A low signal-to-noise ratio track fitting method based on spatial transformation

Abstract

The application relates to a low signal-to-noise ratio track fitting method based on spatial transformation, and belongs to the radio field.The method comprises the following steps: S1, acquiring original point cloud data, and performing preliminary rough filtering and candidate point cloud extraction to obtain an initial candidate point cloud set; S2, constructing a uniform straight line motion verification model, performing model consistency measurement and interference elimination, and then performing iterative optimization on the model and selecting an optimal model; and S3, clustering target point clouds to form a target point cloud sequence, constructing a weighted least square optimization problem, and solving the problem to obtain a final track.The application directly utilizes original point clouds for global optimization fitting, fully utilizes all available observation information, and suppresses noise through smoothness constraint, so that the obtained track is continuous and smooth, is more reasonable in physics, and has a precision significantly higher than that of a track obtained through interpolation based on filtered discrete point tracks.

Description

Technical Field

[0001] This invention relates to the field of radio, and more particularly to a low signal-to-noise ratio trajectory fitting method based on spatial transformation. Background Technology

[0002] Target detection radar (or range measurement radar) plays a crucial role in naval weapons testing and performance evaluation of high-speed moving targets. Its core mission is to accurately track and measure the trajectory of high-speed moving targets. In practical applications, target detection radar faces severe challenges, including multipath reflections and sea clutter on the sea surface; targets themselves may release decoys or generate debris; and islands, birds, and other vessels in the environment can create false or interfering points. These interfering points are highly overlapping with the real target point cloud in terms of distance, velocity, and amplitude, making it difficult to effectively separate them using traditional threshold-based or statistical filtering methods. The sparseness and discontinuity of the point cloud, such as the high maneuverability of high-speed targets and the potential for radar echo flickering, result in uneven spatial and temporal distribution and discontinuities in the point cloud sequence, posing difficulties for traditional point-track correlation tracking algorithms and easily leading to target loss or trajectory jumps. Target detection evaluation requires trajectory data with sub-meter or even higher precision, and interference and point cloud noise directly cause a significant decrease in trajectory fitting accuracy.

[0003] Existing technologies typically employ filtering based on Doppler velocity or RCS (radar cross section). While effective for uniformly moving targets, these methods are less effective against high-speed maneuvering targets or targets with changing RCS. Kalman filtering or particle filtering tracking methods are sensitive to initial states and motion models, and are prone to divergence in strong clutter. Traditional DBSCAN or Euclidean distance clustering methods struggle to distinguish between spatially adjacent real targets and interference points in densely jammed environments. Therefore, existing methods lack sufficient anti-jamming capabilities and trajectory extraction accuracy in high-speed maritime target detection scenarios. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a low signal-to-noise ratio trajectory fitting method based on spatial transformation, thus solving the deficiencies of the prior art.

[0005] The objective of this invention is achieved through the following technical solution: a low signal-to-noise ratio trajectory fitting method based on spatial transformation, the method comprising:

[0006] S1. Obtain the raw point cloud data, and perform preliminary coarse filtering and candidate point cloud extraction to obtain the initial candidate point cloud set;

[0007] S2. Construct a uniform linear motion verification model, and after performing model consistency measurement and interference removal, iteratively optimize the model and select the optimal model.

[0008] S3. Cluster the target point cloud to form a target point cloud sequence, construct a weighted least squares optimization problem and solve it to obtain the final trajectory.

[0009] S1 specifically includes the following:

[0010] S101, the target detection radar scans and detects the monitored sea area to acquire raw three-dimensional point cloud data containing high-speed targets at sea, sea clutter, multipath reflections and decoys. Each point cloud data includes at least a timestamp t, radial distance r, azimuth angle θ, elevation angle ϕ, Doppler velocity v and echo intensity I.

[0011] S102. Using amplitude thresholds and sea surface height-based thresholds, the most obvious clutter and static interference are filtered out to obtain the initial candidate point set. .

[0012] The construction of the uniform linear motion verification model includes:

[0013] S201, from Two point clouds, a and b, randomly selected from a spacetime distance exceeding a set distance, are represented as follows: and Assuming these two point clouds originate from the same uniformly moving linear target, a predetermined trajectory, i.e., the velocity vector, is determined based on these two point clouds. ,in, , These are the timestamps for point cloud a and point cloud b, respectively. , They are respectively and Position vector, initial position vector .

