prediction and covariance prediction are specifically:

[0143]

[0144] In the formula, represents the state prediction, represents the covariance prediction, is the i-th Sigma point in the Sigma point set, W i (m) is the weight of each Sigma point, Q is the prior process noise covariance matrix, and n represents the total number of points in the Sigma point set.

[0145] S62. Calculate the model probability values of each target motion model at each moment using the set of track quality scores.

[0146] Optionally, the above-mentioned calculation of the model probability values of each target motion model at each moment using the set of track quality scores is specifically as follows:

[0147]

[0148] In the formula, μ j (t + 1) represents the model probability value of model M j at moment t + 1, represents the quality score of track , κ j (t) is a coefficient calculated based on the matching degree between the actual observation and model M j , and p represents the total number of target motion models.

[0149] S63. Calculate the comprehensive measurement vector of each sensor based on the set of sensor weights.

[0150] Optionally, the above-mentioned calculation of the comprehensive measurement vector of each sensor based on the set of sensor weights is specifically as follows:

[0151]

[0152] In the formula, z h (t) represents the comprehensive measurement vector of sensor k, W k represents the weight of sensor k, z k (t) is the measurement vector of sensor k, and K is the total number of sensors.

[0153] S64. Obtain the track fusion result using the comprehensive measurement vector and the model probability value based on state prediction and covariance prediction.

[0154] Optionally, the above-mentioned track state is specifically as follows:

[0155]

[0156] Among them:

[0157]

[0158] In the formula, is the track state, μ j (t) represents the model probability value of model M j at moment t, κ j (t) is a coefficient calculated based on the matching degree between the actual observation and model M j , represents track The quality score, p represents the total number of target motion models, represents state prediction, K t represents the Kalman gain, z h (t) represents the integrated measurement vector of sensor k, H is the prior observation matrix, represents covariance prediction, R is the prior measurement noise covariance.

[0159] Furthermore, the above trajectory covariance matrix is specifically:

[0160]

[0161] Where:

[0162]

[0163] In the formula, P(t + 1) represents the trajectory covariance matrix, is the track state, μ j (t) represents the model probability value of model M j at time t, κ j (t) is the coefficient calculated according to the matching degree between the actual observation and model M j The matching degree calculation, represents the track The quality score, p represents the total number of target motion models, represents state prediction, K t represents the Kalman gain, z h (t) represents the integrated measurement vector of sensor k, H is the prior observation matrix, represents covariance prediction, R is the prior measurement noise covariance, I represents a positive definite matrix, that is, a matrix with diagonal elements equal to 1 and the rest equal to 0.

[0164] Example 2: This example provides a multi-source heterogeneous multi-target track fusion method based on online incremental Dirichlet process and multi-model filtering. Refer to Figures 1-7 , and the overall flowchart is shown in Figure 1 , specifically as follows in steps 1 - 7:

[0165] Step 1, preprocessing of multi-source observation data, as Figure 2 shown:

[0166] 1) Collect multi-source sensor observation data and construct an initial data set:

[0167] On the time series T, the observation output of the radar sensor is represented as {x r (t k )}, and the observation output of the electronic reconnaissance equipment is represented as {x e (t k )}.

[0168] At the same observation time t k Store the observed values collected by the radar sensor and the electronic reconnaissance equipment to form an initial data set D0. For the time stamp t included in D0 k Perform formatting to make the data set D0 match the subsequent time series alignment process.

[0169] 2) Execute time synchronization and unified format conversion:

[0170] On a single time axis T, perform a sorting operation on the obtained initial data set D0. For the radar sensor observation sequence {x r (t k )} and the electronic reconnaissance equipment observation sequence {x e (t k )}, pair them up at each moment t k to form a multi-source observation matrix M0.

[0171] Rearrange the fields output by each sensor and map them to a unified dimension to obtain an observation sequence M1 with a consistent format. For individual moments with a large sampling delay, perform linear calibration according to the clock offset parameters obtained on site and update the calibrated observation sequence to M1.

[0172] 3) Missing data interpolation and abnormal data filtering:

[0173] In M1, perform piecewise function interpolation on the missing observed values and filter the data that deviates from the normal distribution range to obtain an observation sequence M2. Let the sensor number be i, and the two adjacent valid observation times be t k and t k+1 . For sensor i at time t k and t k+1 , the observed values collected are denoted as x i (t k ) and x i (t k+1 ).

[0174] Furthermore, define the interpolation function F i (t) as:

[0175]

[0176] where F i (t) is the interpolation function for missing data, t is the moment to be interpolated, (x i (t k+1 ) - x i (t k )) represents the observation increment of this sensor at adjacent moments, and (t k+1 - t k) represents the interpolation interval length. For t not within any valid observation interval, set F i (t) to 0 and mark it as invalid, ignoring this part of the data; for abnormal observations, use the threshold method with an absolute deviation much greater than the mean interval to filter them, obtaining the data sequence M2 without anomalies.

