Multi-sensor target trajectory fusion method and system

Abstract

The application belongs to the technical field of radar detection, and discloses a multi-sensor target trajectory fusion method and system; the method comprises the following steps: based on the beam pointing characteristics of a phased array antenna, combining the coupling mechanism of unmanned aerial vehicle maneuvering and beam scanning, a nonlinear coupling model is constructed to predict beam pointing error and actively correct the beam pointing parameters of the radar; the data collected by all sensors are time-synchronized, the synchronized sensor data are subjected to coordinate conversion to obtain target data in a world coordinate system; the target data are analyzed to extract motion fingerprints; the initial trajectory and the motion fingerprints are analyzed to obtain an effective trajectory set; the optimal trajectory is obtained by weighted fusion between each effective trajectory in the effective trajectory set, and the nonlinear coupling model is subjected to feedback correction; the application significantly improves the removal rate of multi-path false targets in a complex maneuvering scene, and effectively suppresses the generation of new false trajectories caused by platform maneuvering.

Description

Technical Field

[0001] This invention relates to the field of radar detection technology, and more specifically, to a multi-sensor target trajectory fusion method and system. Background Technology

[0002] Unmanned aerial vehicle (UAV) platforms equipped with phased array radar have become core equipment for target detection due to their advantages such as flexibility, wide-area scanning, and high-precision detection.

[0003] Chinese patent CN115343700B discloses a method for removing multipath false targets in tunnels based on multi-radar video: S1, Single radar video data association: A radar and a camera are installed outside the tunnel entrance, with the detection direction facing outwards; a vehicle drives into the tunnel from a distance, and the vehicle feature information captured by the camera is matched and superimposed with the radar track information, generating a unique track ID for each vehicle target; S2, Target matching in adjacent overlapping areas of multiple radars: The detection directions of multiple radars are the same, and there are overlapping areas between adjacent radars. The vehicle target of the previous radar is matched with all targets of the current radar through the overlapping area to obtain the true target of the current radar, and the track ID and vehicle feature information are continuated; S3, Multipath target filtering in non-overlapping areas of radar: It is determined whether there is vehicle feature information on each target. If not, it is a multipath target and is filtered out to obtain the final target detection result.

[0004] While the above methods can meet the needs of most scenarios, research and practical application of these methods and existing technologies have revealed at least the following shortcomings:

[0005] The above method does not fully consider and resolve the dynamic coupling effect between the UAV platform's own maneuvering and the radar beam scanning strategy. Therefore, when applied to a moving UAV platform, its effect on removing multipath false targets will be significantly reduced, and it may even generate new and more complex false trajectories due to platform maneuvering.

[0006] In view of this, the present invention proposes a multi-sensor target trajectory fusion method and system to solve the above problems. Summary of the Invention

[0007] To overcome the aforementioned deficiencies of the prior art and to achieve the above objectives, the present invention provides the following technical solution: a multi-sensor target trajectory fusion method, comprising:

[0008] Based on the beam pointing characteristics of phased array antennas and combined with the coupling mechanism of UAV maneuvering and beam scanning, a nonlinear coupling model is constructed to predict beam pointing error and actively correct the radar beam pointing parameters.

[0009] The corrected radar and all sensor data are synchronized in time, and the synchronized sensor data are transformed to obtain target data in the world coordinate system.

[0010] Analyze the target data to extract motion fingerprints; analyze the initial trajectory and motion fingerprints to obtain a set of valid trajectories;

[0011] The effective trajectories in the effective trajectory set are weighted and fused to obtain the optimal trajectory, and the nonlinear coupling model is then corrected based on the optimal trajectory.

[0012] Furthermore, methods for constructing nonlinear coupling models include:

[0013] Collect beam pointing parameters of the phased array antenna, UAV maneuver parameters, and beam scanning parameters;

[0014] Calculate the time series mean of the target factor's time series data, and combine the time series data, time series mean, original bias, and original bias mean to calculate the Pearson correlation coefficient between the target factor and the original bias;

[0015] Target factors with Pearson correlation coefficients higher than the correlation threshold were selected as significant influencing factors.

[0016] Interaction terms were constructed based on significant influencing factors, and horizontal orthogonal experiments were designed. The F-value of the interaction terms was calculated through analysis of variance, which is the statistical measure of the significance of the interaction terms on beam pointing deviation. Interaction terms with F-values ​​greater than the interaction threshold were selected as core interaction terms.

[0017] Based on the coupling mechanism, a nonlinear initial model is constructed using a multinomial model to select the core interaction term and the original deviation. Then, by stepwise regression, significant influencing factors and core interaction terms are substituted into the nonlinear initial model. The nonlinear model is optimized to minimize the Akaike information criterion.

[0018] The objective function is constructed with the goal of minimizing the sum of squared residuals between the predicted and actual values ​​of the training set. The nonlinear model parameters are then solved through matrix operations to obtain the nonlinear coupled model.

[0019] Furthermore, the beam pointing parameters include azimuth and pitch angles; the UAV maneuvering parameters include pitch rate, roll rate, and yaw rate; and the beam scanning parameters include azimuth scanning rate and pitch scanning rate.

[0020] The original deviation was obtained by designing a full combination experiment combining different maneuvering modes and different scanning strategies, and collecting the difference between the actual beam pointing parameters calibrated by the lidar and the radar beam pointing parameters.

[0021] Each parameter in the UAV maneuvering parameters and beam scanning parameters is used as a target factor in turn. Only the target factor is changed each time, while the other parameters are fixed, and the time series data of the target factor is obtained.

[0022] Furthermore, methods for obtaining motion fingerprints include:

[0023] The state vector is composed of the target data of the UAV in the world coordinate system, the velocity of the UAV in the x and y directions, and the acceleration of the UAV in the x and y directions. The state vector is used as the input of the Kalman filter algorithm to obtain the initial trajectory.

[0024] For trajectories with more than the number of points, they are divided into K trajectory segments by sliding segmentation according to the time window length W and step size U; for trajectories with no more than the number of points, they are directly treated as a single trajectory segment; the average value of the features of each segment is taken as the feature value of the entire trajectory.

[0025] The curvature of each point within the trajectory segment is calculated based on three adjacent trajectory points, where the curvature of the first and last points is the average of the curvatures of the adjacent trajectory points; the rate of change of curvature is calculated based on the curvature of the adjacent trajectory points; a Fourier transform is performed on the rate of change of curvature, and the frequency component with the largest amplitude in the Fourier transform result is taken as the frequency of curvature change;

[0026] Based on the acceleration in the x and y directions of the trajectory points, an acceleration vector sequence within the trajectory segment is constructed. The beam scanning parameters are then converted into unit vectors in the world coordinate system to obtain the beam scanning direction vector sequence.

