A bearing-only angle tracking method based on OPTICS clustering preprocessing

Abstract

This invention discloses a pure azimuth tracking method based on OPTICS clustering preprocessing, belonging to the field of pure azimuth tracking technology. This invention addresses the problems of high computational burden and poor tracking performance in existing data association methods under low signal-to-noise ratio (SNR) environments. The invention employs a sliding window approach, updating the data within the sliding window in real time at each moment. Based on the spatiotemporal correlation characteristics of the target trajectory data, it uses the OPTICS clustering algorithm based on connectivity distance to cluster the measurement data within the sliding window. This improves the problem of excessively high noise in the measurement data during pure azimuth tracking under low SNR conditions. By reducing noise in the measurement data, the tracking system performance is improved, reducing computation time while increasing tracking accuracy. This method can be applied to pure azimuth tracking.

Description

Technical Field

[0001] This invention belongs to the field of pure azimuth tracking technology, specifically relating to a pure azimuth tracking method based on OPTICS clustering preprocessing. Background Technology

[0002] Underwater target tracking is an important research area in the field of underwater acoustics, and it is widely used in underwater acoustic countermeasures, underwater target search, and maritime security monitoring. Pure azimuth multi-target tracking systems rely on passive sonar to receive data and do not require signal transmission for target detection. They have advantages such as strong concealment, high security, and low operating costs, making them one of the important means of underwater target tracking. Target tracking under low signal-to-noise ratio conditions is a challenge in the field of passive underwater acoustic detection and has received widespread attention from researchers for many years.

[0003] Underwater target tracking is a complex problem, requiring the handling of potential target interruptions, false alarms, and outliers. It also involves several technical challenges, including threshold discrimination, multi-target resolution, and data association. Common tracking algorithms include Kalman filtering, extended Kalman filtering, unscented Kalman filtering, and particle filtering. However, due to factors such as clutter, missed detections, and multiple targets in real-world scenarios, simple tracking algorithms are insufficient. To achieve accurate target tracking, data association algorithms are introduced. Common data association algorithms include nearest neighbor methods, probabilistic data association methods, joint probabilistic data association methods, and multi-hypothesis tracking methods. In low signal-to-noise ratio (SNR) environments, the target's signal strength is close to or below the noise level, resulting in numerous false alarms in the azimuth estimation results. The persistent presence of false azimuth data increases the computational burden on the algorithm for data association and affects the tracking results, leading to trajectory breaks, target label migration, and even the generation of false trajectories. Therefore, improving the performance of weak target tracking while simplifying computation remains an important and challenging problem. Summary of the Invention

[0004] This invention addresses the problems of high computational burden and poor tracking performance of existing data association methods in low signal-to-noise ratio environments by proposing a pure azimuth tracking method based on OPTICS clustering preprocessing.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a pure azimuth tracking method based on OPTICS clustering preprocessing, the method specifically including the following steps:

[0006] Step 1: Build a window with a length of [length to be specified]. The sliding window, when it obtains After measuring the data at time 1, using the first Measurement data up to the first moment The measurement data at each moment constitutes the data within the current sliding window;

[0007] Step 2: Use the OPTICS clustering algorithm to process the measurement data within the current sliding window to obtain the initial reachable distance sequence;

[0008] The initial reachability distance sequence is then smoothed to obtain the smoothed reachability distance sequence.

[0009] Step 3: Based on the connectivity distance, perform cluster extraction on the smoothed reachability distance sequence to obtain non-noise data from the measurement data. Input the non-noise data into the tracking system to complete the tracking of the target.

[0010] Furthermore, the data objects of the OPTICS clustering algorithm are obtained based on the measurement data and the time corresponding to the measurement data, and the current sliding window corresponds to the first... Each data object is denoted as ,in, Indicates the first Azimuth angle Indicates the first The time corresponding to each azimuth angle.

