A spaceborne radar group target multi-modal fusion tracking method

Abstract

This invention belongs to the field of target tracking technology and discloses a multimodal fusion tracking method for swarm targets using spaceborne radar. Addressing the problems of single-sensor data association criteria being singular, insufficient utilization of multimodal information, and difficulty in handling dynamic changes in the swarm target structure in high-speed, densely clustered target scenarios, this invention employs an interactive multi-model framework to maintain the target motion state. It uses radial distance residuals as the primary cost of association and structural similarity of high-resolution range images and statistical consistency of multidimensional attributes as conditional auxiliary evidence to construct a three-channel multimodal association criterion system. Furthermore, it introduces dual representations of separable and ungroupable tracks and four types of dynamic structure transformation operations to achieve unified management of swarm targets in groups during the dense phase and orderly disgrouping when they become distinguishable. This invention effectively improves the association tracking accuracy and robustness of single sensors in high-speed, densely clustered target scenarios.

Description

Technical Field

[0001] This invention belongs to the field of single-sensor multi-target tracking technology in the field of target tracking, specifically involving a multi-modal fusion tracking method for spaceborne radar swarm targets. Background Technology

[0002] In space-based detection systems, continuous and precise tracking of high-speed swarm targets using radar is one of the core tasks. During flight, high-speed swarm targets are often accompanied by the separation of passive jamming objects and various accompanying targets. The real target and various jamming targets move at similar high speeds near their flight paths, forming a dense swarm target scenario with a spatial scale of several kilometers and a considerable number of targets. Unlike typical multi-target scenarios such as aircraft formations and ship formations, high-speed swarm targets are characterized by a large number of targets, dense spatial distribution, rapid and unpredictable evolution of their motion, posing a significant challenge to traditional target tracking methods.

[0003] Existing multi-target tracking methods typically employ a recursive processing framework of "track prediction - data association - state update". In the data association stage, mainstream methods mainly include: non-probabilistic methods based on assignment (such as nearest neighbor, global nearest neighbor), probabilistic data association methods (such as joint probabilistic data association filter JPDA, multi-hypothesis tracker MHT), and methods based on random finite set theory (such as probabilistic hypothesis density filter PHD, generalized labeled multi-Bernoulli filter GLMB). These methods achieve good tracking results in general multi-target scenarios, but they have significant shortcomings in high-speed, densely clustered target conditions: First, relying solely on the spatial distance (such as Euclidean distance and Mahalanobis distance) between the kinematic prediction position and the measurement of the target as the association criterion, when multiple targets are at similar heights in space and their tracks intersect, the simple spatial geometric information is insufficient to provide enough distinguishing criteria, easily leading to misassociation and track mixing; Second, although the random finite set method can avoid explicit data association, its computational complexity and uncertainty management problems remain prominent in scenarios with a large number of densely clustered targets; Third, existing methods make very limited use of the physical characteristic information of clustered targets (such as radar high-resolution range profile (HRRP) and radar cross section (RCS), failing to fully utilize the multimodal information acquired by sensors to improve association reliability.

[0004] Furthermore, high-speed swarm targets may split and merge during their movement, i.e., a dynamic transformation between "separable" and "indivisible" states. Existing methods typically assume targets as independent point targets, lacking dynamic modeling and management mechanisms for the separability between targets and the swarm structure, leading to track breakage or track mixing when targets are densely adjacent. In summary, existing single-sensor multi-target tracking methods in high-speed, dense swarm target scenarios suffer from core problems such as single association criteria, insufficient utilization of multimodal information, and difficulty in handling dynamic changes in the swarm target structure. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-modal fusion tracking method for spaceborne radar swarm targets, in order to solve the problems of existing single-sensor multi-target tracking methods in high-speed, dense swarm target scenarios, such as single association criteria, insufficient utilization of multi-modal information, and difficulty in handling dynamic changes in the separable / indivisible structure of swarm targets.

[0006] To achieve the above objectives, the present invention employs the following technical solution: A multi-modal fusion tracking method for spaceborne radar swarm targets includes: Step 1: Construct the target's motion state model and measurement model, and predict the state of each track based on the interactive multi-model framework; Step 2: For each track and the current frame measurement, construct the distance channel cost matrix, the HRRP channel cost matrix, and the attribute channel cost matrix respectively to form a three-channel multimodal correlation cost. Step 3: Compress the distance channel cost and attribute channel cost to a preset range, and perform conditional fusion in combination with the HRRP channel cost to obtain the total cost of each track and measurement pairing, and construct a global fusion cost matrix based on the total cost; Step 4: Based on the global fusion cost matrix, perform global minimum cost bipartite matching using the Hungarian algorithm to complete the hard allocation of tracks and measurements; Step 5: Based on the matching results, perform the following four types of separable / ungroupable structure transformation operations in a fixed order: merging individual entities into existing groups, generating new groups from individual entities, merging groups and combinations, and degenerating groups back into individual entities. Step 6: Using the successfully associated measurements, update the measurements for each track using unscented Kalman filtering, and update the interactive multi-model probability based on the model likelihood, finally outputting the fused target state estimate.

[0007] Furthermore, in step 1, an interactive multi-model framework is used to construct a dual-model set containing a constant acceleration model and a gravity model. In the ECEF coordinate system, the target state vector contains position, velocity, and acceleration components in three coordinate axis directions. Each track maintains two sets of model states and their corresponding model probabilities simultaneously. At the beginning of each frame, interactive multi-model state mixing is performed. Subsequently, linear state prediction is applied to the constant acceleration model, and nonlinear state prediction is performed by generating Sigma points using unscented transformation for the gravity model. Based on the predicted states, the predicted radial distance and predicted radial velocity of each track are calculated, and the predicted radial velocity is used for subsequent coupling correction.

