Backward filter construction method based on radial constant speed model

Abstract

The application discloses a backtracking filter construction method based on a radial constant speed model; the method comprises the following steps: establishing a radial constant speed model, describing target scanning interval motion as constant speed motion superimposed with random acceleration disturbance; calculating the mean value and standard deviation of the radial distance of the target at each backtracking depth based on the model, determining the discrete distance unit set where the target is located, and constructing a corresponding fast widening backtracking filter; further, the method further determines a velocity sampling interval according to the radial velocity resolution and the overlap constraint of the filter boundary, so as to generate a group of central velocities and constitute a backtracking filter group. When detection is performed, the backtracking filter closest to the central velocity is selected according to the radial velocity of each detection point for detection. The application associates the filter widening characteristics with physical parameters such as random acceleration variance, has better interpretability, reduces the artificial parameter adjustment cost through the setting of the velocity sampling interval, and realizes the balance between the detection performance, robustness and calculation complexity.

Description

Technical Field

[0001] This invention belongs to the field of radar target detection technology, specifically relating to a method for constructing a backtracking filter based on a radial constant velocity model. Background Technology

[0002] High-resolution fast-scan maritime radars, due to their high scanning rate and good range resolution, have significant application value in the detection of small targets on the sea surface. However, these radars have very short dwell times at each wave position, and the number of pulses that can be coherently accumulated in a single scan is limited. This leads to insufficient signal-to-clutter ratio for small targets within a single scan, a phenomenon known as the "false alarm rate vs. missed alarm rate seesaw effect." To address this issue, multi-scan joint detection methods are often employed in engineering, performing cross-scan accumulation along the target's movement path on the range-scan time plane to improve the reliability of detection and tracking.

[0003] Currently, multi-scan joint detection methods mainly fall into three categories: first, the multi-scan accumulation method using a fan-shaped backtracking filter bank; second, the rigorous linear search multi-scan detection method based on Hough transform; and third, the cross-scan accumulation method based on radial velocity guidance. Among these, the fan-shaped backtracking filter bank multi-scan accumulation method has become a widely used technical solution in this field due to its simple structure, ease of implementation, and ability to tolerate positioning errors and target maneuvers to a certain extent.

[0004] The basic idea of ​​the fan-shaped backtracking filter bank multi-scan accumulation method is to use a set of fan-shaped search templates on the range-scan time plane to backtrack and verify the motion trajectory of candidate targets, thereby distinguishing between real targets and sea clutter. This method consists of two stages: first, in a single scan, algorithms such as a constant false alarm rate detector or a generalized likelihood ratio tester are used to extract candidate points; second, backtracking integration is performed between scans, and the attributes of candidate points are determined by examining their extendable trajectories in historical scans. In practical applications, to tolerate target velocity uncertainty and positioning errors, the fan-shaped backtracking filter bank typically employs… The fan-shaped template structure, in the first The allowable distance cell range at each backscan location varies. Approximately linear growth is used to form a fan-shaped support domain that gradually widens with depth; then, a fan-shaped backtracking filter bank is formed by multiple fan-shaped backtracking filters with different center velocities to achieve complete coverage and parallel matching accumulation of the target velocity range.

[0005] However, the multi-scan accumulation method using a sector-shaped backtracking filter bank has the following prominent problems in practical applications: First, the method's characterization of inter-scan maneuvers is relatively coarse. The design of the sector-shaped backtracking filter mainly relies on empirical parameters to ensure that the target's trajectory does not leave the coverage area of ​​the sector-shaped backtracking filter during multi-frame backtracking. When the target has inter-scan maneuvers (acceleration disturbances), range divergence errors, or positioning errors, insufficient filter broadening can easily lead to the target's true trajectory deviating from the central velocity template, resulting in ineffective energy accumulation and missed detections. Second, when the velocity interval or template overlap is forced to be increased to improve robustness, it will introduce too much sea clutter and false alarm points, leading to an increased false alarm rate and increased computational load. Finally, the parameters of the sector-shaped backtracking filter bank lack interpretable physical basis, making it difficult to automatically determine the filter shape and velocity sampling interval based on radar system parameters and target maneuver intensity. This seriously affects the engineering feasibility and portability of the method, requiring repeated experiments and parameter adjustments under different radar platforms or sea conditions.