[0027] The acceleration vector sequence and the beam scanning direction vector sequence are projected onto the XY joint dimension, and the Pearson correlation coefficient between the acceleration vector sequence and the beam scanning direction vector sequence is calculated to obtain the correlation.

[0028] The velocity of the trajectory point is calculated based on the velocity in the x and y directions. The rate of change of velocity between adjacent points is calculated based on the velocity of the trajectory point. The reciprocal of the mean of the rate of change of velocity between adjacent points within the trajectory segment is calculated and the smoothness index is obtained through normalization.

[0029] The velocity direction angle is calculated based on the velocity in the x and y directions of the trajectory point. The change in velocity direction angle between adjacent trajectory points within the trajectory segment is calculated based on the velocity direction angle. If the change in velocity direction angle is greater than the change threshold, it is determined as a turning event. The total number of turning events within the trajectory segment is counted, and the ratio of the total number of turning events to the total duration of the trajectory segment is calculated. Then, the standardization process is performed to obtain the turning frequency.

[0030] The motion fingerprint is obtained by standardizing the curvature change frequency, correlation, smoothness index, and turning frequency by combining the corresponding maximum and minimum values.

[0031] Furthermore, methods for obtaining an effective trajectory set include:

[0032] Calculate any initial trajectory and The association cost is calculated using a joint probabilistic data association algorithm. The association probability of the same target among all sensor trajectories is calculated based on the association cost. Initial trajectories with association probabilities greater than the association probability threshold are selected to obtain a set of candidate associated trajectories for the same target. If a single trajectory has no other trajectory with an association probability that meets the threshold, it is retained as a single sensor candidate trajectory.

[0033] Extract motion fingerprints from candidate associated trajectories, retrieve all false trajectory features matching the current scene from the coupling error database; calculate the Euclidean distance between the extracted motion fingerprint and each false trajectory feature; if the trajectory Euclidean distance is lower than the similarity threshold, it is determined to be a suspicious trajectory.

[0034] Perform kinematic constraint verification and morphological anomaly verification on candidate associated trajectories;

[0035] If a candidate associated trajectory satisfies any one of the suspicious trajectory marking rules, it is marked as a suspicious false trajectory; otherwise, it is marked as a normal candidate trajectory. The marked candidate trajectory set is obtained by combining the candidate trajectories of a single sensor.

[0036] Calculate the overall confidence score of each candidate trajectory in the labeled candidate trajectory set; if the overall confidence score is higher than the confidence score threshold, it is determined to be a valid trajectory; otherwise, it is determined to be a false trajectory, and a valid trajectory set is obtained.

[0037] Furthermore, calculate any initial trajectory and Methods for determining associated costs include:

[0038] Calculate the initial trajectory at the same timestamp. and The Euclidean distance normalized value is used to obtain the position deviation;

[0039] Calculate the mean of the rate of change of velocity at adjacent points at the same time stamp to obtain the velocity deviation;

[0040] calculate and The cosine similarity of the motion fingerprints of the two initial trajectories is used to obtain feature similarity.

[0041] The association cost is obtained by weighting the calculation based on positional deviation, velocity deviation, and feature similarity.

[0042] Furthermore, methods for obtaining the optimal trajectory include:

[0043] If there is only one single-sensor candidate trajectory for the effective trajectory, it is directly used as the optimal trajectory; otherwise, the fusion weight corresponding to the effective trajectory is calculated based on the comprehensive confidence of the effective trajectory and the inverse matrix of the effective trajectory covariance matrix.

[0044] The states of all valid trajectories are weighted and fused based on the fusion weights to obtain the optimal trajectory state for each timestamp;

[0045] The optimal covariance matrix is ​​obtained by fusing and inverting the inverse matrix of the effective trajectory covariance matrix based on the fusion weights.

[0046] The optimal trajectory is obtained by concatenating the optimal trajectory state and the optimal covariance matrix.

[0047] Furthermore, methods for feedback correction of nonlinear coupled models based on optimal trajectories include:

[0048] Calculate the actual beam pointing based on the location information of the optimal trajectory;

[0049] Calculate the deviation between the actual beam pointing and the corrected beam pointing to obtain the optimized error signal;

[0050] With the goal of minimizing the error signal, the gradient descent method is used to update the parameters of the nonlinear coupling model online. If the change in error before and after the parameter update is lower than the first change threshold, or the change in parameter is lower than the second change threshold, the parameters are determined to have converged, the update is stopped, and the updated parameters of the nonlinear coupling model are fed back into the nonlinear coupling model.

[0051] Furthermore, methods for obtaining target data in the world coordinate system include:

[0052] A 2D rigid body transformation is used to obtain the static data in the world coordinate system after the transformation;

[0053] The static data in the world coordinate system is converted into the target data in the world coordinate system based on the dynamic coordinate transformation matrix.

[0054] Furthermore, including:

[0055] Feedforward compensation module: Based on the beam pointing characteristics of the phased array antenna and combined with the coupling mechanism of UAV maneuvering and beam scanning, a nonlinear coupling model is constructed to predict the beam pointing error and actively correct the radar's beam pointing parameters.

[0056] Data conversion module: synchronizes the corrected radar and all sensor data in time, performs coordinate transformation on the synchronized sensor data, and obtains target data in the world coordinate system;

[0057] Trajectory Analysis Module: Analyzes target data and extracts motion fingerprints; analyzes the initial trajectory and motion fingerprints to obtain a set of valid trajectories;

[0058] Trajectory fusion module: It weights and fuses the effective trajectories in the effective trajectory set to obtain the optimal trajectory, and performs feedback correction on the nonlinear coupling model based on the optimal trajectory.