[0011] Furthermore, the OPTICS clustering algorithm processes the data objects corresponding to the measurement data that enter the current sliding window later, according to the order in which the measurement data enters the current sliding window.

[0012] Furthermore, the distance radius of the OPTICS clustering algorithm Set it to infinity.

[0013] Furthermore, the point count threshold of the OPTICS clustering algorithm Set to 2.

[0014] Furthermore, the smoothing process for the initial reachable distance sequence specifically includes:

[0015] The initial reachability distance sequence was smoothed five times using a two-point moving average method to obtain the smoothed reachability distance sequence.

[0016] Furthermore, the specific process of step three is as follows:

[0017] Step 31: Set the reachable distance cutoff threshold The less than in the smoothed reachable distance sequence The reachable distance is taken as the minimum point, and the first... The coordinates of the local minimum points are: , The total number of local minima is given, and each local minima is used as a cluster center.

[0018] Step 3.2: Set the platform length threshold and from the cluster center Starting from the left, simultaneously search along the reachable distance sequence in both left and right directions, and calculate the distance between each data object found and the target data. The connection distance is such that when the search stops, the search in the current direction is immediately stopped.

[0019] When cluster center After the search in both directions is completed, the cluster centers will be used as the basis for the final result. The interval corresponding to all the data objects found in the search is denoted as ,in, Index the data object at the left endpoint of the searched interval. The index of the data object at the right endpoint of the searched interval, the interval The measurement data corresponding to all data objects within the scope are non-noise data;

[0020] Step 3: Input the non-noise data found based on each cluster center into the tracking system to complete the tracking of the target.

[0021] Furthermore, the stopping condition for the search specifically refers to satisfying (1) or (2):

[0022] (1) During the current direction search, the calculated connected distance is greater than the connected distance threshold. ;

[0023] (2) Continuous search in the current direction After finding the same connectivity distance value, continue searching along the current direction until the reachable distance increases significantly.

[0024] Furthermore, the significantly increased reachability distance refers to: connecting the searched next data object with... The connectivity distance and the previous data object found The difference between the connected distances is greater than a set threshold. .

[0025] Furthermore, for two data points The method for calculating the connected distance is as follows:

[0026] Obtain the connection between the two data points respectively For any given path, the minimum distance between any two adjacent points on that path can be obtained. Then, the minimum distances for each path are compared to find the maximum distance among all minimum distances. This maximum distance is then used as the two data points. The connectivity distance between them, i.e.:

[0027]

[0028] In the formula, Represents two data points The connection distance between them This indicates connecting two data points. The set of all paths This represents a path in a set of paths. Representing a path The total number of data points on the data point. and Representing a path Any two adjacent data points on the data, Representing data points and data points The Euclidean distance between them.

[0029] The beneficial effects of this invention are:

[0030] This invention proposes a pure azimuth tracking method based on OPTICS clustering preprocessing. Specifically, it adopts a sliding window approach, updating the data within the sliding window in real time at each moment. Based on the spatiotemporal correlation characteristics of the target trajectory data, the OPTICS clustering algorithm based on connectivity distance is used to cluster the measurement data within the sliding window. This improves the problem of excessive noise in the measurement data during pure azimuth tracking under low signal-to-noise ratio conditions. By reducing the noise in the measurement data, the performance of the tracking system is improved, which can reduce computation time while improving tracking accuracy. Attached Figure Description

[0031] Figure 1 This is a flowchart of a pure azimuth tracking method based on OPTICS clustering preprocessing according to the present invention;

[0032] Figure 2 This is a flowchart of the cluster extraction process;

[0033] Figure 3 This is a flowchart of a one-sided search during the cluster extraction process;

[0034] Figure 4 This is a tracking result diagram of the present invention after processing by the OPTICS clustering preprocessing algorithm;

[0035] Figure 5The image shows the tracking results before the OPTICS clustering preprocessing algorithm was applied.