[0177] 4) Output the preprocessed observation sequence:

[0178] Define the obtained sequence without missing values and anomalies as M3 and output it as the final preprocessed observation sequence M4, providing high-quality and uniformly formatted input data for subsequent classification, track association, and fusion steps.

[0179] Step 2, Online incremental Dirichlet target classification, as Figure 3 shown:

[0180] 1) Extract multi-source pulse features and construct a feature vector set:

[0181] In the preprocessed observation sequence M4 output in Step 1, select the carrier frequency f(t), pulse width w(t), and pulse repetition frequency r(t) at each observation time t, and represent this three-dimensional feature combination as a vector x(t) = [f(t), w(t), r(t)]. Collect the features at all times t and denote them as the feature vector set X = {x1, x2, …, x n}), where n is the total number of observed samples.

[0182] 2) Construct and initialize an improved incremental DP-GMM model:

[0183] For the feature vector set X, set the initial hyperparameter α based on the Dirichlet process prior and set the preliminary distribution form for the Gaussian mixture components.

[0184] Given that the number of mixture components is theoretically unlimited, use an incremental approach to dynamically increase and adjust the number of components according to new data. For each potential mixture component j, define the mean vector μ j and the covariance matrix ∑ j , and assign a prior weight π j (0) to each component in the initial stage.

[0185] 3) Iteratively update the clustering structure and complete incremental learning:

[0186] Perform clustering assignment for each sample x n in the feature vector set X, and update the mixture component parameters and adjust the number of components in real time when new samples arrive. Let z n represent the clustering label of x n , and for each possible label k, construct the incremental assignment probability p(z n = k|xn , α, x1: n-1 ) is as follows:

[0187]

[0188] Among them, π k represents the weight of the current k-th mixture component, p(x n |θ k ) represents the likelihood of the Gaussian distribution corresponding to the k-th component for x n , θ k represents the set of parameters of the mixture component k (mean μ k , covariance ∑ k ), α represents the concentration parameter of the Dirichlet process, x1: n-1 represents the prior data, and K represents the number of mixture components existing in the current model.

[0189] That is, by performing a maximization selection on the assignment probability for each k, the membership label z n of x n is determined, and after the assignment is completed, the mixture component parameters are updated. If the sample x n is to be assigned to a new mixture component, then a new component is added to the model according to the non-parametric mechanism of the Dirichlet process and its parameters are initialized.

[0190] Furthermore, after determining that the membership label z n of the sample x n = k, if this x n is classified into the existing k-th mixture component, then the statistical parameters of this component are updated in the following online incremental manner, and the mean and covariance of the mixture component can be corrected in real time when new samples arrive:

[0191] ① First, update the total number of samples of this component:

[0192]

[0193] Among them, represents the number of samples of the k-th mixture component before update, represents the total number of samples of this component after update (including the new sample).

[0194] ② Further calculate the difference between the new sample and the old mean:

[0195]

[0196] Among them, x n is the newly arrived sample vector, represents the mean vector of the k-th mixture component before update, and δ measures the deviation between the new sample and this old mean.

[0197] ③ Further perform online incremental update of the mean value:

[0198]

[0199] Among them, is the updated mean vector of the k-th mixture component after the inclusion of the new sample.

[0200] ④ Further calculate the difference between the new sample and the updated mean value:

[0201]

[0202] Among them, δ′ represents the difference between the new sample and the updated mean of the k-th mixture component, which is used to correct the covariance.

[0203] ⑤ Finally, perform online incremental update of the covariance:

[0204]

[0205] Among them, and respectively represent the covariance matrix estimates of the k-th mixture component before and after the update, is the incremental compensation of the covariance of the new sample x n for this component covariance, so that the updated covariance can reflect the influence of the new sample on the component distribution.

[0206] Through the above, this application can incorporate the information of each new sample into the parameter estimation of the k-th mixture component in sequence without repeatedly reading all historical data, forming a continuous and real-time online incremental learning process. If a new mixture component needs to be added according to the non-parametric mechanism of the Dirichlet process prior, after initializing its mean μ and covariance Σ for the new component, the subsequent iterative update is similarly performed using the above online incremental formula, so that the network can dynamically adapt to target changes and overcome the limitations brought by a fixed number of components; this sub-step adjusts the model structure in real time when new targets and target features change through an incremental update strategy, reducing the limitations brought by a fixed number of components.

[0207] 4) Output the classification label and complete the target category recognition:

[0208] After the calculation and update are completed, for each feature vector x n cluster label z n perform convergence determination and recording to form the target category label set Z = {z1, z2,..., z n}. Through Z, the recognized target category and its allocation information are obtained, and this result is output and provided for track tracking and association call.