[0014] The process of iteratively optimizing the model and selecting the optimal model after performing model consistency measurement and interference removal includes:

[0015] S202, will All points are projected onto a set trajectory over time, and the calculation is performed for each point. Spatial consistency residuals of the trajectory Consistency residuals of velocity along the trajectory direction ,in, It is a point The projection of the velocity onto the trajectory direction, The point cloud of the j-th point;

[0016] S203, Spatial Consistency Residual Represented as Speed ​​consistency residual Represented as ,in, This is the initial position;

[0017] S204. Set the joint space consistency residual threshold. and speed consistency residual threshold At the same time satisfy and The point is considered to be consistent with the setting of the uniform linear motion, and is used as the judgment point. Let each interior point of the current model be an interior point, and all interior points form a consistent point set. ,calculate The number of points and the average residual;

[0018] S205. Repeat steps S102 and S201-S204 to obtain a series of trajectory models and their corresponding set of consistent points. Select the model with the most interior points and the smallest average residual of interior points as the optimal uniform linear motion model. ,at this time, corresponding The points that are identified as the real target point cloud are completely filtered out as interference.

[0019] S3 specifically includes the following:

[0020] S301, Directly to Generate a target point cloud sequence based on time;

[0021] S302, for Each point in Its observation equation is ,in, Let x, y, and z be the coordinates of the j-th point, respectively. Let j be the observation time at point j. , and They represent Observation noise;

[0022] S303. The objective function is to minimize the weighted sum of squared residuals for all observation points, i.e. Where L represents the weighted sum of squared residuals for all observation points, Indicates weight;

[0023] S304. The optimization problem is a linear least squares problem, and its solution yields... Where A and B are observation matrices composed of timestamps, W is a weight matrix, and T represents the transpose;

[0024] S305, Optimal position vector parameters and optimal velocity vector Substituting into the observation equation, we obtain the result from the initial time. End time The continuous and precise position and velocity status of the target at any given moment;

[0025] S306. Calculate the points on the fitted line and... The residuals at the observation points are used to evaluate the confidence level of the trajectory fitting, and finally, a parameterized expression of uniform linear motion is output.

[0026] The present invention has the following advantages:

[0027] 1. By constructing a spatiotemporal-feature joint space and performing targeted transformations, interferences with different characteristics are mapped to separable regions. Uniform linear motion is moved forward from the optional model for subsequent fitting to become the core discrimination criterion for guided filtering. This fundamentally defines all interferences that do not conform to this physical law (regardless of their amplitude or density) as outliers. This achieves the mechanism-based differentiation and filtering of various interferences such as sea clutter, multipath, and false alarms, which is superior to single-dimensional filtering methods.

[0028] 2. By adopting model-based global fitting instead of point-by-point recursive tracking, even if there are time intervals in the point cloud, as long as the overall motion trend is consistent, a reasonable trajectory can still be fitted, avoiding the divergence problem of traditional tracking algorithms when point cloud is lost.

[0029] 3. Directly using the original point cloud for global optimization fitting makes full use of all available observation information and suppresses noise through smoothness constraints. The resulting trajectory is continuous and smooth, physically more reasonable, and has significantly higher accuracy than the trajectory obtained by interpolation based on filtered discrete points. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the process of the present invention;

[0031] Figure 2 This is the original point cloud data image with noise.

[0032] Figure 3 This is a distance-time distribution graph;

[0033] Figure 4 This is a graph showing the filtered target point and trajectory fitting results;

[0034] Figure 5 This is a graph showing the algorithm's performance statistics. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application provided below with reference to the accompanying drawings is not intended to limit the scope of protection of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The present invention will be further described below with reference to the accompanying drawings.

[0036] Specifically, this invention relates to a low signal-to-noise ratio trajectory fitting method based on spatial transformation, which can robustly filter out interference from the original radar point cloud containing a large number of false points and noise points, and accurately fit the continuous and smooth motion trajectory of the target.

[0037] like Figure 1 As shown, it specifically includes the following:

[0038] Step 1: Acquire raw point cloud data; The target detection radar scans and detects the monitored sea area to acquire raw 3D point cloud data containing high-speed targets at sea, sea clutter, multipath reflections, decoys, and other environmental interference. Each point cloud data point must contain at least: timestamp t, radial distance r, azimuth angle θ, elevation angle ϕ, Doppler velocity v, and echo intensity I; Convert the point cloud positions to a Cartesian coordinate system. .