[0036] Figure 6 A comparison chart of OSPA errors before and after the OPTICS clustering preprocessing algorithm;

[0037] Figure 7 This is a comparison chart showing the average number of targets before and after the OPTICS clustering preprocessing algorithm. Detailed Implementation

[0038] Specific implementation method one: Combining Figure 1 This embodiment describes a pure azimuth tracking method based on OPTICS clustering preprocessing. The method specifically includes the following steps:

[0039] Step 1: Build a window with a length of [length to be specified]. The sliding window, when it obtains After measuring the data at time 1, using the first Measurement data up to the first moment The measurement data at each moment constitutes the data within the current sliding window;

[0040] Upon receiving measurement data at a new time step, the sliding window is moved forward by one time step to update the data within the window. For example, the measurement data from the first time step is used to update the data from the second time step. The measurement data at each moment constitutes the data within the sliding window. When received... After obtaining the measurement data at time 2, the sliding window is moved forward by one time, that is, the measurement data at time 2 is used until time 3. The measurement data at each moment constitutes the data within the sliding window;

[0041] It should be noted that the selection of the sliding window length should satisfy the following conditions: sufficient data should accumulate within the window to display the statistical characteristics of local clustering; and premature measurement data should not be accumulated within the window, so that the clustering results cannot accurately describe the signal density at the current moment. The appropriate length can be determined based on these two constraints. The value of .

[0042] Step 2: Use the OPTICS clustering algorithm to process the measurement data within the current sliding window to obtain the initial reachable distance sequence;

[0043] Specifically, the OPTICS clustering algorithm is an improved version of the DBSCAN algorithm, specifically involving distance radius. and point threshold Two parameters. The OPTICS clustering algorithm does not explicitly generate clustering results, but instead generates an ordered sequence of data points, called the reachability distance sequence. By adjusting the neighborhood radius parameter, the corresponding clustering results can be obtained in this sequence, which can effectively handle data with different densities.

[0044] For a given parameter and The OPTICS clustering algorithm contains two core definitions: core distance and reachability distance;

[0045] (1) Core distance: For data objects If there exists that makes the data object The smallest neighborhood radius that becomes the core object is called the core object. The core distance is denoted as If data object If it is not a core object, then its core distance is... It can be considered as infinity. The calculation formula is as follows:

[0046]

[0047] (2) Reachable distance: Let Reachability distance is defined as the distance between objects. To object European distance With object core distance The larger value between them is denoted as If the object If it is not a core object, then its reachability distance is It can be considered as infinity. The calculation formula is as follows:

[0048]

[0049] The traditional OPTICS clustering algorithm starts from any unprocessed sample, calculates its core distance and reachability distance, and adds the points to an ordered list containing reachability distances in the order of processing.

[0050] In this invention, the input to the OPTICS clustering algorithm is a two-dimensional data matrix composed of all resolved units in the time window of the above steps. The data object of the OPTICS clustering algorithm is obtained based on the measurement data and the time corresponding to the measurement data. The current sliding window corresponds to the first... Each data object is denoted as ,in, Indicates the first The azimuth angle (i.e., the azimuth angle within the current window) (individual measurement values) Indicates the first The time corresponding to each azimuth angle;

[0051] To reduce the probability of missed detections in the current result, the data objects corresponding to the measurement data that enter the current sliding window are processed first, according to the order in which the measurement data enters the current sliding window. Furthermore, to more sensitively capture target emergence and disappearance information, as well as local density features, this invention sets the distance radius of the OPTICS clustering algorithm. (Infinity), Point Threshold That is, by setting the distance radius and the number of points threshold, each measurement value is a potential core object.

