A Track Association Method Based on the Fusion of Local and Global Similarities

Abstract

A track association method based on the fusion of local and global similarities, belonging to the technical field of track association, includes the following steps: S1. Preprocess the obtained track pair data, including outlier removal and interpolation alignment of the time overlap part; S2. Extract the local similarity features and global similarity features of the track pair respectively; S3. Weightedly fuse the local and global similarity features, input them into the random forest classifier model for training, and determine the optimal weight combination of different similarity features; S4. Weightedly fuse the local and global similarity features of the unknown track pair according to the optimal weight combination, and input them into the trained random forest classifier model for association judgment. The present invention can reduce the influence caused by misjudgment of local similarity features when the time overlap degree of the track pair is low, so that it still has good association accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of track association, and particularly relates to a track association method based on the fusion of local and global similarities. Background Art

[0002] In the field of track data analysis, track association is an important task, which plays an important role in both civilian and military fields. By analyzing the position information of an object at different time points, track matching and association can be effectively carried out, and then the understanding and prediction of the object's behavior can be realized. However, with the increasing amount of track data and the increasing complexity of track forms, the track association task is facing more and more challenges.

[0003] Traditional track similarity discrimination methods usually focus on the local similarity features of tracks, and mostly only target one-dimensional features among them. This leads to the situation that when facing complex multi-dimensional track scenarios, the extracted features cannot fully represent the overall similarity relationship of tracks, resulting in misjudgment. Therefore, existing track association methods often show deficiencies when dealing with complex scenarios, especially in scenarios where the time overlap between tracks is low. Summary of the Invention

[0004] In order to overcome the deficiencies of the prior art, the present invention proposes an association method based on the fusion of local and global similarities. This method first performs interpolation and time alignment on the tracks to extract local similarity features, and at the same time extracts global similarity features from the original tracks, and determines the optimal weight combination of all features through an optimization scheme, finally realizing accurate association and matching of tracks. This scheme of fusing local and global similarities still has a high association accuracy in scenarios where the time overlap between tracks is low.

[0005] The solution adopted by the present invention to solve the above problems is as follows:

[0006] A track association method based on the fusion of local and global similarities, comprising the following steps:

[0007] S1. Preprocess the obtained track pair data, including removing outliers from the track data and interpolating and aligning the time overlap part;

[0008] S2. Extract the local similarity features and global similarity features of the track pair respectively;

[0009] S3. Perform weighted fusion on the local and global similarity features, input them into a random forest classifier model for training, and determine the optimal weight combination of different similarity features;

[0010] S4. Weightedly fuse the local and global similarity features of the unknown track pair according to the optimal weight combination, and input them into the trained random forest classifier model for association judgment.

[0011] Further, in the step S1, outlier rejection adopts the method based on median sliding window filtering. This method can effectively process sampling noise and outlier data, enhance the robustness of the model, and ensure the stability of association judgment. The process is as follows:

[0012] S111. Determine the size of the sliding window. The window usually has an odd number of data points, such as 3, 5, 7, etc.

[0013] S112. Start the window from the starting position of the signal and slide it one by one data point to the right.

[0014] S113. For each window, sort all the data points in the window, and take the median value after sorting as the output value at the current window position. Compare the current point with the median value. If the difference exceeds the threshold, it is determined as an outlier, and then the outlier is replaced with the median value of the adjacent two points.

[0015] S114. Slide the window to the next position and repeat step S113 until all the data points of the signal are processed.

[0016] Furthermore, in the step S1, for the time overlapping part of the track pair, cubic spline interpolation method is used for interpolation alignment. This method makes the interpolated track smoother, can more accurately reflect the real motion state, and reduces the error caused by data missing. The process is as follows:

[0017] S121. Construct a cubic polynomial on each interval.

[0018] S122. Determine the interpolation conditions, continuity conditions and boundary conditions of the polynomial.

[0019] S123. Solve the relevant coefficients.

[0020] Suppose that after outlier replacement processing, two tracks from two data sources are respectively

[0021] ;

[0022] ;

[0023] where and respectively represent the position information of the and th moment of the sequences and , and and respectively represent and the number of waypoints of the and the After interpolation, the time-aligned parts of the tracks are respectively represented as and ,

[0024] ;

[0025] ;

[0026] wherein, after interpolation and have been aligned on the time axis, and respectively represent the and position information at the th moment of the interpolation sequence, while is the corresponding timestamp, represents the number of waypoints of the interpolated part of the track.