[0039] Step 2: Preliminary coarse filtering and candidate point cloud extraction; First, using a simple amplitude threshold and a threshold based on sea surface height, the most obvious clutter and static interference are filtered out to obtain an initial candidate point cloud set. .

[0040] Step 3: Construct a verification model for uniform linear motion; from Two point clouds that are randomly selected from each other and whose spatiotemporal distance exceeds a set distance are considered as a whole. and , , The timestamps of the two points are given, and it is assumed that they originate from the same uniformly moving linear target. Based on the cloud of these two points, a hypothetical trajectory can be uniquely determined: the velocity vector. ,in , Point clouds and Position vector, initial position vector The parameters of this trajectory are: .

[0041] Step 4: Model consistency measurement and interference removal; For all points in the given time, project them onto the hypothetical trajectory and calculate the time value for each point. Spatial consistency residuals of the trajectory Consistency residuals of velocity along the trajectory direction ,in It is a point The projection of the velocity onto the trajectory direction. Spatial consistency residual. It can be represented as:

[0042] ,

[0043] in, For the point cloud of the j-th point, Initial position. Velocity consistency residual. It can be represented as:

[0044] ,

[0045] Set a joint space consistency residual threshold. and speed consistency residual threshold Simultaneously satisfy and The point is considered to be consistent with the assumption of uniform linear velocity, and is used as the determination point. Let each interior point of the current model be an interior point, and all interior points form a consistent point set. ,calculate The number of points (interior points) and the average residual.

[0046] Step 5: Iterative Optimization and Optimal Model Selection; Repeat steps 2-4 multiple times (using a random sampling consensus mechanism similar to RANSAC) to obtain a series of hypothetical trajectory models and their corresponding "consistency point sets". Select the model with the largest number of interior points and the smallest average residual among the interior points as the optimal uniform linear motion model. At this point, the model corresponds to The points that are identified as the real target point cloud are completely filtered out as interference.

[0047] Step 6: Target point cloud clustering; directly targeting... Sort the points in chronological order to form a target point cloud sequence.

[0048] Step 7: Construct a weighted least squares optimization problem; for Each point in , Let x, y, and z be the coordinates of the j-th point, respectively. Let j be the observation time of the j-th point. Its observation equation can be written as:

[0049] ,

[0050] in and The trajectory parameters to be optimized are... , and They represent The observation noise is considered. The objective function is to minimize the weighted sum of squared residuals for all observation points.

[0051] ,

[0052] Among them, weight It can be set according to the signal-to-noise ratio or echo intensity of the point cloud.

[0053] Step 8: Analytical Solution; This optimization problem is a linear least squares problem, which can be solved in a closed form (analytical solution). The computational efficiency is extremely high, and the solution is unique and stable.

[0054] ,

[0055] Where A and B are observation matrices composed of timestamps, W is the weight matrix, and T represents the transpose.

[0056] Step 9: Output the final trajectory; extract the optimal position vector parameters. and optimal velocity vector Substituting into the observation equation, we can obtain the result from the start time. End time The continuous and precise position and velocity status of the target at any given time.

[0057] Step 10: Calculate the sum of the points on the fitted line and the line length. The residuals at the observation points can be used to assess the confidence level (e.g., standard deviation) of the trajectory fit. The final output is a parameterized representation of the uniform linear motion: trajectory equation, velocity, starting point, and any interpolation point on the trajectory.

[0058] The present invention will be further described in conjunction with the embodiments and accompanying drawings to illustrate the implementation process and beneficial effects of the present invention, including: setting the signal simulation measurement frequency to 200Hz, the measurement noise standard deviation to 2m, the observation time to 0.5s, the target velocity vector to [400m / s, 300m / s, 300m / s], the number of sea clutter points to 200, the number of decoy points and multipath interference points to 430, the number of algorithm iterations to 1000, the distance threshold to 2m, and the velocity threshold to 5m / s.