[0052] After obtaining the initial reachability distance sequence, cluster extraction is required. The smaller the reachability distance of a data object in the sequence, the closer it is to its neighbors. The steep descending and ascending regions in the reachability distance sequence output by the algorithm form high-density clusters, which can be considered as a cluster. The data corresponding to the minimum value within this cluster can be considered the cluster center. For measurement data during the tracking process, each cluster corresponds to a potential target. However, when there is a lot of noise in the measurement data, the reachability distance sequence fluctuates wildly, making it difficult to identify the cluster location. Therefore, smoothing is necessary. To balance smoothing effectiveness with preserving the sequence's trend, this invention uses a 2-point moving average method to smooth the initial reachability distance sequence five times consecutively, resulting in a smoothed reachability distance sequence. Multiple smoothing processes remove transient random fluctuations, highlighting the data sequence's trend. The smoothed reachability distance sequence shows more pronounced concave regions, making it easier to determine the cluster center location.

[0053] Step 3: Based on the connectivity distance, perform cluster extraction on the smoothed reachability distance sequence to obtain non-noise data from the measurement data.

[0054] Specifically, such as Figure 2 and Figure 3 As shown:

[0055] Step 31: Set the reachable distance cutoff threshold The less than in the smoothed reachable distance sequence The reachable distance is taken as the minimum point, and the first... The coordinates of the local minimum points are: , Let be the total number of local minima. The physical meaning of the coordinates of each local minima is the number of local minima processed by the OPTICS clustering algorithm. Each of the data objects is used as a cluster center for each local minimum point;

[0056] The algorithm calculates the distances from each point in the plane to the next point. The connectivity distance is used to determine the target cluster. The data from the target in the measurement data are more tightly combined than the noise data, and show obvious concave and plateau characteristics in the connectivity distance map. The plateau area is composed of locally high-density data, and the connectivity distance increases rapidly after passing through the plateau area.

[0057] For targets that are newly discovered or have a high false alarm rate, the connectivity distance results lack platform characteristics, so an upper limit on the connectivity distance can be set. The connectivity length is truncated, and the target cluster extraction continues based on step 32.

[0058] Step 3.2: Set the platform length threshold and from the cluster center Starting from the left, simultaneously search along the reachable distance sequence in both left and right directions, and calculate the distance between each data object found and the target data. The connection distance is such that when the search stops in one direction, the search in that direction is immediately stopped.

[0059] The search stops when either (1) or (2) is satisfied.

[0060] (1) During the current direction search, the calculated connected distance is greater than the connected distance threshold. ;

[0061] (2) Continuous search in the current direction After finding the same connectivity distance value, continue searching along the current direction until the reachable distance significantly increases. A significant increase in reachable distance means that the next data object found in the search is compared with... The connectivity distance and the previous data object found The difference between the connected distances is greater than a set threshold. ;

[0062] When cluster center After the search in both directions is completed, the cluster centers will be used as the basis for the final result. The interval corresponding to all the data objects found in the search is denoted as ,in, Index the data object at the left endpoint of the searched interval. The index of the data object at the right endpoint of the searched interval, the interval The measurement data corresponding to all data objects within the scope are non-noise data;

[0063] Step 3: Input the non-noise data found based on each cluster center into the tracking system to complete the tracking of the target.

[0064] Furthermore, it should be noted that connectivity distance readily reflects manifold structure. The connectivity distance between two adjacent data points within the same manifold is relatively short, while the connectivity distance between two adjacent data points spanning different manifolds is relatively long. This property can be used to transform a slender structure on the Euclidean distance scale into a compact structure on the connectivity distance scale. Therefore, for two data points... data points With data points The method for calculating the connectivity distance between them is as follows:

[0065] Obtain the connection between the two data points respectively All paths (it should be noted that...) As the starting point of the path, The endpoint of the path, on the path, and (The path may pass through some data points). For any path, the minimum distance between any two adjacent points on that path can be obtained. Then, the minimum distances for each path are compared, and the maximum distance among all minimum distances is obtained. The maximum distance is then used as the two data points. The connectivity distance between them, i.e.:

[0066]

[0067] In the formula, Represents two data points The connection distance between them This indicates connecting two data points. The set of all paths This represents a path in a set of paths. Representing a path The total number of data points on the data point. and Representing a path Any two adjacent data points on the data, Representing data points and data points The Euclidean distance between them.