[0008] Furthermore, in step 2, for non-groupable tracks, they are expanded into a corresponding number of proxy lines according to the number of group members, so that the group track allows multiple measurements to compete in one frame; the distance channel cost is calculated as follows: when coupling correction is enabled, the corrected predicted radial distance is calculated based on the coupling coefficient and the predicted radial velocity, and the normalized radial distance residual is calculated as the distance channel base cost based on the corrected predicted radial distance. At the same time, dual hard gating constraints of spatial gating and radial gating are applied, and the spatial threshold and radial threshold are dynamically scaled according to the number of frames from the last measurement update; for group tracks, they are additionally multiplied by preset spatial and track path threshold scaling factors to match their multi-measurement acceptance modeling objectives.

[0009] Further, in step 2, the calculation of the HRRP channel cost is as follows: for each track-measurement candidate pair that passes through the range gate, the historical HRRP sequence is extracted and a translation template is generated within the translation window. The maximum translation cosine similarity between each historical HRRP and the currently detected HRRP is calculated, and the HRRP channel cost is obtained by weighting and summing according to the time decay weight. The calculation of the attribute channel cost is as follows: a 7-dimensional attribute vector containing centroid, standard deviation, skewness, kurtosis, radar cross section, range broadening, and number of scattering points is extracted from the HRRP. A difference vector is constructed based on the common effective dimension, and the Mahalanobis distance is calculated using the attribute covariance submatrix. The attribute channel cost is obtained by weighting and averaging according to the time weight.

[0010] Further, in step 3, the distance channel cost and attribute channel cost are compressed to a preset range through monotonically compressed mapping. During conditional fusion, for each track and measurement pairing, the three-channel weighted fusion is performed to obtain the total cost only when the distance channel cost is not infinite and the HRRP channel cost and attribute channel cost simultaneously meet the activation conditions. When any of the three channels is invalid, it degenerates to using only the scaled distance channel cost as the total cost. Based on the final total cost of all pairings, according to the extension logic of the proxy row, the row index is restored to the original track index through the mapping function from row index to track index, thereby constructing a global fusion cost matrix.

[0011] Further, in step 4, the Hungarian algorithm solves the global minimum cost bipartite matching problem based on the global fusion cost matrix to obtain the decision variables for each extended row and measurement. After the Hungarian algorithm is completed, the row indexes in the global fusion cost matrix are folded back to the corresponding track indexes at the bottom layer through a mapping function, and the successfully matched measurements are assigned to the original track. Finally, two levels of matching information are output: the first level is the matching result, that is, the physical pairing of all extended rows and measurements output by the Hungarian algorithm; the second level is the association success relationship, that is, the association success relationship obtained by filtering the matching results for cost validity.

[0012] Furthermore, in step 5, for each mature ungroupable track, the mature separable tracks that meet the conditions are assigned to the track group using the Hungarian algorithm; from the mature separable tracks that have not yet been merged into any group, multiple separable tracks that maintain a continuous spatial proximity relationship are identified to form a spatial candidate group, and the HRRP distance and attribute distance are used to refine the judgment and form a new ungroupable track. The state of the new track group is initialized using the moment matching method; existing track pairs are scanned, and if the distance between groups meets the grouping threshold, the clusters are identified and merged through graph connected components.

[0013] Furthermore, the process of group degenerating back to individual is as follows: First, within the set first sliding window length, the number of echoes associated with the group track is counted, and the number of group members is updated with the maximum number of echo frames. If the updated Then, within the set second sliding window length, imaging frames are selected, and a minimum spanning tree is constructed based on the echo positions within the group. The maximum edge of the minimum spanning tree is calculated. and to The average splitting gap is obtained by performing a time-weighted average. ;like Greater than the splitting determination threshold If the split is confirmed, the number of group members will be reduced by one; when the number of members is updated in a certain frame... When the original group of tracks is terminated, a new separable track is created based on the current group state. The initial state and covariance of the new track directly inherit the state estimate and covariance of the original group of tracks.

[0014] Further, in step 6, the measurement set assigned to the current frame is collected for each track; if the measurement set contains multiple echoes, the radial distance, azimuth angle, pitch angle and coupling coefficient are averaged to form an equivalent measurement; for each model, the Sigma point is generated based on the predicted state and propagated through the measurement function to obtain the measurement prediction mean and innovation covariance. The equivalent measurement is used to update the state estimate mean and covariance through the unscented Kalman filter equation, and the probability of each model is updated according to the Gaussian likelihood function of the measurement innovation. Finally, the updated model probabilities are weighted and output to obtain the fused target state estimate.

[0015] An electronic device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the multimodal fusion tracking method for spaceborne radar swarm targets.

[0016] A computer-readable storage medium storing a computer program; when the computer program is executed by a processor, it implements the multi-modal fusion tracking method for spaceborne radar swarm targets.

[0017] Compared with the prior art, the present invention has the following technical features: 1. Breaking through the technical limitations of traditional methods that rely solely on spatial distance for data association, this paper constructs a three-channel multimodal association criterion system with "radial distance residual as the main cost and HRRP spectral similarity and multidimensional attribute Mahalanobis distance as conditional auxiliary evidence". This fully utilizes the target radiation feature information acquired by sensors to enhance the association discrimination capability, thereby increasing the accuracy of track association in high-speed, densely clustered target scenarios from 49.73% to 93.15%.

[0018] 2. By introducing dual representations of separable and non-groupable tracks and four types of dynamic structural transformation operations (merging individual targets into existing groups, generating new groups from individual targets, merging groups and combinations, and degenerating groups back into individual targets), the problem of track mixing and frequent breakage caused by forced target-by-target discrimination during the spatial proximity phase of target clusters is effectively solved. This transforms track maintenance during the target-dense phase from "passive breakage followed by restart" to "orderly disgrouping when distinguishable after unified management." Combined with a three-channel multimodal association strategy, the association accuracy is further improved to 98.57%.