[0059] The technical effects and advantages of the multi-sensor target trajectory fusion method and system of this invention are as follows:

[0060] This invention first synchronizes the data from various sensors with time and performs static rigid body transformation to correct installation deviations, and then performs dynamic coordinate transformation to adapt to the platform's maneuvering coordinate transformation, obtaining target data in a unified world coordinate system to eliminate spatiotemporal biases. Next, it generates an initial trajectory based on Kalman filtering, extracts and fuses multi-dimensional motion fingerprints such as curvature change frequency, acceleration and beam scanning direction correlation, and smoothness. Combining a joint probability data association algorithm with false feature matching from a coupling error database and multi-dimensional kinematic constraint verification, it filters out a high-purity set of valid trajectories to accurately eliminate coupled false trajectories. Then, it weights and fuses the valid trajectories by adaptively allocating weights based on confidence level and the inverse of the covariance matrix, generating an optimal trajectory with both high accuracy and reliability. Simultaneously, using the actual beam pointing derived from the optimal trajectory as a benchmark, it calculates the error signal between the beam pointing and the model prediction, and corrects the nonlinear coupling model parameters online using gradient descent. This significantly improves the removal rate of multipath false targets in complex maneuvering scenarios, effectively suppresses the generation of new false trajectories caused by platform maneuvering, and greatly improves the positioning and tracking accuracy of target trajectories, enhancing the system's robustness to dynamically coupled scenarios. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the multi-sensor target trajectory fusion method of the present invention;

[0062] Figure 2 This is a schematic diagram of the method for constructing a nonlinear coupling model according to the present invention;

[0063] Figure 3 This is a schematic diagram of the method for obtaining an effective trajectory set according to the present invention;

[0064] Figure 4 This is a schematic diagram of the multi-sensor target trajectory fusion system of the present invention. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] Example 1:

[0067] Please see Figure 1 As shown, this embodiment provides a multi-sensor target trajectory fusion method, including:

[0068] Based on the beam pointing characteristics of phased array antennas and combined with the coupling mechanism of UAV maneuvering and beam scanning, a nonlinear coupling model is constructed to predict beam pointing error and actively correct the radar beam pointing parameters.

[0069] Reference Figure 2 Methods for constructing nonlinear coupled models include:

[0070] The system collects beam pointing parameters from a phased array antenna, UAV maneuvering parameters, and beam scanning parameters. The phased array antenna's beam pointing parameters include azimuth and elevation angles; the UAV maneuvering parameters include elevation, roll, and yaw rates; and the beam scanning parameters include azimuth and elevation scanning rates. The phased array antenna's beam pointing parameters serve as the benchmark and correction target for model output deviation calculations, directly impacting radar target detection accuracy and addressing the core issue of false trajectory generation caused by beam pointing deviations in existing technologies. The UAV maneuvering and beam scanning parameters comprehensively cover the dual core influencing sources of UAV maneuvering and beam scanning coupling, providing a fundamental input for quantifying coupling effects and compensating for the lack of clearly defined coupling influencing factors in existing technologies.

[0071] Each parameter in the UAV maneuvering parameters and beam scanning parameters is sequentially used as a target factor. Only the target factor is changed each time, while other parameters are fixed. Time-series data of the target factors are acquired, and the time-series mean of the target factor time-series data is calculated. The Pearson correlation coefficient between the target factor and the original deviation is calculated by combining the target factor time-series data, the time-series mean, the original deviation, and the mean of the original deviation. The original deviation is obtained by designing a full-combination experiment combining different maneuvering modes and different scanning strategies, collecting the difference between the actual beam pointing parameters calibrated by the lidar and the radar beam pointing parameters. The original deviation obtained from the full-combination experiment is used to traverse all scenarios of maneuvering modes and scanning strategies to ensure full-scenario coverage of the deviation data, avoiding the problem of insufficient model generalization ability caused by missing data scenarios in existing technologies.

[0072] Target factors with Pearson correlation coefficients higher than the correlation threshold are selected as significant influencing factors. The correlation threshold is set based on empirical values, preferably 0.7-0.8. This method can accurately locate the linear correlation strength between a single factor and the beam pointing deviation, providing a quantitative basis for eliminating redundant factors and solving the model complexity problem caused by the failure to distinguish the importance of factors in existing technologies. Irrelevant factors with weak correlation to the deviation are eliminated, simplifying the model input dimension, reducing subsequent computational complexity, improving model interpretability, and avoiding overfitting caused by factor stacking in existing technologies.

[0073] Interaction terms were constructed based on significant influencing factors, and horizontal orthogonal experiments were designed. The F-value of the interaction terms was calculated through analysis of variance, which is the statistical measure of the significance of the interaction terms on beam pointing deviation. Interaction terms with F-values ​​greater than the interaction threshold were selected as core interaction terms. The interaction threshold was set based on empirical values, preferably 0.7-0.8. To address the core deficiency of existing technologies that do not consider the dynamic coupling between maneuvering and scanning, the coupling effect was quantified by constructing interaction terms. The orthogonal experiments efficiently covered the interaction scenarios, and the F-value of the analysis of variance accurately quantified the significance of the interaction, ultimately locking in the core coupling correlation.

[0074] Based on the coupling mechanism, a nonlinear initial model is constructed using a polynomial model to select core interaction terms and the original deviation. Through stepwise regression, significant influencing factors and core interaction terms are substituted into the nonlinear initial model. With the goal of minimizing the Akaike information criterion, insignificant terms in the nonlinear initial model are gradually eliminated to optimize and obtain the nonlinear model. The polynomial model is adapted to the nonlinear characteristics of the coupling effect. Stepwise regression combined with the Akaike information criterion achieves redundancy removal and core retention, which controls the complexity while ensuring the model fitting effect and solves the problems of structural redundancy and poor generalization of existing nonlinear models.

[0075] The objective function is constructed with the goal of minimizing the sum of squared residuals between the predicted and actual bias values ​​in the training set. The nonlinear model parameters are solved through matrix operations to obtain a nonlinear coupled model. With the goal of improving the fitting accuracy of the training data, the model coefficients are accurately solved through matrix operations. This provides a reliable model foundation for the accurate prediction of beam pointing deviation and avoids the correction failure caused by inaccurate model parameters in existing technologies.

[0076] Methods for actively correcting the beam pointing parameters of a radar include:

[0077] Real-time data is collected, substituted into a nonlinear coupling model, and the deviation prediction results at the current moment are calculated, including beam azimuth deviation and elevation deviation.

[0078] Based on the deviation prediction results, the original radar beam pointing parameters are inversely compensated to generate a corrected beam pointing. Real-time prediction adapts to the dynamic maneuvering scenarios of UAVs. Inverse compensation directly offsets the beam pointing deviation caused by the coupling between maneuvering and scanning, suppressing the generation of false trajectories from the source. This solves the problem of reduced false target removal effect under the coupling effect of existing technologies and is the core step of active correction.

[0079] The data collected by the corrected radar and all sensors are synchronized in time, and the synchronized sensor data is transformed in coordinate to obtain target data in the world coordinate system. By synchronizing the time of each sensor, the time asynchrony deviation of the multi-sensor data is eliminated, which can ensure the spatiotemporal matching of multi-source data of the target at the same time, avoid the false trajectory association caused by coordinate misalignment due to time difference, and lay the premise for accurate coordinate transformation.