[0209] Step 3, Generate the initial track of the multiple association gate, such asFigure 4 As shown in:

[0210] 1) Receive the target classification label and organize the observation data:

[0211] Denote the set of target classification labels output in step 2 as Z = {z1, z2, …, z n} and compare it with the preprocessed observation sequence M4 obtained in step 1. For each observation time t k and its observation vector x k , retrieve the corresponding classification label z k , and group the data according to the classification result to form the observation subset D j of class j.

[0212] 2) Construct a multiple association gate function:

[0213] In the observation subset D j of class j, this application proposes to construct association gates of three shapes: rectangular gate R j (x, y), elliptical gate E j (x, y), sector gate S j (r, θ). Let represent the gate center, (Δx j , Δy j ) represent the half-width of the rectangular gate, (a j , b j ) represent the semi-major and semi-minor axes of the elliptical gate, represent the radial and azimuth angle ranges of the sector gate. For each class j, write R j (x, y), E j (x, y), S j (r, θ) into the following formula uniformly to realize the screening of different position coordinate forms under the same gating framework:

[0214]

[0215] where x and y represent the rectangular coordinates of the observation point, (r, θ) represents the polar coordinate form of the observation point, and the value of the gating function being 1 indicates that the observation point is within the corresponding gating area, and the value being 0 indicates that the observation point falls outside the gate. This sub-step adapts to the possible rectangular, elliptical or specific azimuth angle distribution characteristics of different targets through the gate functions of multiple shapes, overcoming the problem of insufficient adaptability caused by only using a single gating shape in the prior art.

[0216] 3) Perform gating operations and conduct measurement associations:

[0217] For the observation points (x k , y k ) of each class j, calculate R j (xk , y k ), E j (x k , y k ), S j (r k , θ k ) value

[0218] Considering the differences in the adaptability of different gates to the target, this application proposes to construct a weighted combination of gating functions G j (x k , y k ), and with the threshold τ j Comprehensive gating decision criterion:

[0219]

[0220] Where w r , w e , w s are the weight factors of the rectangular gate, elliptical gate, and sector gate respectively, and τ j is the comprehensive gating threshold for class j.

[0221] If G j (x k , y k ) = 1, then include this measurement point in the set of observations to be associated with the current class j;

[0222] If G j (x k , y k ) = 0, then discard this data point.

[0223] This sub-step is based on the parallel screening and weighted fusion of multiple gate shapes, and can, to a certain extent, accurately retain the measurement point information that best fits the target motion pattern.

[0224] 4) Generate the initial track and output:

[0225] Let H j represent the set of initial tracks for class j, and further let T j represent a certain track corresponding to it. By performing time proximity and spatial consistency analysis on the observation points that meet G j (x k , y k ) = 1, use an improved track splicing method to construct T j ; it is established that during this process, joint constraints on the temporal and position deviations of each segment of candidate points to be spliced are performed, and a cost function L j (T j ) is defined to measure the smoothness and continuity of the track:

[0226]

[0227] Among them, (k, u) represents the index number of adjacent observation point pairs in the trajectory T j In, (x k , y k ) and (x u , y u ) represent the coordinates of adjacent observation points respectively, and t k , t u represent the corresponding acquisition times; Ω j represents the gating coincidence region of category j, and ω(ξ, η) represents the penalty weight for the deviation between discrete measurement points and the trajectory path.

[0228] By minimizing this cost function, the optimal initial track T j * of category j can be obtained, and the set of initial tracks of all category j is output as H = {H1, H2,...} for use in the subsequent association filtering stage. The improved track splicing method in this sub-step has certain performance improvements in the spatio-temporal continuity of observation points and noise suppression, overcoming the limitations of traditional fixed-rule splicing methods in dealing with multi-target distribution and measurement uncertainty.

[0229] Step 4: Track association of dynamic constraint and optimization algorithm, as Figure 5 shown:

[0230] 1) Obtain the initial tracks and construct the association evaluation set:

[0231] Denote the set of initial tracks output in step 3 as H = {H1, H2,..., H m}, where each track consists of several observation points. Define the association evaluation set A according to the distribution of tracks on the time series T, and put all track pairs (H i , H j ) with time overlap or spatial proximity into A. Based on this sub-step, potential interactive and conflicting track pairs are screened out by predicting the time and position relationships between the initial tracks.

[0232] 2) Identify cross tracks and dense target interference based on dynamic constraints:

[0233] For each track pair (H i , H j ) in A, construct a dynamic constraint judgment function D(H i , H j ) to quantify whether there is cross and dense interference between tracks.