[0019] 3. A "gated evidence" fusion strategy is adopted, meaning that multimodal weighted fusion is only activated when the range channel, HRRP channel, and attribute channel are all valid in a certain track-measurement pair; otherwise, it automatically degenerates into range-only decision-making. This mechanism avoids introducing misleading noise into the associated decision-making process from the source by low-quality or missing auxiliary modal information, ensuring that the multimodal enhancement effect is always based on reliable evidence. Attached Figure Description

[0020] Figure 1 This is a block diagram of single-sensor multimodal multidimensional correlation tracking technology; Figure 2 A timeline of the evolution of clustered targets across the entire scenario; Figure 3 A Cartesian coordinate flight trajectory diagram of clustered targets across the entire scene; Figure 4 This is a time-varying graph of the target evolution of a detection cluster using a certain sensor in the embodiment; Figure 5 For the distance analysis of a relatively close target pair of a certain sensor in the embodiment, (a) is a timeline of the spatial set of different targets, and (b) is a graph of the distance between targets changing over time; Figure 6 This is a spatial distance-based Gantt chart of the flight paths in the embodiment. Figure 7 This is a spatial distance-only correlation track purity map in the embodiment; Figure 8 This is the HRRP-assisted associated track Gantt chart in the embodiment; Figure 9 This is the HRRP-assisted correlation track purity map in the embodiment; Figure 10 The example uses HRRP-assisted association + non-groupable transformed track Gantt chart. Figure 11 This is the HRRP-assisted + non-grouping transformation associated track purity map in the embodiment. Detailed Implementation

[0021] This invention provides a multimodal fusion tracking method for swarm targets using spaceborne radar. Addressing the problems of limited single-sensor data association criteria, insufficient utilization of multimodal information, and difficulty in handling dynamic changes in swarm target structure in high-speed, densely clustered target scenarios, this invention employs an Interacting Multiple Model (IMM) framework to maintain target motion states. It uses radial distance residuals as the primary association cost and structural similarity and statistical consistency of multidimensional attributes from High Resolution Range Profiles (HRRPs) as conditional auxiliary evidence to construct a hierarchical multimodal association criterion system. Furthermore, it introduces a dual representation and dynamic transformation mechanism for separable and ungroupable tracks, enabling unified management of swarm targets in groups during dense phases, orderly disgrouping when distinguishable, and stable association tracking of high-speed, densely clustered targets. The specific steps of this invention are as follows: Step 1: Construct the motion state model and measurement model of the target. Based on the interactive multi-model framework, perform state prediction for each track to obtain the predicted position, predicted radial distance, and predicted radial velocity.

[0022] Step 1.1: Using an interactive multi-model framework, a dual-model set is constructed, comprising a constant acceleration model CA (Model 1) and a gravitational model GRAV (Model 2); in the ECEF coordinate system, the target state vector is taken as 9-dimensional: ; in, They represent The position components of the target on the three coordinate axes of the ECEF coordinate system at any given time. These represent the corresponding velocity components. These represent the corresponding acceleration components, with superscripts indicating the components. This represents the vector transpose, and the same applies below; each track maintains two sets of model states simultaneously. and and their corresponding model probabilities and (The probability that the model best represents the target's current true motion pattern at the current moment); where the superscripts 1 and 2 represent the parameters of the constant acceleration model and the gravitational model, respectively. They represent The posterior state estimation vector maintained by the constant acceleration model and the gravitational model. These represent the corresponding state estimation error covariance matrices. Target state vector. It forms the basis for state propagation and prediction in subsequent steps 1.2 to 1.4.

[0023] Step 1.2, the constant acceleration model CA adopts a discrete constant acceleration motion model; let... For the sensor sampling period, the third-order discrete CA state transition submatrix on a single coordinate axis of the ECEF coordinate system is: ; The third-order discrete CA state transition submatrix corresponding to the three coordinate axes By combining the components, we obtain a 9-dimensional state transition matrix. The process noise covariance is obtained by discretizing the white noise acceleration template. ; Represents the block diagonal matrix operator.

[0024] Gravitational models no longer use linear state transition matrices, but instead employ nonlinear functions. Perform state propagation: ; in This represents the nonlinear function of state propagation in the gravitational model, whose dynamics include geocentric gravitational terms, Coriolis force terms in the Earth's rotational reference frame, and centrifugal force terms. For zero-mean Gaussian process noise, its covariance matrix is: ; They represent Time and The target state vector at time t.

[0025] Step 1.3: At the beginning of each frame, using the state estimates and model probabilities from the previous frame for both the constant acceleration model and the gravity model, perform interactive multi-model (IMM) state mixing; let... Time model The model probability is ,Model To model The transition probability is The mixture probability is: ; ; in, The normalization constant representing the probability of the prediction model. 1 represents the mixed probability; 1 and 2 represent the constant acceleration model and the gravitational model, respectively.

[0026] The initial state and covariance after mixing are as follows: ; ; in, Indicates the index of the previous discrete time frame; Indicates the index of the model. Represents a constant acceleration model. Represents a gravitational model; Indicates the index of the target model, also Represents a constant acceleration model. Represents a gravitational model; Indicates in Time, Model Independently maintained posterior state estimation vector; Indicates the mixed probability; Indicates the model The calculated mixed initial state, with the superscript 0 used to mark this state as the initial state; Indicates in Time model Independently maintained posterior state estimation error covariance matrix; This represents the calculated initial covariance of the mixture.

[0027] Step 1.4: Perform state prediction for each model; for the constant acceleration (CA) model, use linear prediction: ; ; in and These are the mixed initial state and mixed initial covariance of the constant acceleration model obtained in step 1.3, respectively. and The predicted state and predicted covariance for the constant acceleration model; and The state transition matrix obtained in step 1.2 and the discretized process noise covariance are given.

[0028] For the gravity model, an unscented transformation is used to generate Sigma points for nonlinear propagation to obtain the predicted state. and predicted covariance .

[0029] For the Gravitational Aspect-Oriented Model (GRAV), an unscented transformation is used to generate sigma points for nonlinear propagation to obtain the predicted state. and predicted covariance .