[0006] In summary, existing multi-scan accumulation methods using sector-shaped backtracking filter banks rely on empirical adjustments for parameter settings when facing random maneuvers between target scans. This lack of effective correlation with radar system parameters and target motion characteristics makes it difficult to simultaneously achieve reliable target acquisition and effective suppression of false alarms in complex sea conditions. Therefore, how to design backtracking filters to adapt to the randomness of target maneuvers and control clutter introduction while ensuring energy accumulation efficiency has become a pressing technical problem to be solved in this field. Summary of the Invention

[0007] To address the aforementioned problems in the prior art, this invention provides a method for constructing a backtracking filter based on a radial constant velocity model.

[0008] The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a method for constructing a backtracking filter based on a radial constant velocity model, comprising: Acquire radar system parameters; the radar system parameters include radar scanning period and range cell width; A radial constant velocity model of the target is established, which describes the target's motion between scans as a superposition of constant velocity motion and random acceleration perturbations following a zero-mean Gaussian distribution, thus obtaining the backtracking depth. The radial distance of the target at that time; where, , Indicates the maximum backtracking depth; For a given center velocity, the backtracking depth is calculated based on the radial constant velocity model and the radar system parameters. The mean and standard deviation of the radial distance to the target are calculated. Based on the mean and standard deviation of the radial distance to the target, the radial distance interval where the target is located is determined according to the normal distribution confidence interval theory, and the radial distance interval is mapped to a set of discrete distance cells according to the width of the distance cell. Based on the set of discrete distance cells, a fast-broadening backtracking filter corresponding to the center velocity is constructed; the fast-broadening backtracking filter has a backtracking depth The effective distance unit at a given location is determined by the set of discrete distance units.

[0009] Optionally, the radial constant velocity model describes the backtracking process in a recursive form: ; ; ; ; in, Indicates the backtracking depth The radial distance of the target at that time Indicates the backtracking depth radial velocity at time Indicates the radial distance of the target currently being scanned. Indicates the radial velocity of the current scan. Indicates the radar scan period. Indicates the backtracking depth Random acceleration at time, This indicates that the mean is 0 and the variance is 0. The normal distribution This represents the standard deviation of random acceleration. This indicates that they are independent and identically distributed.

[0010] Optionally, determining the radial distance interval of the target based on the mean and standard deviation of the target's radial distance, using the normal distribution confidence interval theory, specifically includes: The radial distance interval is determined as follows: ; in, This represents the mean radial distance from the target. The standard deviation of the radial distance of the target is represented by the following: The expansion coefficient is determined based on a preset coverage probability. Indicates the radial distance range.

[0011] Optionally, the expansion coefficient can be 2 or 3.

[0012] Optionally, mapping the radial distance interval to a set of discrete distance cells according to the distance cell width includes: Based on the width of the distance cell, calculate the lower and upper bounds of the index of the discrete distance cells corresponding to the radial distance interval to obtain the set of discrete distance cells: ; ; ; in, Indicates the index of a discrete distance cell. This represents the lower bound of the index of the discrete distance cell corresponding to the lower bound of the radial distance interval. This represents the upper bound of the index of the discrete distance cell corresponding to the upper bound of the radial distance interval. Represents a set of discrete distance cells. This represents the floor function. This represents the floor function. This represents the mean radial distance from the target. The standard deviation of the radial distance of the target is represented by the following: The expansion coefficient is determined based on a preset coverage probability. Indicates the width of the distance unit.

[0013] Optionally, the fast-expanding backtracking filter is a two-dimensional binary mask acting on the distance-scan time plane, which takes a value of 1 when the index of the discrete distance cell falls into the set of discrete distance cells, and 0 otherwise.

[0014] Optionally, the method further includes: Based on the preset target speed range and the determined speed sampling interval, a set of center speeds is generated, and fast broadening backtracking filters corresponding to each center speed in the set of center speeds are constructed to form a backtracking filter group.

[0015] Optionally, the velocity sampling interval is jointly determined based on the interval overlap relationship of adjacent fast-expanding backtracking filters at each backtracking depth, the radial velocity resolution within the scan, and the double sampling criterion. Specifically, the interval overlap relationship ensures that there are no uncovered velocity gaps between backtracking filters corresponding to adjacent velocity channels, thus avoiding missed detections when the target's true radial velocity lies between adjacent filters. The radial velocity resolution constraint within the scan and the double sampling criterion ensure that the velocity sampling interval is no greater than half of the radial velocity resolution within the scan, thereby reducing the cumulative performance loss caused by velocity mismatch. The velocity sampling interval is jointly determined based on the radial velocity resolution within the scan, the double sampling criterion, and the overlap relationship of the boundary intervals of adjacent backtracking filters. ; in, Indicates radial velocity resolution. This represents the standard deviation of random acceleration. Indicates the radar scan period. Indicates the velocity sampling interval. This indicates the minimum value operation.