[0234] Let the set of time moments in track H i be T i , H jThe set of moments is T j Let the track be H i At moment t k The position is (x ik , y ik ). The position of track H j At moment t r The position is (x jr , y jr ). Then, select the fixed dynamic distance threshold d0 and the time interval threshold Δt0, and construct the following piecewise constraint function for determination:

[0235]

[0236] Among them, Represents the indicator function, which takes the value of 1 when the condition in the parentheses holds, and 0 otherwise. D(H i , H j ) = 1 indicates that there is a cross or dense interference between track H i and track H j in terms of time and space. That is, this sub-step jointly determines through dynamic elements (time and space thresholds) to distinguish the conflict status between different tracks, providing a prior constraint for cost optimization in the subsequent optimization algorithm.

[0237] 3) Construct the associated framework of the optimization algorithm and define the global cost function:

[0238] Adopt the optimization idea to globally optimize the association relationship of all track pairs (H i , H j ) in A. For example, the simulated annealing strategy can be used to search between track merging and elimination. Define the global cost function E(σ) related to track association, where σ represents the current association scheme. Let Represents the set index of all tracks. Let L(H i |σ) represent the retention and merging status of track H i under the scheme σ. Let W(H i , H j ) represent the mismatch penalty coefficient of the track pair (H i , H j ), and obtain the following fractional form of the global cost function:

[0239]

[0240] Among them, the value of L(H i |σ) is related to whether track H i is retained or merged. The value of W(H i , H j ) is dynamically set according to the severity of track crossing. If D(H i,H j ) = 1, then a higher penalty is imposed on the case where (H i ,H j ) is still regarded as an independent track under σ, so as to promote the prior merging or filtering of cross tracks. By performing multiple iterations of E(σ) and adaptively adjusting the annealing temperature during the simulated annealing process, a track association scheme with the minimum global cost is searched for.

[0241] 4) Output the associated tracks and update the track set:

[0242] After completing the search of the optimization algorithm, the final converged association scheme σ* is analyzed, and the track pairs (H i ,H j ) in A are processed according to the merging and retention flags in σ*, and a new track set is generated This sub-step summarizes and outputs the results of merging or eliminating, forming a track set after removing crosses or interferences, and providing a more consistent and conflict-free target track input for the filtering and fusion stages.

[0243] Step 5, Track quality analysis and sensor weight calculation, as Figure 6 shown:

[0244] 1) Obtain and organize the associated tracks and multi-source sensor information:

[0245] The associated track set generated in step 4 is denoted At the same time, the observation records of multiple sensors on the time series T and the device performance indicators such as noise and range are obtained. The tracks are archived with their corresponding sensor measurement indices to form a structured data set U for track quality assessment and sensor weight calculation.

[0246] 2) Calculate the track quality score

[0247] For each track Based on the comprehensive ranging error, angle measurement error, and the difference from historical data, a quality function is defined Let e dist (t) represent the ranging error, e ang (t) represent the angle measurement error, e hist (t) represent the difference between the track and the historical track, and a quality function is constructed based on the weighted integral form:

[0248]

[0249] Among them, w d , w a , w h represent the weights of the ranging, angle measurement, and historical difference terms respectively, t0 and t n represent the start and end times of the track respectively, edist (t), e ang (t), e hist (t) quantifies the corresponding errors respectively.

[0250] By integrating the three types of errors of the track at each moment and summing them with weights, the overall quality score of the track is obtained. Based on this sub-step, the comprehensive influence of multiple error sources is introduced in the quality measurement, overcoming the problem that some schemes only focus on single error and lead to distorted evaluation.

[0251] 3) Calculate the reliability weights of multi-source sensors:

[0252] Further, in the multi-source sensor data, for each sensor k, its range R k , noise variance σ k and working stability index s (k) are introduced, and the reliability weight W k of sensor k is defined as:

[0253]

[0254] Among them, represents the time-varying noise distribution of the sensor itself, R k represents the effective range of the sensor, and s (k) represents the working stability evaluated in the given environment. The integral term in the denominator is used to measure the cumulative influence of noise on the range, and s (k) comprehensively corrects the working stability by multiplying with the fraction to ensure that sensors with higher measurement stability contribute higher weights in subsequent fusion.

[0255] 4) Output the track quality and sensor weight results:

[0256] The set of track quality scores obtained from the above steps and the set of sensor reliability weights W = {W1,..., W k} are archived and output, providing a data-driven basis for the track fusion step.

[0257] Step 6, multi-model unscented Kalman filter fusion, as Figure 6 and Figure 7 shown:

[0258] 1) Establish a multi-model state description and initialize the model probability:

[0259] Denote the set of sensor weights output in step 5 as W = {W1,..., W k}, and denote the set of track quality scores as For different possible motion modes of the target, set the multi-model set M = {M1,..., Mp}, where each model M j defines different state transition equations and process noise.

[0260] Let μ j (t) represent the probability of model M j at time t, and set the corresponding model probability initialization for each track. Introduce the track quality score into the model update process to provide a basis for allocating higher confidence to high-quality tracks in the filtering stage. Directly define the update method of the model probability as follows, where κ (t) is a coefficient calculated according to the matching degree between the actual observation and model M j : j

[0261]

[0262] where represents the quality score of track , and μ j (t + 1) is the probability of model M j at the next time. By introducing in the numerator and denominator, improve the participation of the model corresponding to the high-quality track in the subsequent filtering process and enhance the adaptation ability to high-confidence tracks.

