An improved PCA-KNN method for multi-feature track association
By optimizing the K-nearest neighbor algorithm through PCA dimensionality reduction and a dynamic K-policy driven by signal-to-noise ratio, the problems of high computational overhead and noise adaptation in high-dimensional feature track association are solved, and efficient track association discrimination is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN INST OF TECH AT WEIHAI
- Filing Date
- 2026-05-27
- Publication Date
- 2026-07-24
AI Technical Summary
Existing K-nearest neighbor algorithms suffer from high computational overhead and weak dynamic noise adaptation in high-dimensional feature trajectory association scenarios. Redundant features easily amplify noise, resulting in poor accuracy and real-time performance in trajectory association discrimination.
The algorithm optimizes the track association algorithm by removing feature redundancy through PCA dimensionality reduction, adopting a dynamic K-strategy driven by weighted Euclidean distance and signal-to-noise ratio, and combining principal component weights to calculate the neighborhood size.
It significantly reduces the computational complexity under high-dimensional features, improves the real-time performance and accuracy of track association, adapts to different noise conditions, and maintains optimal association performance.
Smart Images
Figure CN122281934B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of track association technology, and more specifically, relates to an improved PCA-KNN method for multi-feature track association. Background Technology
[0002] Multi-sensor target tracking systems integrate observation information from various heterogeneous sensors with local track data through multi-source data fusion technology. Track correlation is an indispensable core component, and its correlation performance directly determines the accuracy and overall reliability of multi-sensor fusion tracking.
[0003] The essence of track association is to determine whether different track segments and their corresponding feature vectors originate from the same moving target, which is a prerequisite for the effective fusion of multi-source tracks. In practical engineering applications, tracks are usually represented by high-dimensional features by fusing multiple types of information such as kinematic parameters, spatial position, and signal attributes. While this can enrich the dimensions of track description and improve the robustness of association in complex scenarios, the introduction of high-dimensional features also significantly increases the computational overhead and processing latency of the algorithm.
[0004] The existing K-Nearest Neighbors (KNN) algorithm, with its advantages of simple principle and strong interpretability, is often used as the benchmark algorithm for track association tasks. However, when applied to high-dimensional heterogeneous multi-feature track association scenarios, it still has obvious technical defects: First, the high-dimensional feature space is prone to distance concentration effect, which significantly reduces the separability of target categories and increases the computational load. Second, in actual working conditions, the sensor measurement quality changes dynamically with the environment, and the signal-to-noise ratio (SNR) fluctuates significantly. The traditional fixed neighborhood size K cannot adapt to different noise conditions and it is difficult to maintain the optimal association effect. Third, there are a large number of redundant features and weakly correlated features in the original feature space, which can easily amplify environmental noise interference and seriously weaken the accuracy of KNN track association decisions based on distance metrics. Summary of the Invention
[0005] The purpose of this application is to provide an improved PCA-KNN method for multi-feature track association, in order to solve the technical problems in the existing track association methods, such as high computational cost under high-dimensional features, weak dynamic noise adaptation capability, and the tendency of redundant features to amplify noise, resulting in poor accuracy and real-time performance of track association discrimination.
[0006] To achieve the above objectives, embodiments of this application provide an improved PCA-KNN method for multi-feature track association, comprising the following steps: Obtain high-dimensional feature vectors representing track pairs and construct training data; use the training data to fit a PCA model to obtain principal components and their eigenvalues; select the top k principal components whose cumulative explained variance reaches a preset threshold; project them to obtain the trained PCA model; and calculate the principal component weights based on the eigenvalues. Based on the trained PCA model, the features of the sample to be queried are projected onto the low-dimensional principal component space to obtain the dimensionality-reduced feature vector. The neighborhood size is calculated based on the signal-to-noise ratio of the dimensionality-reduced feature vector, and the weighted Euclidean distance is calculated in combination with the principal component weights. K nearest neighbors are selected based on the weighted Euclidean distance and the track association results are output by majority vote.
[0007] Preferably, the formula for calculating the track association results is: ; In the formula, The result of the track association judgment for the track pair to be queried. Let be the feature vector of the track pair to be queried in the low-dimensional space of PCA. To determine the K nearest neighbor labels, a majority vote is required. The associated label of the Kth nearest neighbor training sample after sorting by weighted Euclidean distance from smallest to largest, where K represents the number of nearest neighbor samples that participated in the majority vote.