[0068] Implementation example:

[0069] This example presents a set of simulation experiments to verify the OPTICS clustering preprocessing method based on pure azimuth angle tracking of the present invention. The results are compared with those of a tracking method without OPTICS clustering preprocessing (referred to as the comparison algorithm). Simulation results for multi-target tracking scenarios considering missed detections, noise, and clutter interference are given. During the simulation, target signals are generated and a certain amount of noise is added. A simulated hydrophone array is used to receive the signal, and DOA estimation is performed at each time step using a conventional beamforming algorithm to obtain the azimuth measurement of each target. The bandwidth of the simulated target noise signal is 100Hz - 4000Hz; the signal sampling rate is 1.6kHz; the number of uniform linear array hydrophones is 40; and the underwater acoustic velocity is set to... m / s; the spacing between adjacent array elements is the center frequency in the processing frequency domain. The corresponding half wavelength, i.e. The spatial spectral azimuth resolution is 0.5 degrees; the total target tracking time is 300 seconds, and the tracking interval is 1 second.

[0070] The performance of the method of this invention was tested based on the RBMCDA algorithm, a multi-hypothesis tracking algorithm under the Rao-Blackwellized particle filter framework. This algorithm divides the multi-target tracking problem into two parts: estimating the posterior probability of multi-target data association and estimating the state of a single target. Particle filtering is used for the multi-target data association part, and Kalman filtering is used for the target state part. This combination of particle filtering and Kalman filtering reduces the dimensionality of the target state model, achieving near-optimal estimation results with low computational cost. The RBMCDA algorithm parameters are set as follows: number of particles... ; Target extinction model Distribution parameters , Covariance clutter density Target newborn probability .

[0071] For the OPTICS clustering preprocessing algorithm, the algorithm parameters are set as follows: sliding window length. truncation threshold Platform length Connectivity distance threshold The threshold for the difference between the two terms .

[0072] A simulation is conducted using a scenario with three targets within a certain area as an example, where clutter is uniformly distributed. Within the range, the total measurement time is 300s, of which the appearance time of target one is 0~300s, the appearance time of target two is 0~250s, and the appearance time of target three is 100~300s. The overall signal-to-noise ratio of the target signals is low. Figure 4 This invention demonstrates the tracking results after data processing based on the OPTICS clustering preprocessing algorithm. Figure 5 The results show the tracking results without data processing based on the OPTICS clustering preprocessing algorithm.

[0073] It can be seen that the false alarm data in the azimuth estimation results after OPTICS clustering algorithm preprocessing is significantly reduced, and the algorithm successfully retains the azimuth angle data from the set target; for the tracking results obtained by using RBMCDA algorithm in the same scenario, the accuracy of target tracking is improved after OPTICS clustering preprocessing algorithm. Figure 6 This is a comparison chart of OSPA errors in the tracking results obtained before and after OPTICS clustering algorithm preprocessing. Figure 7 The chart shows a comparison of the average number of targets obtained before and after OPTICS clustering algorithm preprocessing. It can be seen that before OPTICS clustering algorithm preprocessing, the data is severely affected by noise, the OSPA distance is generally large, and the estimate of the average number of targets is generally high. After OPTICS clustering algorithm preprocessing, the OSPA distance is only slightly higher at the time of target birth and disappearance, and the estimated value of the average number of targets is closer to the actual number of targets.

[0074] The performance of the comparative algorithms was tested using average running time. As shown in Table 1, the running times of the algorithm designed in this invention and the comparative algorithm were 198.96 seconds and 614.69 seconds, respectively.