[0030] Step 1.5: Based on the predicted state, calculate the predicted radial distance for each track; project the predicted position onto the radar polar coordinate space using a measurement function. ; in, This indicates the predicted radial distance of the trajectory; This is the geometric transformation function that converts ECEF coordinates to radar radial range; To utilize the predicted state of the trajectory obtained in step 1.4; simultaneously calculate the predicted radial velocity (target velocity relative to radar): ; in, Indicates the target's predicted radial velocity; The predicted velocity vector of the target; This is the velocity vector of the radar sensor itself. The predicted position vector of the target; The position vector of the radar sensor; symbol Dot product of vectors; symbol This represents the Euclidean norm of the vector. The predicted radial velocity... Used for coupling correction in subsequent step 2.2.

[0031] Step 2: For each track and the current frame measurement, construct the distance channel cost matrix, the HRRP channel cost matrix, and the attribute channel cost matrix respectively to form a three-channel multimodal correlation cost.

[0032] Step 2.1, expand the track correlation matrix.

[0033] In order to base the fusion cost matrix in step 4 Perform algorithmic matching; for non-groupable tracks, match by the number of group members. Expand as Each proxy line shares the prediction results of the same set of tracks, allowing multiple measurements (a complete, independent set of echo data detected by a radar sensor for a specific target within a single scan cycle) to compete within a single frame for a set of tracks; these proxy lines are then used in the fusion cost matrix in step 4. The position number occupied in the middle is called the row index (denoted as in step 4). The unique identifier of the original group track stored at the system's underlying layer is called the track index; the mapping function from the row index to the track index... Fold the proxy line back to the original group track. After step 4 (Hungarian algorithm) is completed, use... Fusion cost matrix row index in This provides the premise for restoring the track index and updating the original group track.

[0034] This scheme introduces a dual representation and dynamic conversion mechanism for separable and non-groupable tracks. A separable track refers to a single track consisting of an independent target, without an internal member list. A non-groupable track refers to a group track consisting of multiple spatially adjacent targets with similar motion states, maintaining a list of members within each group. The system includes a member list and a unified group state; during association, multiple metrics can compete via the proxy line expansion mechanism in step 2.1; and during state updates, multiple associated metrics are aggregated into an equivalent metric via step 6. It performs overall updates and can dynamically transform structures such as merging between groups and degenerate individual units according to steps 5.3 and 5.4; it enables unified management of clustered targets in groups during dense phases, orderly disgrouping when distinguishable, and stable correlation tracking of high-speed dense clustered targets.

[0035] Step 2.2, Calculate the distance channel cost.

[0036] When coupling correction is enabled, the track is first... With measurement Calculate the corrected predicted radial distance: ; If the track does not meet the conditions for enabling coupling correction (non-separable stable track or cumulative measurement update count not reaching the configured threshold), then... ;in For the track With measurement Coupled-corrected prediction of radial distance after pairing; To utilize the track calculated in step 1.5 The predicted radial distance; For the first The coupling coefficient of each measurement; For the track The predicted radial velocity; The radar beam center pointing velocity. The range channel fundamental cost is taken as the normalized radial range residual: ; in, Indicates the flight path With measurement Distance channel cost; For measurement radial distance, The standard deviation of the radial distance measurement noise is used. Simultaneously, a double hard-gating constraint is applied: Spatial gating: After back-calculating the measurements to ECEF coordinates, the Euclidean distance is compared with the predicted position. ,like ,but ; Radial gating: if ,but .

[0037] in, For measurement Calculate the position vector in the ECEF coordinate system; For the track Predicted position vector in the ECEF coordinate system; Spatial distance threshold; This is the radial distance threshold.

[0038] Step 2.3, Adaptive prediction frame number gating.

[0039] Based on the number of frames since the last measurement update. Dynamically scaling threshold; if Then the space gate scaling factor is (its upper limit is) The radial gate scaling factor is (its upper limit is) For group tracks, multiply by a preset group track spatial threshold scaling factor. Radial threshold scaling factor of the group track This allows the group of tracks to have a more relaxed threshold to match its multi-measurement acceptance modeling objectives.

[0040] in, The sequence number of the current frame; For the track The frame number of the last measurement update; This is the spatial threshold scaling index; This is the radial threshold scaling exponent.

[0041] Step 2.4, HRRP channel cost calculation.

[0042] For each track-measurement candidate pair that passes distance gating, extract the historical HRRP sequence of that track; assuming that the track has a total of Each historical HRRP record is normalized and then displayed in a panning window. A set of translation templates is generated internally; the cosine similarity between each historical HRRP and the currently detected HRRP is: ; in, Indicates the maximum number of units allowed for translation; Indicates the first Maximum translational cosine similarity between historical HRRPs and the currently detected HRRPs; For the first Historical HRRP translation Template vector after distance units; This is the HRRP vector detected in the current frame.

[0043] After time-weighted aggregation, the HRRP channel cost is: ; in, Indicates the flight path With measurement HRRP channel cost; Indicates the first The historical HRRP has a time decay weight, and the weight setting makes the more recent historical HRRP contribute more to the cost.

[0044] That is, HRRP channel cost for (Time-weighted maximum translational cosine similarity), the smaller the cost, the stronger the HRRP spectrum consistency. The time decay weight (normalized) makes the contribution of more recent historical HRRPs to the cost greater. The HRRP channel is only enabled when the track has available historical HRRP data, the current echo is filtered through the kurtosis threshold, and the candidate line is not a group track agent line.

[0045] Step 2.5, Calculate the attribute channel cost.

[0046] Extracting a 7-dimensional attribute vector from HRRP: ; Each dimension is represented in turn: Indicates the center of mass; Indicates standard deviation; Indicates skewness; Indicates kurtosis; Represents the radar cross section (RCS); Indicates widening of distance; This indicates the number of scattering points.