[0027] Furthermore, in step S2, the local similarity features are extracted from the interpolated and aligned parts of the track pair, and the global similarity features are extracted from the overall parts of the original track pairs without interpolation. The local similarity features include: average Euclidean distance, Hausdorff distance, and average Frechet distance; the global similarity features include: centroid distance, bounding box difference, and normalized DTW distance.

[0028] Preferably, the average Euclidean distance is used to measure the average spatial distance between two tracks at the same time point, reflecting the local position characteristics; the Hausdorff distance is used to measure the distance between the farthest points of two tracks, capturing extreme differences and reflecting the local difference characteristics; the average Frechet distance is used to reflect the overall similarity of the track shapes, reflecting the local shape characteristics;

[0029] The extraction of local similarity features is performed on the interpolated tracks and , and the local similarity feature set is represented as,

[0030] ;

[0031] wherein, represents the average Euclidean distance, represents the Hausdorff distance, represents the average Frechet distance;

[0032] The centroid distance is used to calculate the distance between the centroids (center points of the trajectories), reflecting the global position feature; the bounding box difference is used to compare the minimum bounding boxes of the trajectories, measuring the difference in the trajectory ranges and reflecting the global difference feature; the normalized DTW distance uses an algorithm based on dynamic time warping to calculate the shape similarity of the trajectories, and after normalization, it reflects the overall shape similarity of the trajectories, reflecting the global shape feature;

[0033] Global similarity feature extraction is performed on the original trajectories and The global similarity feature set is expressed as

[0034] ;

[0035] wherein, represents the centroid of the trajectory, represents the bounding box difference, represents the normalized DTW distance.

[0036] In step S3, the method for determining the optimal weight combination of different similarity features adopts a method based on Bayesian optimization; this method approximates the objective function through a surrogate model and selects evaluation points based on the acquisition function. Compared with traditional grid search or random search, it significantly reduces the computational cost required for feature weight optimization, and at the same time can still approximate the optimal weight combination, reducing the model tuning time. The process is as follows:

[0037] S31. Define the optimization objective, using the model accuracy as the objective function of Bayesian optimization, with the goal of maximizing the accuracy;

[0038] S32. Determine the variables to be optimized, including the weights of local and global similarity features;

[0039] S33. Construct the optimization problem, taking the feature weights as the optimization variables and defining the upper and lower limits of the parameters;

[0040] S34. Perform Bayesian optimization, gradually select parameter combinations through the Bayesian optimization framework, evaluate the effects of each group of parameters, and update the search strategy to approximate the optimal solution;

[0041] S35. Verification and evaluation, according to the optimal parameter combination obtained by Bayesian optimization, retrain the model and evaluate the model performance through cross-validation.

[0042] In S32, let the weight of the local similarity feature obtained by Bayesian optimization be , and the weight of the global similarity feature be . The weighted fusion feature

[0043] ;

[0044] ;

[0045] ;

[0046] Among them, is the local similarity weighted fusion feature, is the global similarity weighted fusion feature, is the final input feature vector.

[0047] In the step S4, the input of the random forest classifier model is the local and global similarity features weighted and fused according to the optimal weights for the unknown track pair, and the output is the association result, where 0 means not associated and 1 means associated.

[0048] The beneficial effects of the present invention are mainly manifested in:

[0049] (1) High association accuracy: This method uses local and global similarity features to jointly judge whether a track pair is associated, and determines the importance of different features through Bayesian optimization and assigns corresponding weights, avoiding the situation that due to the low time coincidence degree of the track pair, the local similarity feature is not sufficient to judge whether the track is associated, thus misjudging the association result. The described track association method has a high association accuracy, and can still maintain a high association accuracy even in the case of a low time coincidence degree of the track pair.

[0050] (2) High association versatility: The local and global similarity features used in this method are mainly extracted from three dimensions: position feature, difference feature and shape feature, and do not rely on motion features such as speed and acceleration, avoiding the situation that the association scheme is not versatile due to the large difference in the motion modes of the associated objects. This makes the method have strong adaptability in different types of object association tasks (such as airplanes, ships, vehicles, etc.), especially suitable for scenarios with variable track motion modes. In addition, the importance of different similarity features may vary in different scenarios. The present invention uses Bayesian optimization technology to automatically optimize the weight combination of local and global features, maximizing the association accuracy. Compared with the fixed weight scheme, this method can adapt to different scenarios and different track complexities, improving the generalization ability and accuracy of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a schematic flow chart of a track association method based on local and global similarity fusion provided by an embodiment of the present invention.