[0075] Table 1

[0076]

[0077] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A bearing-only tracking method based on OPTICS clustering preprocessing, characterized in that, The method specifically includes the following steps: Step one, construct a sliding window with window length of , when the measurement data of time point is obtained, use the measurement data from the first time point to the last time point to form the data in the current sliding window; Step 2: Use the OPTICS clustering algorithm to process the measurement data within the current sliding window to obtain the initial reachable distance sequence; The initial reachability distance sequence is then smoothed to obtain the smoothed reachability distance sequence. Step 3: Based on the connectivity distance, perform cluster extraction on the smoothed reachability distance sequence to obtain non-noise data from the measurement data. Input the non-noise data into the tracking system to complete the tracking of the target.

2. The pure azimuth tracking method based on OPTICS clustering preprocessing according to claim 1, characterized in that, The data object of the OPTICS clustering algorithm is obtained according to the measurement data and the time corresponding to the measurement data, and the first data object corresponding to the current sliding window is recorded as , wherein, , wherein, represents the first azimuth angle, , wherein, represents the time corresponding to the first azimuth angle, .

3. The bearing-only tracking method based on OPTICS clustering preprocessing according to claim 2, characterized in that, The OPTICS clustering algorithm processes the data objects corresponding to the measurement data that enter the current sliding window first, according to the order in which the measurement data enters the current sliding window.

4. The pure azimuth tracking method based on OPTICS clustering preprocessing according to claim 3, characterized in that, The distance radius of the OPTICS clustering algorithm is set to infinity.

5. The pure azimuth tracking method based on OPTICS clustering preprocessing according to claim 4, characterized in that, The point threshold of the OPTICS clustering algorithm is set to 2.

6. The bearing-only tracking method based on OPTICS clustering preprocessing according to claim 5, characterized in that, The smoothing process for the initial reachable distance sequence specifically involves: The initial reachability distance sequence was smoothed five times using a two-point moving average method to obtain the smoothed reachability distance sequence.

7. The bearing-only tracking method based on OPTICS clustering preprocessing according to claim 6, characterized in that, The specific process of step three is as follows: Step three, setting the reachable distance threshold value The reachable distance less than is regarded as the minimum point, and the coordinate of the first minimum point is recorded as , the total number of minimum points is , , and each minimum point is regarded as a clustering center respectively. Step three two, set the platform length threshold and from the cluster center , and search in both left and right directions along the reachable distance sequence, and calculate the communication distance between each searched data object and , and when the search stop condition is reached, stop the search in the current direction immediately; When the clustering center After the search in both directions is finished, the intervals corresponding to all the data objects searched are recorded as wherein, is the data object index of the left end point of the searched interval, is the data object index of the right end point of the searched interval, and all the measurement data of the data objects in the interval are non-noise data.​ Step 3: Input the non-noise data found based on each cluster center into the tracking system to complete the tracking of the target.

8. The pure azimuth tracking method based on OPTICS clustering preprocessing according to claim 7, characterized in that, The stopping condition for the search is specifically defined as satisfying (1) or (2): (1) During the current direction search, the calculated connected distance is greater than the connected distance threshold. ; (2) Continuous search in the current direction After finding the same connectivity distance value, continue searching along the current direction until the reachable distance increases significantly.

9. A pure azimuth tracking method based on OPTICS clustering preprocessing according to claim 8, characterized in that, The significantly increased reachability distance refers to: connecting the next searched data object with... The connectivity distance and the previous data object found The difference between the connected distances is greater than a set threshold. .

10. A pure azimuth tracking method based on OPTICS clustering preprocessing according to claim 9, characterized in that, For two data points The method for calculating the connected distance is as follows: Obtain the connection between the two data points respectively For any given path, the minimum distance between any two adjacent points on that path can be obtained. Then, the minimum distances for each path are compared to find the maximum distance among all minimum distances. This maximum distance is then used as the two data points. The connectivity distance between them, i.e.: In the formula, Represents two data points The connection distance between them This indicates connecting two data points. The set of all paths This represents a path in a set of paths. Representing a path The total number of data points on the data point. and Representing a path Any two adjacent data points on the data, Representing data points and data points The Euclidean distance between them.

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