[0008] Preferably, before constructing the training data, the high-dimensional feature vector needs to be standardized to obtain a standardized feature vector, as shown in the formula: ; In the formula, For standardized feature vectors The Middle The first sample 1 eigenvalue, High-dimensional feature vectors The Middle The first sample 1 eigenvalue, For the first The mean of each feature, For the first The standard deviation of each feature.
[0009] Preferably, the process of fitting the PCA model includes: calculating the covariance matrix of the standardized eigenvectors and performing eigenvalue decomposition to obtain the principal components and their eigenvalues.
[0010] Preferably, the formula for obtaining the principal components and their eigenvalues is: ; ; In the formula, For standardized feature vectors The covariance matrix, The total number of samples, For the first The eigenvalues corresponding to each principal component, i.e., the variance contribution. For the first The eigenvectors corresponding to each principal component represent the principal directions, and M is the total number of principal component directions. For the original D-dimensional features, M = D is usually the case.
[0011] Preferably, based on the trained PCA model, the standardized feature vector input is projected onto the low-dimensional subspace to obtain the dimensionality-reduced data matrix; Using the principal component weights obtained in the offline phase, the weighted Euclidean distance between the dimensionality-reduced data matrix and the dimensionality-reduced eigenvectors is calculated.
[0012] Preferably, the formula for calculating the weighted Euclidean distance is: ; In the formula, Let be the weight corresponding to the m-th principal component, representing the importance of that principal component in the distance calculation. Let be the value of the feature vector of the dimensionality-reduced training sample to be compared along the direction of the m-th principal component. Let be the value of the eigenvector of the track to be queried after dimensionality reduction, taken in the direction of the m-th principal component.
[0013] Preferably, the formula for selecting the first k principal components whose cumulative explained variance reaches a preset threshold is as follows: ; In the formula, This represents the cumulative percentage of variance explained by the top k principal components. For the first The eigenvalues corresponding to each principal component.
[0014] Preferably, the formula for calculating the neighborhood size is: ; In the formula, The neighborhood size is based on the signal-to-noise ratio.
[0015] Preferably, the formula for calculating the principal component weights based on eigenvalues is: ; In the formula, For the first The eigenvalues corresponding to each principal component For the first The eigenvalues corresponding to each principal component.
[0016] The beneficial effects of this application are as follows: This application provides an improved PCA-KNN method for multi-feature track association. First, it fits a PCA model using training data and selects the top k principal components whose cumulative explained variance reaches a preset threshold. The original high-dimensional track features are projected into a low-dimensional principal component space, eliminating redundant and weakly correlated features, avoiding the distance concentration effect in high-dimensional space, significantly reducing distance calculation complexity and processing latency, fundamentally solving the problem of high computational overhead under high-dimensional features, and improving the real-time performance of track association. Next, it assigns principal component weights based on feature values, and uses weighted Euclidean distance for similarity measurement in the low-dimensional space. This strengthens high-contribution principal components and weakens low-energy principal components dominated by noise, avoiding redundant features amplifying environmental noise, and effectively improving the accuracy and robustness of track association decisions. Finally, the neighborhood size K is adaptively determined based on the signal-to-noise ratio of the sample to be queried. When the signal-to-noise ratio is low, K is increased to stabilize voting, and when the signal-to-noise ratio is high, K is decreased to maintain resolution. This overcomes the shortcomings of the traditional fixed K, which cannot adapt to measurement quality fluctuations, and solves the problem of weak dynamic noise adaptation capability. It can maintain the best correlation performance under different working conditions.