[0016] Optionally, the radial velocity resolution is determined by the number of pulses within the coherent processing interval, the pulse repetition interval, and the operating wavelength.

[0017] The backtracking filter construction method based on the radial constant velocity model provided by this invention has the following advantages compared with the prior art: First, the construction of the fast-expanding backtracking filter has clear physical interpretability. This invention establishes a radial constant velocity model incorporating random acceleration perturbations, describing the target's motion between scans as a superposition of constant velocity motion and random perturbations. Based on this model, the mean and variance of the target's radial distance at each backtracking depth are calculated. Furthermore, based on the normal distribution confidence interval theory, the high-probability radial distance interval of the target is determined, thereby deriving the template broadening amount at each backtracking depth. This technical approach directly correlates the broadening characteristics of the fast-expanding backtracking filter with physical quantities such as target maneuvering intensity and radar scan cycle, changing the traditional design mode that relies solely on experience to set the broadening width. This provides a clear physical basis for selecting the parameters of the fast-expanding backtracking filter, significantly improving the portability of the technical solution under different radar platforms and sea states.

[0018] Secondly, this invention achieves a better balance between detection performance and false alarm suppression. Based on the normal distribution signal interval theory, this invention determines the template broadening amount at each backtracking depth, enabling the fast-broadening backtracking filter to adaptively envelop the target's path deviation caused by inter-scan maneuvering and positioning errors with a preset probability. This design avoids missed detections due to target energy leakage caused by insufficient broadening, and also prevents increased false alarms due to excessive clutter introduced by excessive broadening. It fundamentally solves the inherent contradiction in existing technologies where insufficient broadening leads to missed detections or excessive broadening leads to increased false alarms, achieving robust suppression of false alarms while effectively accumulating target energy.

[0019] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the method for constructing a backtracking filter based on a radial constant velocity model provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the process for constructing a backtracking filter bank based on a radial constant velocity model provided in an embodiment of the present invention; Figure 3This is a schematic diagram illustrating the rapid expansion of the backtracking filter template provided in this embodiment of the invention as the backtracking depth increases; Figure 4 This is a schematic diagram of a single fast-stretched backtracking filter constructed according to an embodiment of the present invention for target tracking; Figure 5 This is a schematic diagram of the backtracking filter bank provided in an embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0022] To address the problem that existing multi-scan accumulation methods using sector-shaped backtracking filter banks, which rely on empirical parameter adjustments, cannot adapt to the randomness of target maneuvers and struggle to effectively suppress both reliable target acquisition and false alarms, this invention provides a backtracking filter construction method based on a radial constant velocity model. This method can serve as a front-end template generation module for multi-scan joint detection or tracking, and its output is a rapidly broadened set of backtracking filter templates covering the target velocity range on the range-scan time plane. Figure 1 As shown, the method specifically includes the following steps.

[0023] S10, Obtain radar system parameters.

[0024] In this embodiment of the invention, key parameters of the radar system are first obtained, including but not limited to: radar scanning period. and distance unit width Furthermore, in order to subsequently establish a radial constant velocity model of the target, this embodiment of the invention also needs to obtain a random acceleration standard deviation preset according to the target's maneuvering characteristics. and the preset maximum backtracking depth .

[0025] S20. Establish a radial constant velocity model for the target. This model describes the target's motion between scans as a superposition of constant velocity motion and random acceleration perturbations following a zero-mean Gaussian distribution, thus obtaining the backtracking depth. The radial distance of the target at that time; where, , Indicates the maximum backtracking depth.

[0026] Specifically, let the current scan time be... The target's state in the current scan is obtained through single-scan detection processing. ,in The radial distance of the target being scanned. Let be the radial velocity of the target at the current scan moment. In this invention, considering the random maneuvering of the target between scans, a random acceleration term is used. To represent the backtracking from the current scan to the th One historical scan (i.e., a backtracking depth of 1) Velocity perturbation during the process. Assume random acceleration. It follows a zero-mean Gaussian distribution, and the standard deviation of its random acceleration is . The radial constant velocity model then uses a recursive form to describe the backtracking process: ; ; ; ; in, Indicates the backtracking depth The radial distance of the target at that time Indicates the backtracking depth radial velocity at time Indicates the radial distance of the target currently being scanned. Indicates the radial velocity of the current scan. Indicates the radar scan period. Indicates the backtracking depth Random acceleration at time, This indicates that the mean is 0 and the variance is 0. The normal distribution (i.e., Gaussian distribution). This represents the standard deviation of random acceleration. This indicates that they are independent and identically distributed.