[0263] 2) Generate the multi-model state Sigma points of the unscented Kalman filter:

[0264] For model M j , at each time, construct the Sigma point set required for the unscented transformation according to the current state estimate x j (t) and its covariance P j (t). Let the dimension be n, and define the constant λ = α 2 (n + κ) – n, where α and κ are hyperparameters. Denote the Sigma point set generated at time t as

[0265]

[0266] where represents the column vector obtained by taking the p-th column or the (p - n)-th column of the symmetric decomposition matrix of (n + λ)P j (t). After each Sigma point passes through the state transition equation of model M j , the predicted Sigma point set can be obtained, which is used to capture the possible nonlinear maneuvers of the target under this model.

[0267] Then, the state prediction covariance prediction

[0268]

[0269] is the i-th Sigma point. is the predicted state value (weighted average of Sigma points). W i (m) are the weights of each Sigma point. Q is the prior process noise covariance matrix.

[0270] 3) Measurement fusion based on sensor weights and unscented transform update:

[0271] Let z k (t) represent the measurement vector of sensor k, W k represent its weight. For each model M j , after obtaining the predicted state Sigma points, the predicted measurement Sigma points are calculated through the observation equation and weighted fusion is performed. Define the comprehensive measurement vector z h (t) as:

[0272]

[0273] where, for all sensors k, multiply the measurement z k (t) by W k and sum, then divide by the sum of all weights to obtain the weighted fused measurement z h (t).

[0274] Furthermore, the unscented Kalman filter updates z h (t) and the predicted measurement Sigma points to obtain the state x j of model M j at time t + 1 and the covariance P j (t + 1). Given that the state prediction is the covariance prediction is Let the measurement innovation be The update formula is:

[0275]

[0276] where, K t is the Kalman gain, R is the prior measurement noise covariance, H is the prior observation matrix, x j (t + 1) is the updated state estimate, and P j (t + 1) is the updated covariance matrix.

[0277] By using the above formula in the measurement update process, this step improves the adaptability to multi-source non-uniform measurement quality and overcomes the instability of traditional multi-model filtering in scenarios with large differences in sensor reliability.

[0278] 4) Multi-model fusion outputs the final track state estimate:

[0279] After completing the update of each model M j and combining the obtained model probability μ j (t + 1), weighted fusion of the final track state is performed. Let and P j (t + 1) represent the state estimate and covariance of model M j respectively, and the overall track state and covariance are obtained:

[0280]

[0281] Among them, and P(t + 1) represent the fused track state and track covariance respectively, and μ j (t + 1) represents the final weight of model M j .

[0282] The covariance term between models reflects the differences in different assumptions of each model for the same final fused target through the accumulation of divergence terms. After the established steps are completed, the track state and its covariance P(t + 1) are output, providing a stronger robustness and accuracy for real-time tracking.

[0283] Through multi-model Sigma point propagation and adaptive measurement noise fusion, the tracking ability for non-linear and highly maneuverable targets is enhanced, and finally a reliable track state estimate in a multi-target environment is achieved; compared with the existing technology, the track quality score and sensor weight co-output by this technical solution on the basis of multi-model unscented Kalman filtering introduce the track quality into the model probability update process, and perform weighted fusion on the sensor measurement information, overcoming the deficiency that traditional methods are prone to filtering failure when sensor noise is uneven and target maneuvering behavior is intense.

[0284] Step 7, Fused track output and real-time monitoring:

[0285] 1) Summarize the fused track state and generate system output:

[0286] Archive the final fused track state and covariance obtained in step 6 to obtain the state vector and confidence index of each track at the current moment. According to system requirements, record and label the track state, and send the result to the high-level application module. This sub-step connects the filtering result with the external task interface, providing real-time data support for target monitoring, command and control, and situation analysis.

[0287] 2) Start continuous monitoring and detect critical environmental changes:

[0288] Continuously detect the electromagnetic environment information received during system operation and the target motion elements. If significant changes such as an increase in interference sources, fluctuations in the radar signal coverage range, or large-scale maneuvers of the target are observed in the external environment, trigger a dynamic environment marker. By regularly monitoring the environment and target behavior, ensure that factors affecting track accuracy or sensor measurement stability can be captured in a timely manner, laying a data-driven condition for re-cycling processing.