[0017] In summary, this application organically combines PCA dimensionality reduction, principal component weighting, dynamic K-strategy, and weighted KNN voting to optimize the accuracy and real-time performance of track association while preserving key information, suppressing noise, reducing computational load, and adapting to different operating conditions. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 A schematic diagram of the overall process of the improved PCA-KNN method for multi-feature track association provided in an embodiment of this application; Figure 2 A schematic diagram of an improved PCA-KNN method provided in an embodiment of this application; Figure 3 A flowchart of PCA-based dimensionality reduction provided in an embodiment of this application; Figure 4 A graph showing the association accuracy of different classifiers as a function of SNR, provided in an embodiment of this application; Figure 5 This is a dynamic K-mapping curve diagram driven by SNR provided in an embodiment of this application; Figure 6 This application provides different methods and accuracy heatmaps at SNR levels for an embodiment of the present application; Figure 7 A prediction latency variation curve as a function of feature dimension is provided in one embodiment of this application; Figure 8 This application provides runtime heatmaps for different methods and feature dimensions in one embodiment of the present application. Figure 9 A comparison diagram showing the operation of d=15 in one embodiment of this application. Detailed Implementation
[0020] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.
[0021] This application proposes an improved PCA-KNN method for multi-feature track association. First, high-dimensional track features are reduced in dimensionality using PCA (Principal Component Analysis) to remove feature redundancy, and the original feature space is projected into a compact subspace while retaining a preset variance percentage. Second, weights are assigned in the reduced-dimensional space based on the principal component contributions of the PCA, constructing a weighted Euclidean distance, which serves as a metric for the similarity between track samples. Finally, a dynamic K-strategy driven by signal-to-noise ratio (SNR) is introduced, selecting nearest neighbor samples based on the weighted Euclidean distance, and adapting the neighborhood size K to the measurement quality. Specifically, a larger neighborhood value K is used for low SNR to enhance robustness, while a smaller neighborhood value K is used for high SNR to maintain discriminability. This effectively solves the drawbacks of traditional track association methods, such as high computational cost for high-dimensional features, inability of fixed neighborhoods to adapt to dynamic noise, and the amplification of interference by redundant features, significantly improving the accuracy and real-time performance of track association under complex conditions.
[0022] Please see Figure 1 An improved PCA-KNN method for multi-feature track association, provided in one embodiment of this application, includes: This application models pairwise track association between sensors as a binary classification decision: association indicates that the two tracks originate from the same target; non-association indicates that the two tracks originate from different targets. Each candidate track pair is represented by a high-dimensional feature vector, which includes positional features (such as longitude, latitude, and altitude), motion features (such as speed, heading, and acceleration), and signal features (such as RCS and SNR). This application is implemented in two stages: offline training and online association. A supervised classification model is built based on labeled training samples to determine track association.
[0023] S1: Obtain high-dimensional feature vectors representing track pairs and construct training data; use the training data to fit a PCA model to obtain principal components and their eigenvalues; select the top k principal components whose cumulative explained variance reaches a preset threshold; project them to obtain the trained PCA model; and calculate the principal component weights based on the eigenvalues.
[0024] During the offline training phase of the PCA model, labeled training data (representing the high-dimensional feature vectors of the original track pairs, (x, y)) are used to complete the PCA model fitting and principal component weight calculation, providing a well-trained PCA model and principal component weights for the online phase.
[0025] Please see Figure 1 First, the high-dimensional feature vectors representing track pairs are standardized to construct a dataset. Then, the covariance matrix is estimated, and its eigenvectors and eigenvalues are calculated. The eigenvectors define mutually orthogonal principal directions and are sorted according to the magnitude of their explained variance. The smallest dimension k that satisfies the requirement of 90% cumulative explained variance is retained, and the features are projected onto a k-dimensional subspace to obtain the trained PCA model. This step suppresses redundancy and improves the robustness and computational efficiency of subsequent distance-based association.
[0026] Specifically, firstly, for those containing One sample High-dimensional feature vector of each original feature Standardize the data to construct the training data. The formula is as follows: ; In the formula, For standardized feature vectors The Middle The first sample 1 eigenvalue, High-dimensional feature vectors The Middle The first sample 1 eigenvalue, For the first The mean of each feature, For the first The standard deviation of each feature.
[0027] Then, calculate the standardized eigenvectors. The covariance matrix is obtained by performing eigenvalue decomposition to obtain the principal components: ; ; In the formula, For standardized feature vectors The covariance matrix, The total number of samples, For the first The eigenvalues corresponding to each principal component are the variance contribution (explained variance). For the first The eigenvectors corresponding to each principal component represent the principal directions. The total number of principal component directions, for Dimensional original features, usually include = .
[0028] Select the top k principal components to ensure that the cumulative explained variance reaches a preset threshold (90% in this application), as shown in the formula: ; In the formula, This represents the cumulative percentage of variance explained by the top k principal components. For the first The eigenvalues corresponding to each principal component.