[0059] A low signal-to-noise ratio (SNR) trajectory fitting method based on spatial transformation is applied to the signal according to the above parameters, and the results are as follows. Figures 2-5As shown, where Figure 2 The spatial distribution of the raw point cloud data includes targets, sea clutter, false alarm decoys, multipath interference, etc. Figure 3 As shown in the range-time distribution, the target is obscured by clutter noise in the range-time dimension; Figure 4 The filtered target points and the fitted spatial distribution results are shown. Figure 5 Performance statistics show that the clutter filtering rate can reach 95.6%. This demonstrates that the present invention can accurately extract and fit target point clouds under low signal-to-noise ratio conditions. The fitted trajectory almost perfectly matches the actual target trajectory. Calculations show that the root mean square error of the trajectory position estimation is only 2.2 meters, the maximum residual is 3.62 meters, the velocity magnitude estimation error is 3.73 m / s, and the velocity direction error is 0.39 degrees, proving that the method can achieve estimation accuracy close to the theoretical limit. Furthermore, the method takes only 0.4 seconds, achieving real-time performance. This invention enables the system to simultaneously achieve optimal performance in multiple dimensions, including target trajectory fitting accuracy, situational awareness, and real-time performance, solving the problem that traditional methods cannot simultaneously address these aspects. Simulation results are highly consistent with theoretical analysis, demonstrating the engineering feasibility and technical advantages of this method.

[0060] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and improvements, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A low signal-to-noise ratio track fitting method based on spatial transformation, characterized in that: The method includes: S1. Obtain the raw point cloud data, and perform preliminary coarse filtering and candidate point cloud extraction to obtain the initial candidate point cloud set; S2. Construct a uniform linear motion verification model, and after performing model consistency measurement and interference removal, iteratively optimize the model and select the optimal model. S3. Cluster the target point cloud to form a target point cloud sequence, construct a weighted least squares optimization problem and solve it to obtain the final trajectory; S1 specifically includes the following: S101, the target detection radar scans and detects the monitored sea area to acquire raw three-dimensional point cloud data containing high-speed targets at sea, sea clutter, multipath reflections and decoys. Each point cloud data includes at least a timestamp t, radial distance r, azimuth angle θ, elevation angle ϕ, Doppler velocity v and echo intensity I. S102, using the amplitude threshold and the threshold based on sea surface height, filtering out the most obvious clutter and static interference to obtain an initial candidate point cloud set ; The construction of the uniform linear motion verification model includes: S201, from Two point clouds, a and b, randomly selected from a spacetime distance exceeding a set distance, are represented as follows: and Assuming these two point clouds originate from the same uniformly moving linear target, a predetermined trajectory, i.e., the velocity vector, is determined based on these two point clouds. ,in, , These are the timestamps for point cloud a and point cloud b, respectively. , They are respectively and Position vector, initial position vector ; The process of iteratively optimizing the model and selecting the optimal model after performing model consistency measurement and interference removal includes: S202, will All points are projected onto a set trajectory over time, and the calculation is performed for each point. Spatial consistency residuals of the trajectory Consistency residuals of velocity along the trajectory direction ,in, It is a point The projection of the velocity onto the trajectory direction, The point cloud of the j-th point; S203, Spatial Consistency Residual Represented as Speed ​​consistency residual Represented as ,in, This is the initial position; S204. Set the joint space consistency residual threshold. and speed consistency residual threshold At the same time satisfy and The point is considered to be consistent with the setting of the uniform linear motion, and is used as the judgment point. Let each interior point of the current model be an interior point, and all interior points form a consistent point set. ,calculate The number of points and the average residual; S205. Repeat steps S102 and S201-S204 to obtain a series of trajectory models and their corresponding set of consistent points. Select the model with the most interior points and the smallest average residual of interior points as the optimal uniform linear motion model. ,at this time, corresponding The points that are identified as the real target point cloud are completely filtered out as interference.

2. The low signal-to-noise ratio trajectory fitting method based on spatial transformation according to claim 1, characterized in that: S3 specifically includes the following: S301, Directly to Generate a target point cloud sequence based on time; S302, for Each point in Its observation equation is ,in, Let x, y, and z be the coordinates of the j-th point, respectively. Let j be the observation time at point j. , and They represent Observation noise; S303. The objective function is to minimize the weighted sum of squared residuals for all observation points, i.e. Where L represents the weighted sum of squared residuals for all observation points, Indicates weight; S304. The optimization problem is a linear least squares problem, and its solution yields... Where A and B are observation matrices composed of timestamps, W is a weight matrix, and T represents the transpose; S305, Optimal position vector parameters and optimal velocity vector Substituting into the observation equation, we obtain the result from the initial time. End time The continuous and precise position and velocity status of the target at any given moment; S306. Calculate the points on the fitted line and... The residuals at the observation points are used to evaluate the confidence level of the trajectory fitting, and finally, a parameterized expression of uniform linear motion is output.

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