[0080] Methods for obtaining target data in the world coordinate system include:

[0081] Using 2D rigid body transformation, static data in the world coordinate system after transformation is obtained; such as ,in, The target data in the original coordinate system of the sensor is the basic input for coordinate transformation. It is directly related to the original target information detected by each sensor. Its accuracy determines the reliability of the reference for subsequent transformations and avoids false trajectories caused by the amplification of errors in the original data. This is a 2D rotation matrix, obtained through calibration experiments, used to correct sensor mounting angle deviations. , The angle between the sensor coordinate system and the world coordinate system; It is a 2D translation vector, obtained through calibration experiments, specifically... , for Directional translation amount for Directional translation; 2D rotation matrix and 2D translation vector can correct static deviations in sensor installation angle and position, eliminate system deviations caused by inherent sensor installation errors, provide a precise basis for dynamic correction, and reduce false targets caused by fixed errors; This is static data in the world coordinate system;

[0082] Based on the dynamic coordinate transformation matrix, static data in the world coordinate system is converted into target data in the world coordinate system. The target data in the world coordinate system can unify the target position reference of each sensor, providing consistent data input for subsequent multi-sensor trajectory association and false trajectory identification, and avoiding misjudgments caused by coordinate system inconsistencies. For example, the target data in the world coordinate system... ,in, for The dynamic coordinate transformation matrix, updated in real time by the platform position and attitude angles provided by GPS / INS, is combined with the real-time updates of the dynamic coordinate transformation matrix by GPS / INS to correct changes in platform position and attitude caused by UAV maneuvers. This offsets the coupling effect of maneuvers on beam pointing and target localization at the coordinate level, and is a key step in solving the problem of new false trajectories generated by platform maneuvers. Specifically, this involves the dynamic coordinate transformation matrix. , For the yaw angle of the drone, and They are respectively The system provides real-time information on the drone's position on the X and Y axes of the world coordinate system. By providing the drone's yaw angle and position in real time, it serves as the core data for the dynamic adaptation platform's maneuverability, compensating for the shortcomings of static transformation in handling drone motion.

[0083] Analyze the target data to extract motion fingerprints; analyze the initial trajectory and motion fingerprints to obtain a set of valid trajectories;

[0084] Methods for obtaining motion fingerprints include:

[0085] The state vector is constructed from the target data collected in the world coordinate system, the target's velocity in the x and y directions, and the UAV's acceleration in the x and y directions. This state vector is used as the input to the Kalman filter algorithm to obtain the initial trajectory. Using the state vector composed of position, velocity, and acceleration as the basic data input for the Kalman filter can accurately characterize the target's motion characteristics, providing a reliable data source for initial trajectory generation and reducing false trajectories caused by confusion between the platform and target states from the source. The target motion time-series data smoothed by the Kalman filter provides a continuous trajectory basis for motion fingerprint extraction, solving the feature distortion problem caused by noise in the original data and ensuring the accuracy of subsequent coupling effect feature capture.

[0086] For trajectories with more than one point, they are divided into K trajectory segments by sliding according to the time window length W and the step size U. For trajectories with no more than one point, they are directly treated as a single trajectory segment. The average of the features of each segment is taken as the feature value of the entire trajectory. By adapting to the feature extraction requirements of trajectories of different lengths, features are extracted from long trajectories by segmentation and short trajectories are processed directly, avoiding feature distortion caused by differences in trajectory length and improving the robustness of motion fingerprints.

[0087] Based on 3 adjacent trajectory points , and Calculate the curvature of each point within the trajectory segment, where the curvature of the first and last points is the average of the curvatures of adjacent trajectory points; calculate the rate of change of curvature based on the curvatures of adjacent trajectory points; perform a Fourier transform on the rate of change of curvature, and take the frequency component with the largest amplitude in the Fourier transform result as the frequency of curvature change; as shown in the example... trajectory points curvature rate of change of curvature ,in, For the first trajectory points The curvature; For the first trajectory points The corresponding data collection time; For the first trajectory points The corresponding acquisition time; converting the rate of curvature change into frequency domain features, accurately identifying the periodic curvature abrupt changes of coupled false trajectories, and distinguishing the smooth curvature changes of real targets are the core parts of identifying coupled false trajectories.

[0088] Based on the acceleration in the x and y directions of the trajectory points, an acceleration vector sequence within the trajectory segment is constructed. The beam scanning parameters are then converted into unit vectors in the world coordinate system to obtain the beam scanning direction vector sequence.

[0089] Project the acceleration vector sequence and the beam scanning direction vector sequence onto the joint XY dimension, calculate the Pearson correlation coefficient between the acceleration vector sequence and the beam scanning direction vector sequence, and obtain the correlation; if the correlation... ,in, For the first The acceleration components in the x-direction of each trajectory point; For the first The acceleration components in the y-direction of each trajectory point; and These are the mean values ​​of the acceleration components in the x and y directions, respectively. For the first x-direction beam scanning direction component of each trajectory point; For the first The y-direction beam scanning direction component of each trajectory point; and These are the mean values ​​of the components in the x and y scanning directions, respectively; For the first The weighting coefficients of each trajectory point; the correlation is based on the physical mechanism of the dynamic coupling between UAV maneuvering and beam scanning. The essence of the precise anchoring coupling effect is the dynamic interaction between UAV maneuvering intensity and beam scanning strategy. Acceleration serves as a direct quantitative indicator of UAV maneuvering intensity, while the beam scanning direction vector directly represents the instantaneous state of the scanning strategy. The correlation calculation between the two transforms the abstract coupling mechanism into a quantifiable feature indicator. Specifically, the linear correlation strength between the acceleration vector sequence and the beam scanning direction vector sequence is calculated using the Pearson correlation coefficient: when the coupling effect is significant, the correlation between the two increases significantly, and the corresponding trajectory is prone to exhibiting spurious coupling features such as spirals and abrupt changes; while the real target motion has no direct correlation with beam scanning, and the correlation is usually below 0.3. This feature design breaks away from the limitations of traditional data-driven empirical features, capturing the unique identifiers of spurious coupled trajectories from a physical source, ensuring adaptability to scenarios with different coupling intensities.