[0289] 3) Execute reprocessing of multi-source observation sequences and maintain track results:

[0290] If significant changes in the environment and target are detected, immediately trigger the reprocessing of sensor observation data from step 1 to step 6, including the entire process of data preprocessing, target classification, initial track generation, track association and quality analysis, and unscented Kalman fusion. Repeat the above steps to achieve real-time update and improvement of multi-source track estimation;

[0291] 4) Output and maintain the final track status:

[0292] After reprocessing and updating, write the latest fused track and confidence results into the system track library, and maintain and replace the original tracks to ensure the continuity of global target tracking data. Further, regularly verify the system output and track library, and promptly eliminate invalid and redundant tracks to ensure the track monitoring quality in a multi-target high-dynamic scenario.

[0293] This step can achieve fast adaptive update through a real-time maintenance strategy when the track moves, loses contact, or the target disappears, which is more real-time and accurate than the previous fixed track update method.

[0294] Embodiment 3: The embodiment of the present application provides a track fusion system of an incremental update Gaussian mixture model and multi-state transition filtering, which is applied to the track fusion method of the incremental update Gaussian mixture model and multi-state transition filtering in Embodiment 1 or Embodiment 2, as Figure 9 shown, including:

[0295] A data processing module, configured to perform time synchronization and format conversion on the observation information collected by the radar and electronic reconnaissance equipment at the same moment, and perform missing data filling and / or abnormal data filtering on the observation sequence obtained after time synchronization and format conversion to obtain a multi-source observation sequence;

[0296] A target classification module, configured to obtain feature vectors of the observation information at each time step in a multi-source observation sequence, and use a preset initialized improved incremental DP-GMM model to identify the target category of the feature vector at each time step, so as to obtain a target category label set representing the target category and its allocation information of each feature vector in the multi-source observation sequence;

[0297] An initial track generation module, configured to, based on the target category label set, form an observation subset through the observation information of the same target category in the multi-source observation sequence, use a preset multiple association gate and cost function to generate initial tracks for each observation subset, and obtain an initial track set containing the initial tracks of each observation subset;

[0298] A track association and optimization module, configured to screen and determine track pairs with potential interaction and / or conflict from the initial track set, and merge and / or eliminate each track pair by defining a global cost function related to track association, so as to form a target track set after removing crossing and / or interference;

[0299] A track quality analysis module, configured to obtain the observation records of multiple sensors on the same time series as the multi-source observation sequence, calculate the reliability weights of each sensor and the quality scores of each track in the target track set, and obtain a track quality score set containing the quality scores of each track, and a sensor weight set containing each reliability weight;

[0300] A fused track output module, configured to, based on a preset multiple state transition model, use the track quality score set and the sensor weight set to obtain a track fusion result, where the track fusion result includes a track state and a trajectory covariance matrix.

[0301] Example 4: An embodiment of the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the method of Example 1 or Example 2 is implemented.

[0302] Example 5: An embodiment of the present application provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause a computer to execute the method of Example 1 or Example 2.

[0303] The specific embodiments described above further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An incremental update Gaussian mixture model and multi-state transition filtering track fusion method, characterized in that, It includes the following specific steps: Perform time synchronization and format conversion on the observation information collected by the radar and electronic reconnaissance equipment at the same moment, and complete the missing data and / or filter the abnormal data in the observation sequence obtained after time synchronization and format conversion to obtain a multi-source observation sequence; Obtain the feature vectors of the observation information at each time step in the multi-source observation sequence, and use the preset initialized improved incremental DP-GMM model to identify the target category of the feature vector at each time step, and obtain a target category label set representing the target category and its allocation information of each feature vector in the multi-source observation sequence; Based on the target category label set, form an observation subset through the observation information of the same target category in the multi-source observation sequence, use the preset multiple association gates and cost functions to generate the initial tracks of each observation subset, and obtain an initial track set containing the initial tracks of each observation subset; Screen and determine the track pairs with potential interaction and / or conflict from the initial track set, and merge and / or eliminate each of the track pairs by defining a global cost function related to track association to form a target track set after removing intersections and / or interferences; Obtain the observation records of multiple sensors on the same time series as the multi-source observation sequence, calculate the reliability weights of each sensor and the quality scores of each track in the target track set, and obtain a track quality score set containing the quality scores of each track and a sensor weight set containing each reliability weight; Based on a preset multiple state transition models, use the track quality score set and the sensor weight set to obtain a track fusion result, and the track fusion result includes a track state and a track covariance matrix.

2. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 1, characterized in that Based on a preset multiple state transition models, use the track quality score set and the sensor weight set to obtain a track fusion result, specifically: Obtain the Sigma point set of multiple state transition models, and obtain the state prediction and covariance prediction of the Sigma point set; Calculate the model probability values of each target motion model at each moment by using the track quality score set; Based on the sensor weight set, calculate and obtain the comprehensive measurement vectors of each sensor; Based on the state prediction and covariance prediction, use the comprehensive measurement vector and the model probability value to obtain a track fusion result.

3. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 1, characterized in that The completion of the missing data is realized through an interpolation function, and the interpolation function is specifically: Where F i (t) is the interpolation function for filling in missing data, t is the time to be interpolated, (x i (t k+1 ) - x i (t k )) represents the observation increment of the sensor at adjacent times, (t k+1 - t k ) represents the length of the interpolation interval. For t not within any valid observation interval, set F i (t) to 0 and mark it as invalid, and ignore this part of the data.

4. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 1, characterized in that The identification of the target category of the feature vector at each time step is specifically: where p(z n = k|x n , α, x 1:n-1 ) represents the assignment probability with the feature vector for the target class k, π k represents the weight of the current k-th mixture component, p(x n |θ k ) represents the likelihood of the Gaussian distribution corresponding to the k-th component for x n , θ k represents the set of parameters of the mixture component k, including the mean μ k , the covariance Σ k , α represents the concentration parameter of the Dirichlet process, x 1:n-1 represents the prior data, and K represents the number of mixture components existing in the current model.

5. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 1, characterized in that Use the preset multiple association gates to calculate each observation point in each observation subset, perform weighted fusion on the calculation results of the multiple association gates, and use a preset threshold comprehensive gating judgment criterion specifically: Among them, (x, y) represents the rectangular coordinates of the observation points in one of the observation subsets, and (r, θ) represents the polar coordinate form of the observation points; R j (x, y) represents the gating function of the rectangular gate, E j (x, y) represents the gating function of the elliptical gate, S j (r, θ) represents the gating function of the sector gate. The value of the gating function being 1 indicates that the observation point is within the corresponding gated area, and the value being 0 indicates that the observation point falls outside the gate; represents the center of the gate corresponding to the gating function, (Δx j , Δy j ) represents the half-width of the rectangular gate, (a j , b j ) represents the semi-major and semi-minor axes of the elliptical gate, ρ j 、 respectively represent the radial and azimuth ranges of the sector gate, and the subscript j represents the category of the observation subset; Where, G j (x k , y k ) represents the result of weighted fusion of the calculation results of the multiple association gates, and w r , w e , w s are the weight factors of the rectangular gate, the elliptical gate, and the sector gate respectively, τ j is the comprehensive gating threshold for category j. If G j (x k , y k ) = 1, then the measurement point is included in the set of observations to be associated with the current category j; if G j (x k , y k ) = 0, then the data point is discarded.

6. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 5, characterized in that Represent the initial track in the observation set to be associated by a cost function, and the initial track is represented as: Wherein, represents the initial track of target category j, and (k, u) represents the index number of adjacent observation point pairs in track T j ; (x k , y k ) and (x u , y u ) respectively represent the coordinates of adjacent observation points, and t k , t u represent the corresponding acquisition times; Ω j represents the gating coincidence region of category j, and ω(ξ, η) represents the penalty weight for the deviation between discrete measurement points and the track path.

7. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 1, characterized in that Screen and determine the track pairs with potential interaction and / or conflict from the initial track set, specifically: where D(H i ,H j ) = 1 indicates that the track H i and the track H j have cross or dense interference in terms of time and space. Then the tracks H i and the track H j are a pair of tracks with potential interaction and / or conflict. represents the indicator function, which takes the value of 1 when the condition in the parentheses holds, otherwise 0; the set of moments in the track H i is T i , and the set of moments in H j is T j . The position of the track H i at the moment t k is . The position of the track H j at the moment t r is d0 is the selected fixed dynamic distance threshold, and Δt0 represents the time interval threshold.

8. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 1, characterized in that, The global cost function is specifically: Where, E(σ) is the global cost function, σ represents the current association scheme. Through multiple iterations of E(σ) and adaptive adjustment of the annealing temperature during the simulated annealing process, the track association scheme with the minimum global cost is searched for; represents the set index of all tracks, L(H i |σ) represents track H i 's retention and merging status under scheme σ, W(H i ,H j ) represents the mismatch penalty coefficient of track pair (H i ,H j ). The value of L(H i |σ) is related to whether track H i is retained or merged. The value of W(H i ,H j ) is dynamically set according to the track crossing severity. If D(H i ,H j ) = 1, a higher penalty is imposed on the situation where (H i ,H j ) is still regarded as an independent track under σ, so as to promote the preferential merging or filtering of crossing tracks; Each of the said track pairs is merged and / or removed to form a set of target tracks after removing intersections and / or interferences, specifically: after completing the optimization algorithm search through the global cost function E(σ), the finally converged association scheme σ* is analyzed, and for the track pairs (H i ,H j ) in the set A are processed according to the merge and retention flags in σ* to generate a set of target tracks.

9. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 1, characterized in that The reliability weights of each sensor are specifically: Among them, W k represents the reliability weight of sensor k, represents the time-varying noise distribution of sensor k itself, and R k represents the effective range of sensor k, and s (k) represents the working stability evaluated in a given environment. The integral term in the denominator of the formula is used to measure the cumulative impact of noise on the range, and s (k) comprehensively corrects the working stability by multiplying with the fraction to ensure that sensors with higher measurement stability contribute higher weights in subsequent fusion.