[0052] Figure 2 is a schematic test flow chart of a track association method based on local and global similarity fusion provided by an embodiment of the present invention.

[0053] Figure 3 It is a schematic diagram of the track scene with different time overlaps provided by the embodiments of the present invention. Specific embodiments

[0054] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0055] Refer to Figures 1 to 3 , a track association method based on the fusion of local and global similarities, comprising the following steps:

[0056] S1. Preprocess the obtained track pair data, including removing outliers from the track data and interpolating and aligning the time overlap part;

[0057] In the step S1, the outlier removal adopts the method based on median sliding window filtering; this method can effectively process sampling noise and outlier data, enhance the robustness of the model, and ensure the stability of the association judgment. The process is as follows:

[0058] Let the track sequence be , where represents the position information of the track point.

[0059] S111. Determine the window size (such as etc.), and the window moves to traverse each track point;

[0060] S112. For each window , sort the track point positions in the window by value, and take the median value .

[0061] S113. For each track point , compare it with the median value of the corresponding window:

[0062] If , then determine that is an outlier, and replace it with the median value of the adjacent two points,

[0063] ;

[0064] S114. Repeat the above steps until all points are processed.

[0065] In the step S1, for the interpolation and alignment of the time overlap part of the track pair, the cubic spline interpolation method is used; this method makes the track generated by interpolation smoother, can more accurately reflect the real motion state, and reduces the error caused by data loss; let the track sequence be The corresponding time sequence is , where Indicates the timestamp of the track point, the process is as follows:

[0066] S121. In each interval [ t i , t i +1 ] upper Construct a cubic polynomial,

[0067] ;

[0068] Wherein, , , and are the coefficients to be determined.

[0069] S122. Determine the undetermined coefficients through the following conditions:

[0070] Interpolation condition: The spline curve must pass through each data point,

[0071] , ;

[0072] Continuity condition: For each node, the first derivative and the second derivative of the spline curve are continuous,

[0073] ;

[0074] Boundary condition: For example, the natural boundary condition (the second derivative is 0 at the boundary).

[0075] S123. Solve the corresponding coefficients , , and ;

[0076] After considering the two tracks from two sources and replacing the outliers, track is expressed as , track is expressed as ,

[0077] ;

[0078] ;

[0079] Wherein and respectively represent the position information of the and th moment of the sequences, and and is the corresponding timestamp, and respectively represent and the number of waypoints of the and After interpolation, the time-aligned parts of the trajectories are respectively represented as and ,

[0080] ;

[0081] ;

[0082] Among them, the and after interpolation have been aligned on the time axis, and respectively represent the and position information at the th moment of the interpolation sequence, while is the corresponding timestamp, represents the number of waypoints of the interpolated part of the trajectory.

[0083] S2. Extract the local similarity features and global similarity features of the trajectory pair respectively;

[0084] In the step S2, the local similarity features are extracted from the interpolated and aligned parts of the trajectory pair, and the global similarity features are extracted from the overall parts of the original trajectory pair without interpolation. The local similarity features include: average Euclidean distance, Hausdorff distance, and average Frechet distance. The global similarity features include: centroid distance, bounding box difference, and normalized DTW distance.

[0085] The average Euclidean distance is used to measure the average spatial distance between two trajectories at the same time point, reflecting the local position features; the Hausdorff distance is used to measure the distance between the farthest points of two trajectories, capturing the extreme differences and reflecting the local difference features; the average Frechet distance is used to reflect the overall similarity of the trajectory shapes, reflecting the local shape features.

[0086] The extraction of local similarity features is performed on the interpolated trajectories and as follows:

[0087] (1) Extract the average Euclidean distance ,

[0088] ;

[0089] (2) Extract the Hausdorff distance ,

[0090] ;

[0091] (3) Extract the average Frechet distance :

[0092] The number of dots in the track may be relatively large. To speed up the calculation and facilitate normalization, a method of first segmenting and then calculating the Frechet distance for each segment of the track separately and finally calculating the weighted average Frechet distance is adopted.