[0090] The velocity of a trajectory point is calculated based on its velocities in the x and y directions. The rate of change of velocity between adjacent points is then calculated based on the velocity of the trajectory point. The reciprocal of the mean of the rate of change of velocity between adjacent points within the trajectory segment is calculated, and a smoothness index is obtained through normalization. (Example: Rate of change of velocity between adjacent points...) Smoothness index ,in, For the first trajectory points speed; For the first trajectory points speed; This represents the number of trajectory points;

[0091] The velocity direction angle is calculated based on the velocity in the x and y directions of the trajectory point. The change in velocity direction angle between adjacent trajectory points within the trajectory segment is calculated based on the velocity direction angle. If the change in velocity direction angle is greater than the change threshold, it is determined as a turning event. The total number of turning events within the trajectory segment is counted, and the ratio of the total number of turning events to the total duration of the trajectory segment is calculated. Then, the standardization process is performed to obtain the turning frequency.

[0092] The curvature change frequency, correlation, smoothness index, and turning frequency are standardized by combining the corresponding maximum and minimum values ​​and then stitched together to obtain the motion fingerprint. The motion fingerprint integrates the dynamic characteristics of the target motion and beam scanning coupling, accurately captures the unique pattern of false trajectories generated by the coupling of maneuvering and scanning, and makes up for the deficiency of existing technologies in not quantifying coupling characteristics.

[0093] Reference Figure 3 Methods for obtaining a valid trajectory set include:

[0094] Calculate the initial trajectory at the same timestamp. and The Euclidean distance normalized value is used to obtain the position deviation;

[0095] Calculate the mean of the rate of change of velocity at adjacent points at the same time stamp to obtain the velocity deviation;

[0096] calculate and The cosine similarity of the motion fingerprints of the two initial trajectories is used to obtain feature similarity.

[0097] The association cost is obtained by weighting position deviation, velocity deviation and feature similarity. The weights can be obtained by natural heuristic optimization algorithm. The association cost weighting is dynamically optimized by intelligent algorithm to adapt the association priority under different coupling scenarios and improve the accuracy of multi-sensor trajectory association.

[0098] A joint probabilistic data association algorithm is adopted to calculate the association probability of the same target among all sensor trajectories based on the association cost. It considers all possible trajectory association hypotheses and quantifies the association credibility through likelihood probability and posterior probability to avoid association misjudgment caused by a single hypothesis, and is suitable for complex scenarios with multiple sensors and multiple false trajectories.

[0099] Methods for calculating the probability of association with the same target among all sensor trajectories include:

[0100] For any two initial trajectories and Define the associated states and set constraints; where the associated state is 1. and When they belong to the same target and the association status is 0, and They do not belong to the same target; constraints include: uniqueness constraint: a trajectory is associated with at most one trajectory from other sensors, and trajectories within the same sensor are not associated; sensor mutual exclusion constraint: if the initial trajectory of sensor A... Initial trajectory of sensor B If associated, then the initial trajectory It can no longer be associated with other trajectories of sensor B;

[0101] Define the association hypothesis, which is all combinations of associated states that satisfy the constraints.

[0102] The trajectories are grouped according to sensor type. Starting from the first group, each trajectory is matched with trajectories from other groups in turn to generate all possible association combinations. Association combinations that violate constraints are eliminated to obtain the initial hypothesis set.

[0103] The initial hypothesis set is sorted by likelihood probability, and hypotheses with likelihood probabilities below the probability threshold are removed to obtain an effective hypothesis set.

[0104] Calculate the single-track pair likelihood probability for any trajectory pair under the valid hypothesis. If the association state is 1, calculate the likelihood probability based on a decreasing function of association cost, such as using an exponential decreasing function. ,in, In the first One valid hypothesis Under the condition that it is true, the initial trajectory Compared with the initial trajectory Likelihood probability of a single trajectory pair belonging to the same target; The calibration coefficients are obtained through calibration using historical data to ensure that the likelihood probability of a single trajectory pair is 1 when the association cost is 0. for and Related costs, It is an exponential function with the natural constant as its base;

[0105] If the association state is 0, then the likelihood probability is a fixed value. ;

[0106] Assuming the overall likelihood probability of a valid hypothesis is the product of the likelihood probabilities of all trajectories, such as... ,in, The overall likelihood probability of the effective hypothesis, i.e., the probability under the effective hypothesis. Under the condition that it is established, the current trajectory data is observed. The probability of; for The trajectory number is less than The trajectory pairs with trajectory numbers; Representing the trajectory and trajectory Belonging to the same goal;

[0107] Calculate the likelihood probability of the null hypothesis based on the trajectory and the total number; such as the likelihood probability of the null hypothesis. ,in, Assuming no data is available. This is the basic likelihood probability term corresponding to the associated state when the trajectory pair does not belong to the same target; The total number of trajectory pairs, i.e. The number of combinations of trajectories, The total number of trajectories;

[0108] Based on Bayes' theorem, calculate the posterior probability of each valid hypothesis:

[0109] Assume that the prior probabilities of all valid hypotheses are equal; for example, the prior probabilities... , The number of valid assumptions; add to the denominator. This indicates that the null hypothesis is included;

[0110] Calculate the posterior probability using Bayes' theorem; such as the posterior probability. ,in, As evidence factors, ;in, Assumption The prior probability; In the first One valid hypothesis Likelihood probability under the given condition;

[0111] Ensure that the sum of the posterior probabilities of all hypotheses is 1; such as ;

[0112] Calculate all valid hypotheses and The sum of the posterior probabilities of the associated hypotheses yields a single trajectory pair. and The probability of association with the same target; such as a single trajectory pair and The probability of association with the same target ;in, To determine and Valid assumptions belonging to the same goal .

[0113] Verify whether the sum of the association probabilities of each trajectory with all other trajectories does not exceed 1. If yes, it passes; if no, the corresponding association probability is normalized. If the association probability is lower than the lower limit of the association probability, it is determined to be unrelated, and then the association probability of the same target among all sensor trajectories is obtained.

[0114] Initial trajectories with an association probability greater than the association probability threshold are selected to obtain a set of candidate associated trajectories for the same target; if a single trajectory has no other trajectory with an association probability that meets the threshold, it is retained as a single sensor candidate trajectory.