10. The track fusion method of incremental update Gaussian mixture model and multi-state transfer filtering according to claim 1, characterized in that The quality scores of each track in the target track set are specifically: In the formula, represents the quality score of the track, e dist (t) represents the ranging error, e ang (t) represents the angle measurement error, e hist (t) represents the difference between the track and the historical track, w d , w a , w h respectively represent the weights of the ranging, angle measurement, and historical difference terms, and t0 and t n respectively represent the start and end times of the track.

11. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 2, characterized in that The Sigma point set is specifically as follows: In the formula, denotes the set of Sigma points at time t, and x j (t) represents the state estimate, and P j (t) is the covariance estimate, n represents the dimension, denotes the column vector obtained by taking the p-th column or the (p - n)-th column of the symmetric decomposition matrix of (n + λ)P j (t); The state prediction and covariance prediction are specifically as follows: In the formula, represents state prediction, represents covariance prediction, is the i-th Sigma point in the Sigma point set, and W i (m) are the weights of each Sigma point, Q is the prior process noise covariance matrix, and n represents the total number of points in the Sigma point set.

12. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 2, characterized in that The calculation of the model probability values of each of the target motion models at each moment by using the track quality score set is specifically as follows: where μ j (t + 1) represents the model probability value of model M j at time t + 1, represents the track quality score, κ j (t) is the coefficient calculated according to the matching degree between the actual observation and model M j , and p represents the total number of target motion models.

13. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 2, characterized in that Based on the sensor weight set, the calculation of the comprehensive measurement vectors of each sensor is specifically as follows: where, z h (t) represents the comprehensive measurement vector of sensor k, W k represents the weight of sensor k, z k (t) is the measurement vector of sensor k, and K is the total number of sensors.

14. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 2, wherein The track state is specifically as follows: Where: Wherein, is the track state, and μ j (t) represents the model probability value of model M j at time t, κ j (t) is the coefficient calculated according to the matching degree between the actual observation and model M j . represents the quality score of the track , p represents the total number of target motion models, represents the state prediction, and K t represents the Kalman gain, z h (t) represents the comprehensive measurement vector of sensor k, and H is the prior observation matrix, represents the covariance prediction, and R is the prior measurement noise covariance.

15. The track fusion method of incremental update Gaussian mixture model and multi-state transition filtering according to claim 2, characterized in that The track covariance matrix is specifically as follows: Where: where P(t + 1) represents the trajectory covariance matrix, is the track state, and μ j (t) represents the model probability value of model M j at time t, and κ j (t) is the coefficient calculated based on the matching degree between the actual observation and model M j , represents the quality score of the track , p represents the total number of target motion models, represents the state prediction, and K t represents the Kalman gain, and z h (t) represents the comprehensive measurement vector of sensor k, H is the prior observation matrix, represents the covariance prediction, R is the prior measurement noise covariance, and I represents the positive definite matrix.

16. An incremental update Gaussian mixture model and multi-state transition filtering track fusion system, applied to the incremental update Gaussian mixture model and multi-state transition filtering track fusion method according to any one of claims 1-15, characterized in that, Including: A data processing module, configured to perform time synchronization and format conversion on the observation information collected by a radar and an electronic reconnaissance device at the same moment, and perform missing data complementation and / or abnormal data filtering on the observation sequence obtained after time synchronization and format conversion to obtain a multi-source observation sequence; A target classification module, configured to obtain the feature vectors of the observation information at each time step in the multi-source observation sequence, and use a preset initialized improved incremental DP-GMM model to perform target category recognition on the feature vectors at each time step to obtain a target category label set representing the target categories and their assignment information of each feature vector in the multi-source observation sequence; An initial track generation module, configured to form an observation subset based on the observation information of the same target category in the multi-source observation sequence based on the target category label set, and use a preset multiple association gate and cost function to generate initial tracks for each observation subset, and obtain an initial track set including the initial tracks of each observation subset; A track association optimization module, configured to screen and determine track pairs with potential interaction and / or conflict from the initial track set, and perform merging and / or elimination on each of the track pairs by defining a global cost function related to track association to form a target track set after removing crossing and / or interference; A track quality analysis module, configured to obtain the observation records of multiple sensors on the same time series as the multi-source observation sequence, calculate the reliability weights of each sensor and the quality scores of each track in the target track set, and obtain a track quality score set including the quality scores of each track and a sensor weight set including each reliability weight; A fused track output module, configured to obtain a track fusion result based on a preset plurality of state transition models by using the track quality score set and the sensor weight set, where the track fusion result includes a track state and a track covariance matrix.

17. An electronic device, characterized in that, Including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor implements the method according to any one of claims 1-15 when executing the computer program.

18. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method according to any one of claims 1-15.

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