[0093] The Frechet distance of each segment is defined as,

[0094] F ( T i ( k ) , T j ( k ) )= inf α , β sup t ∈[0,1] P iα ( t ) ' - P jβ ( t ) ' ;

[0095] Among them, represents the th segment, and are parametric functions, indicating the matching of the dot sequences on the track segments and , represents the time parameter, and the value range is [0,1] , and respectively represent the dots at the time and on the track segments ;

[0096] Assume that it is divided into segments in total, and the final average Frechet distance is,

[0097] ;

[0098] Among them, is the length of the th segment;

[0099] (4) Normalize each feature and represent the local similarity feature set is represented as,

[0100] ;

[0101] The centroid distance is used to calculate the distance between the centroids (central points of the trajectories), reflecting the global position feature; the bounding box difference is used to compare the minimum bounding boxes of the trajectories, measuring the difference in the trajectory ranges and reflecting the global difference feature; the normalized DTW distance uses an algorithm based on dynamic time warping to calculate the shape similarity of the trajectories, and after normalization, it reflects the overall shape similarity of the trajectories, reflecting the global shape feature.

[0102] Global similarity feature extraction is performed on the original trajectories and as follows:

[0103] (1) Extract the centroid distance ,

[0104] ;

[0105] (2) Extract the bounding box difference ,

[0106] ;

[0107] Among them, represents the bounding box of the trajectory , that is, the minimum circumscribed rectangle, represented by the minimum and maximum values on each coordinate dimension;

[0108] (3) Extract the normalized DTW distance ,

[0109] ;

[0110] Among them, is the optimal matching path found by the DTW dynamic time warping algorithm, composed of a series of index pairs , is the number of matching point pairs in the path;

[0111] (4) Normalize each feature for representation, and the global similarity feature set is represented as,

[0112] ;

[0113] S3. Weightedly fuse the local and global similarity features and input them into the random forest classifier model for training to determine the optimal weight combination of different similarity features.

[0114] In step S3, the method for determining the optimal weight combination of different similarity features adopts a method based on Bayesian optimization. This method approximates the objective function through a surrogate model and selects evaluation points based on the acquisition function. Compared with traditional grid search or random search, it significantly reduces the computational cost required for feature weight optimization, and still can approximate the optimal weight combination, reducing the model tuning time. The process is as follows:

[0115] S31. Define the optimization objective, use the model accuracy as the objective function of Bayesian optimization, and the optimization objective function can be written as,

[0116] ;

[0117] Where, and represent the weight combinations of local similarity features and global similarity features respectively, is the prediction accuracy of the model, and the goal is to maximize the accuracy.

[0118] S32. Determine the variables to be optimized, including the weights of local and global similarity features,

[0119] ;

[0120] ;

[0121] Where, represents the weight of the th local similarity feature, takes 1, 2, and 3, represents the weight of the th global similarity feature, takes 1, 2, 3.

[0122] S33. Construct the optimization problem, take the feature weights as the optimization variables, and define the upper and lower limits of the parameters,

[0123] , ;

[0124] , ;

[0125] These constraints ensure that the sum of the weights is 1, representing the proportion of each feature weight.

[0126] S34. Execute Bayesian optimization, gradually select parameter combinations through the Bayesian optimization framework, evaluate the effects of each group of parameters, and update the search strategy to approximate the optimal solution. The core of Bayesian optimization is to construct a surrogate model to approximate the objective function .

[0127] Select the initial point , and calculate the corresponding objective function value .

[0128] Then, perform fitting through the Gaussian process to generate an estimated mean function as the expected value, and update the surrogate model ,

[0129] ;

[0130] Select the next evaluation point through the acquisition function,

[0131] ;

[0132] Calculate the new objective function value , and update the model.

[0133] Repeat the above process until the maximum number of iterations is reached or the error is less than the threshold.

[0134] S35. Verification and evaluation: According to the optimal parameter combination obtained by Bayesian optimization, retrain the model and evaluate the model performance through cross-validation.

[0135] Let the local similarity feature weight obtained by Bayesian optimization be , and the global similarity feature weight be , the weighted fused feature,

[0136] ;

[0137] ;

[0138] ;

[0139] Among them, is the local similarity weighted fused feature, is the global similarity weighted fused feature, is the final input feature vector.

[0140] S4. Weightedly fuse the local and global similarity features of the unknown track pair according to the optimal weight combination, and input them into the trained random forest classifier model for association judgment.

[0141] The test process of this embodiment is as Figure 2 shown. For the random forest classifier model described in step S4, the input is the local and global similarity features of the unknown track pair weighted and fused according to the optimal weight, and the output is the association result, where 0 means non-association and 1 means association.