[0115] Motion fingerprints of candidate associated trajectories are extracted, and all false trajectory features matching the current scene are retrieved from the coupling error database. The coupling error database is constructed through offline experiments simulating combinations of different UAV maneuvering modes and beam scanning strategies, collecting false trajectories generated by coupling effects in each scenario, and extracting their motion fingerprint features. The coupling error database employs a systematic construction logic of full scene coverage and precise calibration, focusing on typical combinations of UAV maneuvering and beam scanning. During construction, the full combination dimensions of two key parameters are first identified: UAV maneuvering modes cover different angular velocity levels of pitch, roll, and yaw; beam scanning strategies cover different azimuths, pitch scanning rates, and scanning modes, forming a full combination scene matrix. Subsequently, offline experimental platforms simulate various combination scenarios, collecting false trajectory data generated by coupling effects, extracting motion fingerprints strongly correlated with the coupling mechanism, and storing them in the database after deduplication and scene label calibration. The coupling error database can cover most typical coupling scenarios. During online detection, it can quickly retrieve false trajectory templates consistent with the current scene, achieving precise matching of false trajectories in specific coupling scenarios, thus overcoming the high false trajectory omission rate of traditional general template libraries for scenario-based coupling. The coupling mechanism-driven correlation feature design provides a consistent feature dimension for the coupling error database, ensuring the homology between the false trajectory features entered into the database and the features extracted online. Meanwhile, the scenario-based coupling error database provides a scenario-based judgment benchmark for correlation features, avoiding misjudgments under different coupling scenarios using a single feature threshold. Together, these two elements form a two-layer discrimination logic of mechanism feature extraction and scenario template matching, significantly improving the recognition accuracy of coupled false trajectories.

[0116] Calculate the Euclidean distance between the extracted motion fingerprint and each fake trajectory feature. If the trajectory Euclidean distance is lower than the similarity threshold, it is determined to be highly similar and marked as a suspicious trajectory.

[0117] The candidate associated trajectories are subjected to kinematic constraint verification and morphological anomaly verification, specifically including:

[0118] If there are more than H1 consecutive trajectory points in the candidate associated trajectory with speeds greater than the maximum speed threshold, then it is marked as a speed abnormal trajectory;

[0119] If there are more than H2 consecutive trajectory points with accelerations greater than the maximum acceleration threshold, then the trajectory is marked as an acceleration anomaly.

[0120] The turning angular velocity is obtained by calculating the ratio of the change in the velocity direction angle of adjacent points to the time interval for each point in the trajectory. If the turning angular velocity is greater than the maximum turning angular velocity threshold and the duration is greater than the time threshold, it is marked as an abnormal turning trajectory.

[0121] If the standardized smoothness index is lower than the smoothness threshold, it is judged as an abnormal trajectory. By verifying the rationality of the trajectory from multiple dimensions such as speed, acceleration, turning angular velocity and smoothness, the kinematic anomalies caused by coupling can be accurately identified, and the range of suspicious trajectories can be further narrowed down.

[0122] If a candidate associated trajectory satisfies any one of the suspicious trajectory marking rules, it is marked as a suspicious false trajectory; otherwise, it is marked as a normal candidate trajectory. The marked candidate trajectory set is obtained by combining the candidate trajectories of a single sensor.

[0123] Suspicious trajectory marking rules include:

[0124] Candidate associated trajectories are marked as suspicious trajectories;

[0125] The candidate associated trajectory satisfies at least two kinematic constraint checks;

[0126] Candidate associated trajectories were marked as abnormal turning trajectories and the Euclidean distance of the trajectories was below the similarity threshold;

[0127] Calculate the overall confidence score of each candidate trajectory in the labeled candidate trajectory set:

[0128] For associated trajectories, the mean association probability of each candidate trajectory in the labeled candidate trajectory set is calculated to obtain the association confidence score; for single-sensor candidate trajectories, the mean confidence score of the trajectory points is calculated to obtain the association confidence score.

[0129] The feature confidence is calculated based on the minimum Euclidean distance between the candidate trajectory and the false trajectory features;

[0130] Calculate the kinematic confidence score based on the number of kinematic constraint verification terms satisfied by the candidate trajectory;

[0131] The overall confidence score is obtained by weighting the association confidence score, feature confidence score, and kinematic confidence score.

[0132] If the overall confidence score is higher than the confidence score threshold, it is determined to be a valid trajectory; otherwise, it is determined to be a false trajectory, thus obtaining a set of valid trajectories. The overall confidence score integrates quantitative indicators of correlation probability, feature similarity, and kinematic constraints to provide a unified judgment benchmark for the authenticity of trajectories, avoid misjudgment caused by single-dimensional discrimination, and improve the discrimination reliability in complex coupled scenarios.

[0133] The effective trajectories in the effective trajectory set are weighted and fused to obtain the optimal trajectory, and the nonlinear coupling model is then corrected based on the optimal trajectory.

[0134] Methods for obtaining the optimal trajectory include:

[0135] When there is only one single-sensor candidate trajectory as the effective trajectory, it is directly used as the optimal trajectory; otherwise, the fusion weight corresponding to the effective trajectory is calculated based on the comprehensive confidence of the effective trajectory and the inverse matrix of the effective trajectory covariance matrix. The effective trajectory covariance matrix is ​​composed of the position variance in the x-direction, the position variance in the y-direction, and the covariance in the x and y directions of the sensor trajectory. By accurately matching the contribution of each effective trajectory, the interference of low-confidence trajectories with the accuracy of the optimal trajectory can be avoided, and the fusion deviation problem caused by the fixed weight in the existing technology can be solved. Through scene-based weighted fusion, adaptive fusion with a high proportion of high-reliability trajectories and a high weight of low-uncertainty trajectories can be achieved, solving the problem of insufficient fusion accuracy caused by fixed weight or single index weight in the existing technology.

[0136] The states of all valid trajectories are weighted and fused based on fusion weights to obtain the optimal trajectory state for each timestamp. The accurate fusion result of multi-source valid trajectories is the gold standard for real target motion, which not only eliminates single sensor errors but also removes the influence of coupled false trajectories, providing a reliable benchmark for subsequent feedback correction.

[0137] The optimal covariance matrix is ​​obtained by fusing and inverting the inverse matrix of the effective trajectory covariance matrix based on the fusion weights. The uncertainty of the optimal trajectory is quantified by the trace of the covariance inverse matrix, which intuitively reflects the reliability of the fusion result and provides a quantitative indicator for system performance evaluation. At the same time, it avoids subsequent correction bias caused by blindly trusting the fusion result.

[0138] The optimal trajectory is obtained by concatenating the optimal trajectory state and the optimal covariance matrix. The deviation between the actual beam pointing derived from the optimal trajectory and the model's predicted pointing can directly quantify the prediction error of the nonlinear coupled model and is the core driving force for model parameter updates.

[0139] Methods for feedback correction of nonlinear coupled models based on optimal trajectories include:

[0140] Based on the position information of the optimal trajectory, the actual beam pointing is calculated; using the fused high-precision optimal trajectory as a benchmark, the beam pointing corresponding to the real target is inferred, thus eliminating the interference of single sensor measurement error and providing an unbiased benchmark for error assessment of nonlinear coupling models, solving the deficiency of existing technologies in lacking a real beam pointing reference.