[0047] For each flight path Historical attribute samples With the current detection attribute vector (i.e., the current 7-dimensional attribute vector) Constructing the first dimension on the common effective dimension. The difference vector between each historical attribute sample and the current detected attribute vector Using attribute covariance submatrices on common effective dimensions Calculate the Mahalanobis distance and then perform a time-weighted average: ; in, This indicates the number of historical samples representing the attributes of the flight path. For the first A vector of historical attribute samples; For the first Time weights of historical samples; This represents the attribute channel cost. The superscript T in the parameter indicates transpose, and the same applies below.

[0048] If a historical sample has no common valid dimensions with the current detection, the sample is skipped.

[0049] Step 3: Compress the distance channel cost and attribute channel cost to a preset range, and perform conditional fusion in combination with the HRRP channel cost: For each track-measurement pair, only when the distance cost, HRRP cost and attribute cost are all valid at the same time will the three-channel weighted fusion be performed to obtain the total cost; otherwise, it will degenerate into using only the distance channel cost as the decision basis.

[0050] The multimodal conditional fusion strategy is as follows: Step 3.1, cost compression.

[0051] The distance channel cost obtained in step 2.2 and the attribute channel cost obtained in step 2.5 Compressed to respectively using monotonic compression mapping The interval is obtained and HRRP channel cost It is a similarity-based distance, already... Within the specified range, no additional compression is required.

[0052] Step 3.2, Conditional Fusion. For each track-measurement pairing... Three-channel weighted fusion will only be performed if all three of the following conditions are met simultaneously: (a) (Distance channel is valid, i.e., through dual hard gating); (b) The HRRP channel is valid, meaning the activation conditions in step 2.4 are met. (c) Exists (the attribute channel is valid, i.e., the activation condition in step 2.5 is met).

[0053] If all three conditions are met, the total cost is: ; in, For the track With measurement The final total cost of fusion; For step 2.2, the distance channel cost The value after scaling in step 3.1; For the HRRP channel cost in step 2.4; For the attribute channel cost in step 2.5 The value after scaling in step 3.1; The fusion weights for the three channels satisfy... If any of the three channels is invalid, it degenerates directly to: ; This strategy uses only distance and channel cost as the basis for decision-making. It ensures that multimodal information participates in decision-making only when the evidence is complete, avoiding the introduction of noise from unreliable information from a single modality.

[0054] After step 3.2 is completed, for all track-measurement pairs... The system has obtained the final scalar cost of fusion. In order for step 4 to perform a global match, it must be organized into a dimension of Fusion cost matrix Because in step 2.1, ungroupable tracks were sorted by the number of members. It unfolded One proxy line, therefore the matrix The actual row index becomes ( ). Matrix elements The assignment follows the following mapping logic: first, through the mapping function... Row index Restore to the original track index used in steps 2.2, 2.4, 2.5, and 3.1. Then connect the agency with the measurement Corresponding final channel cost , , Fill in matrix elements middle.

[0055] Step 4, based on the fusion cost matrix The Hungarian algorithm is used to perform global minimum cost binary matching to complete a one-to-one hard allocation of tracks and measurements.

[0056] Let the number of rows after the ungroupable track is expanded be . The number of measurements is Each extended row matches at most one measurement, and each measurement matches at most one extended row; based on the fusion cost matrix Solve the global minimum cost bipartite matching problem using the Hungarian algorithm:

[0057] Satisfy constraints: (Each extended line can match at most one measurement) (Each measurement can match at most one extended line.)

[0058] in The total number of extended rows after expanding a non-groupable track by the number of group members ( , (The original number of tracks) Fusion cost matrix The Middle row (i.e., row index is) (the agency) and measurement The matching cost; Assign a matrix to the global binary system, consisting of all decision variables. The composition serves as the optimization objective of the Hungarian algorithm; ; Indicates the navigation index is Agency and Measurement Match, otherwise .

[0059] Therefore, step 4 ultimately outputs matching information at two levels. The first level is the matching result output by the Hungarian algorithm, i.e., all matching results that satisfy... The hard allocation relationship corresponds to the physical pairing of the proxy line and the measurement; the fusion cost matrix row index in Through mapping function The corresponding track index is collapsed back to the underlying layer, thereby assigning the successfully matched measurements to the group of tracks.

[0060] The second level is the successful association relationship, which means filtering the matching results and only including those that simultaneously meet the criteria. and The pairing is considered a successful association.

[0061] Step 5, based on the matching results obtained in Step 4 (satisfying...) All agent lines and measurement hard assignment relationships, and all paired sets after being folded back to the original track index through the mapping function, are executed in a fixed order, performing four types of separable / ungroupable structure transformation operations: merging individual units into existing groups, generating new groups from individual units, merging groups and combinations, and degenerating groups back into individual units.

[0062] In the operation description of step 5, "single" refers to a separable track that has not formed a group structure and maintains state estimation as an independent individual; "mature" refers to the track that has accumulated a number of updates in the time domain that meet the configuration threshold (corresponding to the cumulative number of measurement updates in the coupling correction enable condition in step 2.2) and has a high correlation confidence.

[0063] The separable / ungroupable conversion management process executes the following four steps frame by frame, using multi-frame spatial / radial geometric relationships as the primary criterion. In the "generating new groups from single entities" stage, HRRP spectral distance and attribute statistical distance are further used to refine the spatial candidate groups: Step 5.1, Merging Individual Tracks into Existing Groups: For each mature existing ungroupable track, scan all mature separable tracks. Construct an allocation cost matrix based on the spatial / radial distance within a multi-frame window and the current frame's hard gating. Use the Hungarian algorithm to assign eligible separable tracks to existing group tracks. Remove the assigned separable tracks from the individual track set and merge them into the group tracks. Update the group's member list, number of members, and structural change timestamps.