[0029] Select the eigenvectors corresponding to the first k principal components and construct the projection matrix. This yields a trained PCA model. The standardized feature vectors are then... Projecting onto this lower-dimensional subspace yields the dimensionality-reduced data matrix: ; In the formula, The eigenvector matrix corresponding to the selected principal components. This is the data matrix after dimensionality reduction.
[0030] According to the contribution of each retained k principal component to the total variance Assigning weights: Principal components with larger explained variances have larger weights. Specifically, principal component weights... From the eigenvalues of principal components The formula is derived and normalized to make the sum of the weights equal to 1. ; ; In the formula, For the first The eigenvalues corresponding to each principal component For the first The eigenvalues corresponding to each principal component.
[0031] S2: Based on the trained PCA model, the features of the sample to be queried are projected onto the low-dimensional principal component space to obtain the dimensionality-reduced feature vector; the neighborhood size is calculated based on the signal-to-noise ratio of the dimensionality-reduced feature vector, and the weighted Euclidean distance is calculated in combination with the principal component weights. K nearest neighbors are selected based on the weighted Euclidean distance and the track association results are output by majority vote.
[0032] The features of the sample to be queried are input into the trained PCA model and projected onto the low-dimensional principal component space to obtain the dimensionality-reduced feature vector. Simultaneously, the neighborhood size K is calculated based on the signal-to-noise ratio of the current dimensionality-reduced feature vectors.
[0033] Specifically, this application employs a dynamic K-strategy based on signal-to-noise ratio (SNR): when the SNR is low, the reliability of feature measurement is low, so a larger neighborhood is used to stabilize majority voting; when the SNR is high, the reliability of feature measurement is high, so a smaller neighborhood is used to maintain local resolution. This application adopts the following SNR adaptive rule: ; In the formula, To determine the neighborhood size based on the signal-to-noise ratio, nested max / min operations restrict the neighborhood size K to the interval [5,9], achieving adaptive adjustment by taking a larger value when the SNR is low and a smaller value when the SNR is high.
[0034] Subsequently, the principal component weights obtained in the offline phase are used to calculate the dimensionality-reduced feature vector. With the dimensionality-reduced data matrix The weighted Euclidean distance between them is: ; In the formula, For the first The weights corresponding to each principal component represent the importance of that principal component in the distance calculation. The feature vectors of the training samples to be compared are reduced in dimensionality at the th... The values taken in each principal component direction, For the dimensionality-reduced feature vector of the track to be queried, at the 1st... The values taken in each principal component direction.
[0035] This distance metric emphasizes the main direction with higher information content and reduces the influence of low-energy directions dominated by noise.
[0036] Finally, the K nearest neighbors of the dimensionality-reduced feature vector are selected based on weighted Euclidean distance, and the track association decision is obtained through majority voting. The output of the KNN majority vote is shown below. for: ; In the formula, The result of the track association judgment for the track pair to be queried. Let be the feature vector of the track pair to be queried in the low-dimensional space of PCA. To determine the K nearest neighbor labels, a majority vote is required. The associated label of the Kth nearest neighbor training sample after sorting by weighted Euclidean distance from smallest to largest, where K represents the number of nearest neighbor samples that participated in the majority vote.
[0037] Example 1: Performance evaluation of track association detection algorithm based on simulated track data.
[0038] This embodiment evaluates algorithm performance on the MATLAB platform based on simulated flight path data. The dataset contains eight feature dimensions: position features (longitude, latitude, altitude), motion features (velocity, heading angle, acceleration), and signal features (RCS and signal-to-noise ratio). 500 samples were generated for each of the two target classes, for a total of 1000 samples. Comparison algorithms include: the traditional KNN with a fixed neighborhood size of K=7, SVM classifiers, and the improved PCA-KNN proposed in this application.