[0141] Calculate the deviation between the actual beam pointing and the corrected beam pointing to obtain the optimized error signal;

[0142] With the goal of minimizing the error signal, the gradient descent method is used to update the parameters of the nonlinear coupling model online. If the change in error before and after the parameter update is lower than a first change threshold, or the change in parameters is lower than a second change threshold, the parameters are considered to have converged, the update is stopped, and the updated parameters of the nonlinear coupling model are fed back into the nonlinear coupling model. To minimize the error signal, the parameters of the nonlinear coupling model are dynamically updated, enabling the model to adapt in real time to the dynamic coupling changes of UAV maneuvers and beam scanning. This avoids the prediction failure problem in complex coupling scenarios caused by fixed model parameters in existing technologies, forming a closed-loop optimization of fusion, correction, and re-fusion, continuously improving the beam pointing correction accuracy. Convergence is determined by dual thresholds for error change and parameter change, avoiding incomplete correction due to insufficient parameter updates and preventing system oscillations caused by excessive update amplitudes, ensuring the stability and adaptability of the model parameters, and improving robustness in complex maneuvering scenarios.

[0143] Traditional technical solutions only model mechanical installation errors and simple linear couplings. The compensation models are mostly linear equations with fixed parameters, which cannot capture the interactive coupling effects between multi-degree-of-freedom maneuvers and dynamic scanning strategies. Even when using data-driven methods such as multinomial regression, the modeling logic often involves substituting all parameters indiscriminately, without anchoring the core coupling mechanism between maneuver intensity (acceleration) and scanning state (scanning direction). This results in the model being unable to distinguish between real errors and random noise, leading to a sharp drop in fitting accuracy in complex coupling scenarios. Furthermore, although conventional adaptive systems correct model parameters through feedback, they cannot provide contextualized ground truth anchors for parameter updates because they do not construct a database of spurious trajectory coupling errors in combined maneuver and scanning scenarios. When the coupling scenario changes, parameter convergence is slow and prone to getting trapped in local optima, resulting in insufficient stability of the compensation effect.

[0144] This embodiment focuses on the correlation between acceleration and scanning direction as its core feature. The dynamic interaction between the acceleration vector of the UAV's complex maneuvers and the beam scanning direction is the physical root cause of high-order coupling errors. During modeling, this feature is used to first identify the core interaction terms that significantly affect the error, which are then substituted into a polynomial model to ensure a deep fit between the model structure and the coupling mechanism. A systematic library of false trajectories is constructed for combined maneuvering and scanning scenarios, covering all typical scenarios and providing a scenario-based error benchmark for the model. During online modeling, the true error range can be quickly calibrated by matching real-time maneuvering and scanning parameters with similar scenarios in the library, solving the problem of true value deviation caused by indiscriminate fitting in traditional models. Furthermore, the optimal trajectory after fusion of multiple effective trajectories is used as the high-precision true value to infer the true beam pointing deviation. Simultaneously, combined with scene labels from the template library, scene recognition, deviation calibration, and parameter updates are linked. When a new coupling scenario is detected, the model structure is adjusted based on the mechanism features first, and then the parameters are optimized using least squares, avoiding the limitations of traditional adaptive models that only adjust parameters without adjusting the structure, ensuring rapid adaptation to new high-order coupling scenarios.

[0145] Example 2:

[0146] Please see Figure 4 As shown, this embodiment provides a multi-sensor target trajectory fusion system, including:

[0147] Feedforward compensation module: Based on the beam pointing characteristics of the phased array antenna and combined with the coupling mechanism of UAV maneuvering and beam scanning, a nonlinear coupling model is constructed to predict the beam pointing error and actively correct the radar's beam pointing parameters.

[0148] Data conversion module: synchronizes the corrected radar and all sensor data in time, performs coordinate transformation on the synchronized sensor data, and obtains target data in the world coordinate system;

[0149] Trajectory Analysis Module: Analyzes target data and extracts motion fingerprints; analyzes the initial trajectory and motion fingerprints to obtain a set of valid trajectories;

[0150] Trajectory fusion module: It weights and fuses the effective trajectories in the effective trajectory set to obtain the optimal trajectory, and performs feedback correction on the nonlinear coupling model based on the optimal trajectory.

[0151] In this embodiment, the computer-readable storage medium may be a read-only memory, a random access memory, a magnetic disk, or an optical disk, etc.

[0152] The computer-readable storage medium provided in this embodiment can implement the multi-sensor target trajectory fusion method provided in Embodiment 1. To avoid repetition, it will not be described again here.

[0153] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0154] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-sensor target trajectory fusion method, characterized in that, include: Based on the beam pointing characteristics of phased array antennas and combined with the coupling mechanism of UAV maneuvering and beam scanning, a nonlinear coupling model is constructed to predict beam pointing error and actively correct the radar beam pointing parameters. The corrected radar and all sensor data are synchronized in time, and the synchronized sensor data are transformed to obtain target data in the world coordinate system. Analyze the target data to extract motion fingerprints; analyze the initial trajectory and motion fingerprints to obtain a set of valid trajectories; The effective trajectories in the effective trajectory set are weighted and fused to obtain the optimal trajectory, and the nonlinear coupling model is then corrected based on the optimal trajectory.

2. The multi-sensor target trajectory fusion method according to claim 1, characterized in that, Methods for constructing nonlinear coupled models include: Collect beam pointing parameters of the phased array antenna, UAV maneuver parameters, and beam scanning parameters; Calculate the time series mean of the target factor's time series data, and combine the time series data, time series mean, original bias, and original bias mean to calculate the Pearson correlation coefficient between the target factor and the original bias; Target factors with Pearson correlation coefficients higher than the correlation threshold were selected as significant influencing factors. Interaction terms were constructed based on significant influencing factors, and horizontal orthogonal experiments were designed. The F-value of the interaction terms was calculated through analysis of variance, which is the statistical measure of the significance of the interaction terms on beam pointing deviation. Interaction terms with F-values ​​greater than the interaction threshold were selected as core interaction terms. Based on the coupling mechanism, a nonlinear initial model is constructed using a multinomial model to select the core interaction term and the original deviation. Then, by stepwise regression, significant influencing factors and core interaction terms are substituted into the nonlinear initial model. The nonlinear model is optimized to minimize the Akaike information criterion. The objective function is constructed with the goal of minimizing the sum of squared residuals between the predicted and actual values ​​of the training set. The nonlinear model parameters are then solved through matrix operations to obtain the nonlinear coupled model.