[0064] Step 5.2, Generation of New Groups from Individual Tracks: From mature separable tracks that have not yet been merged into any group, based on the spatial / radial mixing distance and relative positional relationship stability within a multi-frame window, multiple separable tracks with continuously maintained spatial proximity relationships are identified to form spatial candidate groups. These candidate groups are then refined using HRRP distance and attribute distance, and the final ungroupable track is formed based on the union of available evidence. Multiple separable tracks that meet the criteria are removed from the individual track set, creating a new ungroupable track. The state initialization of the group track uses the moment matching method, fusing the estimated state and covariance of each member track. ; ; in, The state estimation vector for the newly generated group of tracks; The state covariance matrix of the newly generated group of tracks; The number of members in the group; and The first The state estimation vector and covariance matrix of each member's trajectory.

[0065] Step 5.3, Grouping and Merging: Scan all existing group track pairs. Based on the spatial / radial mixing distance in the most recent multi-frames and the hard gate of the current frame, if the inter-group distance meets the merging threshold, identify the groups to be merged through the graph connected components and merge them into a larger group track. The merged state is initialized using the same moment matching method as in Step 5.2.

[0066] Step 5.4, group degenerates back to monomer: When a group degenerates, it first reverts to the nearest monomer. The number of echoes associated with the track within the frame is counted, and the number of group members is updated based on the maximum number of echoes in frames with echoes. If after the update Then in the most recent Within a frame, select imaging frames, construct a minimum spanning tree (MST) based on the echo positions within the group, and calculate the maximum edge of the MST. The average splitting gap was obtained by performing a time-weighted average on the data. ;like (If the persistent splitting condition is met, then update) ;in, This is the length of the sliding window used to count the number of group members; The length of the sliding window used to evaluate the group splitting state; This is the threshold for determining splitting.

[0067] When the number of members is updated in a certain frame When the original group track is terminated, a new separable track is created based on the current group state. The new track is assigned a new track ID, and its initial state is... Covariance It directly inherits the state estimate and covariance of the current group's trajectory.

[0068] Step 6: Using the measurements successfully associated in Step 4, update the measurements for each track using unscented Kalman filtering, and update the interactive multi-model probability based on the model likelihood, finally outputting the fused target state estimate.

[0069] Specifically, for each track, the measurement set assigned to the current frame is collected. If the measurement set contains multiple echoes (e.g., multiple measurements are matched to an ungroupable track via a proxy), the radial distance, azimuth, pitch angle, and coupling coefficient are averaged to form an equivalent measurement. For each model, the sigma points generated based on the predicted state are propagated through the measurement function to obtain the measurement prediction mean and innovation covariance. The equivalent measurement is then used to calculate the state estimate mean and covariance through the UKF update equation. The probabilities of each model are updated based on the Gaussian likelihood of the measurement innovation, and the target state estimate after the fusion of the two models is output. Specifically, this includes: Step 6.1, for the model Based on the predicted state obtained in step 1.4 and predicted covariance Generate sigma points, and obtain the measurement prediction mean after propagation through the measurement function. and new information covariance Using equivalent measurement The mean of the state estimate is calculated using the UKF update equation. Covariance : ; ; in For the model exist The predicted state vector at time step; For the model exist The prediction covariance matrix at time step; For the model The mean of measurement predictions obtained through measurement function propagation; For the model The measurement information covariance matrix; This is the equivalent measurement vector formed at the beginning of step 6; For the model The unscented Kalman filter gain matrix; For the model The updated state estimation vector; For the model The updated state covariance matrix.

[0070] Step 6.2: Calculate the likelihood function for each model based on the measurement innovation and Gaussian likelihood. ; in For the model exist The likelihood function at time t; The mean is Covariance is The multidimensional Gaussian probability density function; updating model probabilities: ; ; in, To the model To model The transition probability; Model of the previous time step The model probability; For the model The probability of the prediction model; For the model Updated model probabilities; For the model exist The likelihood function at time t; For the model The probability of the prediction model.

[0071] Step 6.3, output the fused target state estimate: ; ; in, For the model in step 6.1 The updated state estimation vector; For the model in step 6.1 Updated state covariance matrix; For the model in step 6.2 Updated model probabilities; For the estimation of the overall state after fusion; The total covariance matrix after fusion; It includes position and velocity estimates for the target in the three coordinate axes, with the position component being the target tracking result for the current frame. This is the final tracking result of the target state vector defined in step 1.1.

[0072] Determine whether the measurement in the current frame is the measurement data of the sensor at the last moment. If so, end the tracking; otherwise, jump to step 1 and enter the next frame processing loop.

[0073] Example: Spaceborne radar continuously observes high-speed cluster targets in flight. These sub-targets are spatially highly proximate, exhibit similar motion states, and their radar measurement models display significant nonlinear characteristics. In this scenario, relying solely on a single information source is insufficient for stable and reliable track association: if spatial geometric relationships are relied upon, close-range parallel flight and short-term track intersections can easily lead to batch mixing; if only radiation features such as HRRP are used, they are susceptible to instability and similarity interference, resulting in a significant decrease in discrimination capability at low signal-to-noise ratios or feature degradation. To address the aforementioned issues of easily confused spatial information and unstable feature information, this solution establishes a single-sensor multimodal multidimensional correlation tracking algorithm framework. This framework integrates target motion state, measurement-track correlation, and track group structure into a recursive processing flow, coordinating the coupling relationship among these three elements during sequential observation. The algorithm framework is as follows: Figure 1 As shown.

[0074] The high-speed cluster target flight simulation scenario used for algorithm verification lasted 554.95 seconds, with 19 targets appearing throughout the process. The target with ID 0 is the parent target, and the remaining sub-targets are released during the flight. Figure 2 The appearance and disappearance process of all ID targets in the full-scene cluster is shown. Table 1 contains the detailed evolution time of each target. Figure 3 The flight trajectory of the swarm targets in the Cartesian coordinate system is shown.