[0039] To verify the robustness of different track association detection methods in low signal-to-noise ratio (SNR) environments, experiments were conducted to compare the association detection accuracy of each algorithm under different SNR conditions, as shown in Table 1 below: Table 1: Correlation accuracy (%) at different SNR (Signal-to-Noise Ratio) levels
[0040] Table 1 and Figure 4 The correlation accuracy at different SNR (signal-to-noise ratio) levels is presented. It can be seen that PCA-KNN consistently outperforms the traditional KNN and SVM baselines under low SNR conditions. For example, at an SNR of 5 dB, PCA-KNN improves correlation accuracy by 9.01 percentage points compared to the traditional KNN. As the SNR increases, the three curves gradually converge, indicating reduced measurement noise and improved data reliability. This phenomenon is consistent with... Figure 5 The SNR-driven dynamic K-rule shown is consistent: when the noise is large, the neighborhood is increased to enhance robustness, and when the SNR is high, the neighborhood is decreased to maintain discriminability.
[0041] Figure 5 The mapping scheme from SNR to K used in the experiment is presented. K is restricted to the interval [5,9] and decreases in a stepwise manner with SNR, thereby achieving a dynamic balance between robustness and discriminability while improving measurement quality. Figure 6 Furthermore, the correlation accuracy of different methods under various SNR conditions is summarized in the form of heatmaps, which intuitively reflects the performance differences of each method under low SNR and the convergence trend under high SNR.
[0042] To verify the real-time performance advantage of this application in high-dimensional feature scenarios, the prediction latency of each algorithm was further analyzed as the feature dimension increased. The results are shown in Table 2 and... Figure 7 As shown.
[0043] Table 2: Relationship between Predicted Delay (ms) and Feature Dimension
[0044] As can be seen from Table 2 and Figure 7 it can be seen that the delays of traditional KNN and SVM increase approximately linearly with the dimension because the complexity of distance calculation is proportional to the number of features. In contrast, the PCA-KNN method proposed in this application completes track association within the low-dimensional PCA subspace. Therefore, under the settings of this application, its prediction time is hardly affected by the original feature dimension and is at a low level of about 0.6 ms. Taking the feature dimension d = 15 as an example, PCA-KNN reduces the predicted delay from 4.413 ms of traditional KNN to 0.589 ms, achieving a 86.65% reduction. Figure 8 The running times of different methods at different dimensions are shown in a heat map, which more intuitively reflects the linear growth trend of KNN and SVM and the flat trend of PCA-KNN.
[0045] Furthermore, Table 3 summarizes the key metrics to generalize accuracy and efficiency.
[0046] Table 3: Summary of Key Performance Metrics
[0047] The results show that the PCA-KNN method proposed in this application obtains the highest average association accuracy (79.49%) while maintaining the lowest high-dimensional delay. Figure 9 The comparison of the representative running times of each algorithm when d = 15 is given. Among them, the height of the bar corresponding to PCA-KNN is the lowest, intuitively reflecting the computational efficiency advantage of track association within a compact subspace.
[0048] For newly arrived track association query samples, the traditional KNN method needs to calculate distances in the original D-dimensional space, so the computational amount of each query is O(ND). While PCA-KNN in this application calculates distances in the reduced k-dimensional subspace (k << D), reducing the complexity of each query to O(Nk). Among them, the PCA training step (including covariance estimation and eigen-decomposition) is completed in the offline stage, and the computational cost can be amortized in a large number of online queries. In an actual system, the SNR can usually be directly obtained from the sensor signal processing chain, so the K(SNR) parameter can be updated online with almost no additional overhead. The simplicity of the dynamic K rule also makes it easier to tune parameters compared to interval-based classifiers such as SVM.
[0049] This application includes three practical hyperparameters: an explanatory variance threshold for selecting k, upper and lower bounds of k, and a mapping from SNR to k. A higher variance threshold retains more principal components (larger k), potentially improving accuracy but increasing computational cost. The lower / upper bounds of k control the bias-variance tradeoff in voting: too small a k leads to unstable decisions in track association results at low SNR, while too large a k blurs class boundaries at high SNR. In deployment, the K(SNR) mapping can be calibrated using validation data or adjusted for different sensors and feature definitions, while maintaining the interpretability and ease of implementation of the rules.