[0142] Let the trained random forest classifier be , and input the weighted similarity features of the test track pair . The classifier outputs the predicted label .

[0143] ;

[0144] Among them, represents the association judgment result of the test track pair. Outputting means that the track pair is not associated. Outputting means that the track pair is associated.

[0145] In summary, the method proposed by the present invention extracts the local and global similarity features of the track pair, determines the optimal weight combination of all features through the Bayesian optimization scheme, and finally realizes the accurate association and matching of the tracks. This scheme that fuses local and global similarities has high association accuracy and can be applied to scenarios with a low time coincidence degree between tracks. Schematic diagrams of scenarios with different time coincidence degrees are shown in Figure 3 .

[0146] The above are only the preferred examples of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present application shall be included within the protection scope of the present application.

Claims

1. A track association method based on local and global similarity fusion, characterized in that: The method comprises the following steps: S1. Preprocessing the obtained track data, including removing outliers from the track data and aligning the time-coinciding parts by interpolation; S2, extracting local similarity features and global similarity features of the track pairs respectively; S3, weighted fusion of local and global similarity features, input into the random forest classifier model for training, and determine the optimal weight combination of different similarity features; S4, weighted fusion of local and global similarity features of unknown track pairs according to the optimal weight combination, and input into the trained random forest classifier model for association judgment; In step S2, the local similarity features are extracted from the interpolated aligned part of the track pair, and the global similarity features are extracted from the whole part of the original track pair without interpolation. The local similarity features include the average Euclidean distance, the Hausdorff distance and the average Frechet distance; the global similarity features include the centroid distance, the bounding box difference and the normalized DTW distance; The average Euclidean distance is used to measure the average spatial distance between two tracks at the same time point, reflecting the local position characteristics; the Hausdorff distance is used to measure the distance between the farthest points in the two tracks, capturing extreme differences and reflecting local difference characteristics; the average Frechet distance is used to reflect the overall similarity of track shapes and reflecting local shape characteristics; The centroid distance is used to calculate the distance between the centroids of the tracks, reflecting the global position characteristics; the bounding box difference is used to compare the minimum bounding boxes of the tracks, measure the difference in track ranges, and reflect the global difference characteristics; the standardized DTW distance uses an algorithm based on dynamic time warping to calculate the shape similarity of the tracks, and after normalization, it reflects the overall shape similarity of the tracks, reflecting the global shape characteristics; In step S3, the method for determining the optimal weight combination of different similarity features is based on the Bayesian optimization method, and the process is as follows: S31. Define the optimization goal and use the model accuracy as the objective function of Bayesian optimization; S32, determining variables to be optimized, including weights of local and global similarity features; S33, construct an optimization problem, use feature weights as optimization variables, and define upper and lower limits of parameters; S34, performing Bayesian optimization, gradually selecting parameter combinations through the Bayesian optimization framework, evaluating the effect of each set of parameters, and updating the search strategy to approach the optimal solution; S35, verification and evaluation, based on the optimal parameter combination obtained by Bayesian optimization, retrain the model and evaluate the model performance through cross-validation.

2. A track association method based on local and global similarity fusion according to claim 1, characterized in that: In step S1, outliers are eliminated by using a median sliding window filtering method, and the process is as follows: S111, determine the size of the sliding window, the window is an odd number of data points; S112, starting from the starting position of the signal, slide the window to the right one data point at a time; S113, for each window, sort all data points in the window, take the sorted middle value as the output value of the current window position; compare the current point position with the median value, if the difference exceeds the threshold, it is determined to be an abnormal point, and then replace the abnormal point with the median value of two adjacent points; S114, slide the window to the next position, and repeat step S113 until all data points of the signal are processed.

3. A track association method based on local and global similarity fusion according to claim 1 or 2, characterized in that: In step S1, the track is interpolated and aligned for the time-coinciding part, using a cubic spline interpolation method, and the process is as follows: S121. Construct a cubic polynomial on each interval; S122, determining the interpolation condition, continuity condition and boundary condition of the polynomial; S123. Solve for the correlation coefficient.

4. A track association method based on local and global similarity fusion according to claim 1 or 2, characterized in that: In step S4, the random forest classifier model is inputted with the local and global similarity features of the unknown track pair weighted and fused according to the optimal weight, and the output is the association result, 0 for no association and 1 for association.

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