3. The multi-sensor target trajectory fusion method according to claim 2, characterized in that, The beam pointing parameters include azimuth and pitch angles; the UAV maneuvering parameters include pitch rate, roll rate, and yaw rate; the beam scanning parameters include azimuth scanning rate and pitch scanning rate. The original deviation was obtained by designing a full combination experiment combining different maneuvering modes and different scanning strategies, and collecting the difference between the actual beam pointing parameters calibrated by the lidar and the radar beam pointing parameters. Each parameter in the UAV maneuvering parameters and beam scanning parameters is used as a target factor in turn. Only the target factor is changed each time, while the other parameters are fixed, and the time series data of the target factor is obtained.

4. The multi-sensor target trajectory fusion method according to claim 1, characterized in that, Methods for obtaining motion fingerprints include: The state vector is composed of the target data of the UAV in the world coordinate system, the velocity of the UAV in the x and y directions, and the acceleration of the UAV in the x and y directions. This vector is then used as the input of the Kalman filter algorithm to extract the trajectory point number feature and obtain the curvature change frequency. An acceleration vector sequence is constructed based on the acceleration in the x and y directions of the trajectory points. The beam scanning parameters are converted into unit vectors in the world coordinate system to obtain the beam scanning direction vector sequence. The acceleration vector and beam scanning direction vector sequence are projected onto the joint XY dimension and the Pearson correlation coefficient is calculated to obtain the correlation. The velocity of the trajectory point is calculated based on the velocity in the x and y directions, and the smoothness index is obtained through analysis. Calculate the velocity direction angle based on the velocities in the x and y directions of the trajectory points, and analyze to obtain the turning frequency; The motion fingerprint is obtained by standardizing the curvature change frequency, correlation, smoothness index, and turning frequency by combining the corresponding maximum and minimum values.

5. The multi-sensor target trajectory fusion method according to claim 1, characterized in that, Methods for obtaining a valid trajectory set include: Calculate any initial trajectory and The association cost is calculated using a joint probabilistic data association algorithm. The association probability of the same target among all sensor trajectories is calculated based on the association cost. Initial trajectories with association probabilities greater than the association probability threshold are selected to obtain a set of candidate associated trajectories for the same target. If a single trajectory has no other trajectory with an association probability that meets the threshold, it is retained as a single sensor candidate trajectory. Extract motion fingerprints from candidate associated trajectories, retrieve all false trajectory features matching the current scene from the coupling error database; calculate the Euclidean distance between the extracted motion fingerprint and each false trajectory feature; if the trajectory Euclidean distance is lower than the similarity threshold, it is determined to be a suspicious trajectory. Perform kinematic constraint verification and morphological anomaly verification on candidate associated trajectories; If a candidate associated trajectory satisfies any one of the suspicious trajectory marking rules, it is marked as a suspicious false trajectory; otherwise, it is marked as a normal candidate trajectory. The marked candidate trajectory set is obtained by combining the candidate trajectories of a single sensor. Calculate the overall confidence score of each candidate trajectory in the labeled candidate trajectory set; if the overall confidence score is higher than the confidence score threshold, it is determined to be a valid trajectory; otherwise, it is determined to be a false trajectory, and a valid trajectory set is obtained.

6. The multi-sensor target trajectory fusion method according to claim 5, characterized in that, Calculate any initial trajectory and Methods for determining associated costs include: Calculate the initial trajectory at the same timestamp. and The Euclidean distance normalized value is used to obtain the position deviation; Calculate the mean of the rate of change of velocity at adjacent points at the same time stamp to obtain the velocity deviation; calculate and The cosine similarity of the motion fingerprints of the two initial trajectories is used to obtain feature similarity. The association cost is obtained by weighting the calculation based on positional deviation, velocity deviation, and feature similarity.

7. The multi-sensor target trajectory fusion method according to claim 5, characterized in that, Methods for obtaining the optimal trajectory include: If there is only one single-sensor candidate trajectory for the effective trajectory, it is directly used as the optimal trajectory; otherwise, the fusion weight corresponding to the effective trajectory is calculated based on the comprehensive confidence of the effective trajectory and the inverse matrix of the effective trajectory covariance matrix. The states of all valid trajectories are weighted and fused based on the fusion weights to obtain the optimal trajectory state for each timestamp; The optimal covariance matrix is ​​obtained by fusing and inverting the inverse matrix of the effective trajectory covariance matrix based on the fusion weights. The optimal trajectory is obtained by concatenating the optimal trajectory state and the optimal covariance matrix.

8. The multi-sensor target trajectory fusion method according to claim 1, characterized in that, Methods for feedback correction of nonlinear coupled models based on optimal trajectories include: Calculate the actual beam pointing based on the location information of the optimal trajectory; Calculate the deviation between the actual beam pointing and the corrected beam pointing to obtain the optimized error signal; With the goal of minimizing the error signal, the gradient descent method is used to update the parameters of the nonlinear coupling model online. If the change in error before and after the parameter update is lower than the first change threshold, or the change in parameter is lower than the second change threshold, the parameters are determined to have converged, the update is stopped, and the updated parameters of the nonlinear coupling model are fed back into the nonlinear coupling model.

9. The multi-sensor target trajectory fusion method according to claim 1, characterized in that, Methods for obtaining target data in the world coordinate system include: A 2D rigid body transformation is used to obtain the static data in the world coordinate system after the transformation; The static data in the world coordinate system is converted into the target data in the world coordinate system based on the dynamic coordinate transformation matrix.

10. A multi-sensor target trajectory fusion system, implementing the multi-sensor target trajectory fusion method according to any one of claims 1-9, characterized in that, include: Feedforward compensation module: Based on the beam pointing characteristics of the phased array antenna and combined with the coupling mechanism of UAV maneuvering and beam scanning, a nonlinear coupling model is constructed to predict the beam pointing error and actively correct the radar's beam pointing parameters. Data conversion module: synchronizes the corrected radar and all sensor data in time, performs coordinate transformation on the synchronized sensor data, and obtains target data in the world coordinate system; Trajectory Analysis Module: Analyzes target data and extracts motion fingerprints; analyzes the initial trajectory and motion fingerprints to obtain a set of valid trajectories; Trajectory fusion module: It weights and fuses the effective trajectories in the effective trajectory set to obtain the optimal trajectory, and performs feedback correction on the nonlinear coupling model based on the optimal trajectory.

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