[0050] In summary, this application proposes an improved PCA-KNN method for multi-feature track association. By combining PCA-based dimensionality reduction, contribution-weighted distance, and SNR-adaptive dynamic K-rule, robustness under low SNR is improved, and prediction latency is reduced in high-dimensional settings. In simulation studies, compared with traditional KNN, PCA-KNN improves the accuracy at 5dB low SNR from 50.60% to 59.61% (an improvement of 9.01 percentage points), and reduces the high-dimensional prediction time at d=15 from 4.413ms to 0.589ms (a reduction of 86.65%). Compared with more complex classifiers, this application still maintains interpretability and ease of parameter tuning.
[0051] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0052] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. An improved PCA-KNN method for multi-feature track association, characterized in that, Includes the following steps: Obtain high-dimensional feature vectors representing track pairs and construct training data; use the training data to fit a PCA model to obtain principal components and their eigenvalues; select the top k principal components whose cumulative explained variance reaches a preset threshold; project them to obtain the trained PCA model; and calculate the principal component weights based on the eigenvalues. Based on the trained PCA model, the features of the sample to be queried are projected onto the low-dimensional principal component space to obtain a dimensionality-reduced feature vector; the neighborhood size is calculated based on the signal-to-noise ratio of the dimensionality-reduced feature vector, and the weighted Euclidean distance is calculated in combination with the principal component weights. K nearest neighbors are selected based on the weighted Euclidean distance and the track association results are output by majority vote. The formula for calculating the weighted Euclidean distance is: ； In the formula, Let be the weight corresponding to the m-th principal component, representing the importance of that principal component in the distance calculation. The feature vectors of the training samples to be compared are reduced in dimensionality at the th... The values taken in each principal component direction For the dimensionality-reduced feature vector of the track to be queried, at the 1st... The values taken in each principal component direction The total number of principal components; The formula for calculating the size of the neighborhood is: ； In the formula, The neighborhood size is based on the signal-to-noise ratio; The formula for calculating the principal component weights based on the eigenvalues is as follows: ； In the formula, For the first The eigenvalues corresponding to each principal component For the first The eigenvalues corresponding to each principal component The total number of principal components.
2. The improved PCA-KNN method for multi-feature track association as described in claim 1, characterized in that, The formula for calculating the track association result is as follows: ； In the formula, The result of the track association judgment for the track pair to be queried. Let be the feature vector of the track pair to be queried in the low-dimensional space of PCA. This is a majority voting function used to select the class that appears most frequently from the associated labels of the K nearest neighbor training samples. The associated label of the Kth nearest neighbor training sample after sorting by weighted Euclidean distance from smallest to largest, where K represents the number of nearest neighbor samples that participated in the majority vote.
3. The improved PCA-KNN method for multi-feature track association as described in claim 1, characterized in that, Before constructing the training data, the high-dimensional feature vector needs to be standardized to obtain a standardized feature vector, as shown in the formula: ； In the formula, For standardized feature vectors The Middle The first sample 1 eigenvalue, High-dimensional feature vectors The Middle The first sample 1 eigenvalue, For the first The mean of each feature, For the first The standard deviation of each feature The total number of samples, The total number of features.
4. The improved PCA-KNN method for multi-feature track association as described in claim 3, characterized in that, The process of fitting the PCA model includes: calculating the covariance matrix of the standardized eigenvectors and performing eigenvalue decomposition to obtain the principal components and their eigenvalues.
5. The improved PCA-KNN method for multi-feature track association as described in claim 4, characterized in that, The formula for obtaining the principal components and their eigenvalues is as follows: ； ； In the formula, For standardized feature vectors The covariance matrix, The total number of samples, For the first The eigenvalues corresponding to each principal component, i.e., the variance contribution. For the first The eigenvectors corresponding to each principal component represent the principal directions. The total number of directions of the principal components.
6. The improved PCA-KNN method for multi-feature track association as described in claim 4, characterized in that, Based on the trained PCA model, the standardized feature vector input is projected into a low-dimensional subspace to obtain a dimensionality-reduced data matrix; Using the principal component weights obtained in the offline phase, the weighted Euclidean distance between the dimensionality-reduced data matrix and the dimensionality-reduced feature vector is calculated.
7. The improved PCA-KNN method for multi-feature track association as described in claim 1, characterized in that, The formula for selecting the k principal components whose cumulative explained variance reaches a preset threshold is as follows: ； In the formula, This represents the cumulative percentage of variance explained by the top k principal components. For the first The eigenvalues corresponding to each principal component The total number of principal components, The total number of directions of the principal components.