[0075] Table 1. Timeline of Cluster Target Evolution in All Scenarios (Unit: / s)

[0076] This section only shows the observation and tracking results of the spaceborne radar with ID 34 on a finite time frame for swarm targets. The evolution timeline of the detected swarm targets is shown below. Figure 4 As shown, please refer to Table 2 for details. Figure 5 For the analysis of targets that are spatially close in the scene, it is clear that the parent target with ID 0 will maintain a relatively close distance with the other targets for a period of time after each split when a new target is generated. This distance will increase over time and eventually make the parent target and the targets it splits out become separable again in the spatial distance dimension.

[0077] Table 2. Timeline of target evolution in the detection swarm by sensor 34 (unit: / s)

[0078] First, under the condition of using only spatial distance for cluster target data association, without introducing radial distance and HRRP auxiliary information, and without enabling the dynamic transformation mechanism of separable / non-groupable, cluster target association tracking is performed based on the Bayesian sequential estimation framework, and the results are as follows. Figure 6 The Gantt chart of the tracks, plotted based on the tracking results, shows time on the horizontal axis and each track on the vertical axis. Different colors distinguish the different targets to which the measurements belong. This chart visually reveals the target affiliation of each track during the association process. It is evident that relying solely on spatial distance results in frequent track batch mixing in the tracking results. This indicates that in scenarios with dense targets, relying solely on spatial distance is insufficient to reliably complete data association tasks. Figure 7 This is a purity map of tracks based on the same tracking results. The horizontal axis represents time, and the vertical axis corresponds to the purity of each tracking track. Purity is defined as the proportion of correct measurements among all measurements associated with a track that correspond to the actual target of that track. Observation shows that... Figure 6 The results were consistent: all tracked tracks exhibited significantly lower purity due to batch mixing, while purity essentially measures the association accuracy from a single track perspective. In summary, when relying solely on spatial distance to associate clustered target data, batch mixing of tracks occurs frequently, resulting in an overall low association accuracy.

[0079] Furthermore, after introducing features such as radial distance residuals and HRRP as auxiliary information to participate in the association, the tracking results are as follows: Figure 8 and Figure 9 As shown. Figure 8 For HRRP-assisted track Gantt charts, and Figure 6 In comparison, the target attribution of the measurements associated with each track tends to be consistent, and the phenomenon of mixed batches is significantly suppressed. Figure 9 The corresponding track purity maps show a significant improvement in the purity of each track, indicating a substantial improvement in the proportion of correctly correlated measurements within the tracks. These results demonstrate that the introduction of HRRP auxiliary information effectively enhances the correlation discrimination capability, significantly alleviates the problem of mixed track batches, and markedly improves the correlation accuracy.

[0080] Based on the introduction of radial distance residuals and HRRP auxiliary information (i.e., enabling a three-channel conditional association strategy), a dynamic transformation mechanism for separable / non-groupable targets is further enabled, and cluster target association tracking is performed based on the same Bayesian sequential estimation framework. The results are as follows: Figure 10 and Figure 11 As shown. Figure 10 This is a Gantt chart of the track based on the tracking results. Figure 8 As can be seen from the comparison, the introduction of the group management mechanism significantly suppressed the phenomenon of mixed track batches. A typical scenario in which this mechanism plays a key role is the splitting process of the parent target: such as... Figure 5As shown, in the initial stage after each split of the parent target (number 0) to generate new components, the spatial distance between the new target and the parent target is extremely close, exceeding the resolution capability of the sensor at this stage. At this point, relying solely on the three-channel correlation strategy may still result in unstable correlation. However, the separable / ungroupable conversion mechanism in this method, upon detecting stable maintenance of spatial proximity relationships across multiple frames, promptly merges the multiple indistinguishable targets within this stage into a single ungroupable track and performs a unified estimation of its overall state. Subsequently, as the target spacing gradually increases during flight and the spatial separation trend persists across multiple frames, the ungroupable track automatically disgroups, degenerating into multiple separable tracks, restoring independent tracking of each individual target. Figure 10 The Gantt chart shows that during the grouping-maintaining-ungrouping process, the separable tracks of each target did not become mixed, and the measurements associated with each track basically maintained the correct target attribution.

[0081] Figure 11 This is a track purity map plotted based on the same tracking results. It is associated with only HRRP assistance. Figure 9 Compared to previous models, the overall purity of each track was significantly improved. This result indicates that without a group management mechanism, the system would be forced to perform one-to-one assignments among multiple spatially close measurements during the brief period after target separation, which could easily lead to misassociations and track mixing. However, by enabling the separable / non-groupable conversion mechanism, the system manages dense targets uniformly in the form of non-groupable tracks during this phase, effectively avoiding forced assignments under low reliability. Once targets are fully separated and grouping conditions are no longer met, ungrouping is performed and one-to-one tracking is restored. Thus, the purity of each track can be maintained at nearly 100%, avoiding a decrease in purity caused by dense target convergence. Comparing the association accuracy results, the accuracy was only 49.73% when relying solely on spatial distance, improved to 93.15% after using radial distance residuals and HRRP assistance, and further reached 98.57% after combining the separable / non-groupable dynamic conversion mechanism. In summary, the three-channel association strategy, which is based on radial distance residuals and supplemented by HRRP and attributes, and works in conjunction with the dynamic conversion mechanism of separable / non-groupable, is the key to ensuring the quality of association tracking of clustered targets throughout their entire lifecycle. Simulation results also fully verify the effectiveness of the proposed algorithm.

[0082] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A multi-modal fusion tracking method for spaceborne radar swarm targets, characterized in that, Includes the following steps: Step 1: Construct the target's motion state model and measurement model, and predict the state of each track based on the interactive multi-model framework; Step 2: For each track and the current frame measurement, construct the distance channel cost matrix, the HRRP channel cost matrix, and the attribute channel cost matrix respectively to form a three-channel multimodal correlation cost. Step 3: Compress the distance channel cost and attribute channel cost to a preset range, and perform conditional fusion in combination with the HRRP channel cost to obtain the total cost of each track and measurement pairing, and construct a global fusion cost matrix based on the total cost; Step 4: Based on the global fusion cost matrix, perform global minimum cost bipartite matching using the Hungarian algorithm to complete the hard allocation of tracks and measurements; Step 5: Based on the matching results, perform the following four types of separable / ungroupable structure transformation operations in a fixed order: merging individual entities into existing groups, generating new groups from individual entities, merging groups and combinations, and degenerating groups back into individual entities. Step 6: Using the successfully associated measurements, update the measurements for each track using unscented Kalman filtering, and update the interactive multi-model probability based on the model likelihood, finally outputting the fused target state estimate.

2. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 1, characterized in that, In step 1, an interactive multi-model framework is used to construct a dual-model set containing a constant acceleration model and a gravity model. In the ECEF coordinate system, the target state vector contains position, velocity, and acceleration components in three coordinate axes. Each track maintains two sets of model states and their corresponding model probabilities. At the beginning of each frame, interactive multi-model state mixing is performed. Then, linear state prediction is applied to the constant acceleration model, and nonlinear state prediction is performed by generating Sigma points using unscented transformation for the gravity model. Based on the predicted states, the predicted radial distance and predicted radial velocity of each track are calculated, and the predicted radial velocity is used for subsequent coupling correction.

3. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 1, characterized in that, In step 2, for non-groupable tracks, they are expanded into a corresponding number of proxy lines according to the number of group members, so that the group track can compete for multiple measurements in one frame; the distance channel cost is calculated as follows: when coupling correction is enabled, the corrected predicted radial distance is calculated based on the coupling coefficient and the predicted radial velocity, and the normalized radial distance residual is calculated as the distance channel base cost based on the corrected predicted radial distance. At the same time, dual hard gating constraints of spatial gating and radial gating are applied, and the spatial threshold and radial threshold are dynamically scaled according to the number of frames from the last measurement update; for group tracks, they are additionally multiplied by preset spatial and track path threshold scaling factors to match their multi-measurement acceptance modeling objectives.

4. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 3, characterized in that, In step 2, the calculation of the HRRP channel cost is as follows: for each track-measurement candidate pair that passes through the distance gate, the historical HRRP sequence is extracted and a translation template is generated within the translation window. The maximum translation cosine similarity between each historical HRRP and the currently detected HRRP is calculated, and the HRRP channel cost is obtained by weighting and summing according to the time decay weight. The attribute channel cost is calculated as follows: extract a 7-dimensional attribute vector containing centroid, standard deviation, skewness, kurtosis, radar cross section, range broadening and number of scattering points from HRRP, construct a difference vector based on the common effective dimension and calculate Mahalanobis distance using the attribute covariance submatrix, and obtain the attribute channel cost by time-weighted averaging.

5. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 1, characterized in that, In step 3, the distance channel cost and the attribute channel cost are compressed to a preset range using monotonic compression mapping. During conditional fusion, each track is paired with a measurement, and the three-channel weighted fusion is performed to obtain the total cost only when the distance channel cost is not infinite and the HRRP channel cost and the attribute channel cost simultaneously meet the activation conditions. When any of the three channels is invalid, the process degenerates to using only the scaled distance channel cost as the total cost. Based on the final total cost of all pairings, and following the extension logic of the proxy rows, the row indexes are restored to the original track indexes through the mapping function from row index to track index, thereby constructing the global fusion cost matrix.

6. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 1, characterized in that, In step 4, the Hungarian algorithm solves the global minimum cost bisection matching problem based on the global fusion cost matrix to obtain the decision variables for each extended row and measurement. After the Hungarian algorithm is completed, the row index in the global fusion cost matrix is ​​folded back to the corresponding track index at the bottom layer through a mapping function, and the successfully matched measurement is assigned to the original track. Finally, two levels of matching information are output: the first level is the matching result, that is, the physical pairing of all extended rows and measurements output by the Hungarian algorithm. The second level is the successful association relationship, which is the successful association relationship obtained by filtering the matching results based on cost effectiveness.

7. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 1, characterized in that, In step 5, for each mature ungroupable track, mature separable tracks that meet the conditions are assigned to the track group using the Hungarian algorithm; from the mature separable tracks that have not yet been merged into any group, multiple separable tracks that maintain a continuous spatial proximity relationship are identified to form a spatial candidate group, which is then refined and judged using HRRP distance and attribute distance respectively to form a new ungroupable track, and the state of the new track group is initialized using the moment matching method; existing track pairs are scanned, and if the distance between groups meets the grouping threshold, the clusters are identified and merged through graph connected components.

8. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 7, characterized in that, The process of group degenerating back to single unit is as follows: First, within the set first sliding window length, the number of echoes associated with the group track is counted, and the number of group members is updated with the maximum number of echo frames. If the updated Then, within the set second sliding window length, imaging frames are selected, and a minimum spanning tree is constructed based on the echo positions within the group. The maximum edge of the minimum spanning tree is calculated. and to The average splitting gap is obtained by performing a time-weighted average. ;like Greater than the splitting determination threshold If the split is confirmed, the number of members in the group will be reduced by one; when the number of members in a certain frame is updated... When the original group of tracks is terminated, a new separable track is created based on the current group state. The initial state and covariance of the new track directly inherit the state estimate and covariance of the original group of tracks.

9. The multi-modal fusion tracking method for spaceborne radar swarm targets according to claim 1, characterized in that, In step 6, the measurement set assigned to the current frame is collected for each track. If the measurement set contains multiple echoes, the radial distance, azimuth, pitch angle and coupling coefficient are averaged to form an equivalent measurement. For each model, the Sigma point is generated based on the predicted state and propagated through the measurement function to obtain the measurement prediction mean and innovation covariance. The equivalent measurement is used to update the state estimate mean and covariance through the unscented Kalman filter equation. The probability of each model is updated according to the Gaussian likelihood function of the measurement innovation. Finally, the updated model probabilities are weighted and output to obtain the fused target state estimate.

10. An electronic device comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the multi-modal fusion tracking method for spaceborne radar swarm targets as described in any one of claims 1-9.

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