[0027] From the above recursive relationship, we can see that the backtracking depth is Target radial distance at time It is determined by the initial distance at the current scan time. The radial velocity is accumulated gradually at each backtracking point; however, because the radial velocity is affected by random acceleration perturbations during the backtracking process, therefore... This also includes the distance uncertainty caused by the random changes in speed.

[0028] S30. For a given center velocity, calculate the backtracking depth based on the radial constant velocity model and the radar system parameters. The mean and standard deviation of the radial distance to the target are calculated. Based on the mean and standard deviation of the radial distance to the target, the radial distance interval where the target is located is determined according to the normal distribution confidence interval theory, and the radial distance interval is mapped to a set of discrete distance cells according to the width of the distance cell.

[0029] Specifically, based on random acceleration Statistical properties (such as zero mean, variance) (and the random accelerations between each scan are independent of each other), for the radial distance of the target By finding the mean and variance, we can obtain: , ; ; in, This represents the mean radial distance from the target. This indicates the operation of calculating the mean. The standard deviation of the radial distance of the target is represented by the following: The variance representing the radial distance to the target. This indicates the operation of calculating variance.

[0030] Therefore, for a given center velocity (the center velocity) As radial velocity The estimated value is used to calculate the backtracking depth using the above formula. mean radial distance of the target Standard deviation of radial distance from target : Then, based on the mean radial distance of the target with standard deviation The radial distance interval of the target is determined based on the normal distribution confidence interval theory. Specifically, this radial distance interval is determined as follows: ; in, This represents the mean radial distance from the target. The standard deviation of the radial distance of the target is represented by the following: The expansion coefficient is determined based on a preset coverage probability. Indicates the radial distance range.

[0031] It should be noted that, That is, the first The allowed distance range for the layer backtracking template. In this embodiment of the invention, the expansion coefficient... The value can be 2 or 3. For example, to obtain a coverage probability of approximately 95%, a high-probability radial distance interval is constructed using the method of "mean ± 2 standard deviations", i.e.: ; In another alternative implementation, the radial distance interval can be constructed using the "mean ± 3 standard deviations" method, based on the system's constraints on the false alarm and missed detection rates, with an expansion coefficient of 3, to provide a higher coverage probability. Here, an expansion coefficient of 3 corresponds to approximately 99.7% confidence probability.

[0032] Radar range image plane in range cell width Discretization is performed. Therefore, based on the distance cell width... Radial distance interval The mapping is to a set of discrete distance cells. Specifically, this includes: based on the width of the distance cell... Calculate the lower and upper bounds of the index of the discrete distance cell corresponding to the radial distance interval to obtain the set of discrete distance cells: ; ; ; in, Indicates the index of a discrete distance cell. This represents the lower bound of the index of the discrete distance cell corresponding to the lower bound of the radial distance interval. This represents the upper bound of the index of the discrete distance cell corresponding to the upper bound of the radial distance interval. Represents a set of discrete distance cells. This represents the floor function. This represents the floor function. This represents the mean radial distance from the target. The standard deviation of the radial distance of the target is represented by the following: The expansion coefficient is determined based on a preset coverage probability. Indicates the width of the distance unit.

[0033] The above mapping ensures that: when the target satisfies the radial constant velocity model and the standard deviation of random acceleration is... At that time, the target is at the backtracking depth The true location is likely to fall into Within the corresponding discrete distance unit range.

[0034] S40. Based on the set of discrete distance cells, construct a fast broadening backtracking filter corresponding to the center velocity; this fast broadening backtracking filter has a backtracking depth... The effective distance cell at a given location is determined by the set of discrete distance cells.

[0035] This invention defines a fast-stretching backtracking filter as a two-dimensional binary mask acting on the range-scan time plane, where the index of a discrete range cell falls into the set of discrete range cells. The value is 1 if it is true, and 0 otherwise.

[0036] Specifically, for a given center velocity radial velocity The estimated value at each backtracking depth The effective range unit of the fast-stretched backtracking filter is the set of discrete range units obtained in step S30. Given: , ; , .

[0037] in, This represents the constructed fast-broadening backtracking filter. This indicates that the fast-stretched backtracking filter is in The value at that location. That is, on the distance-scan time plane, when the backtracking depth is... When, if the index of the discrete distance cell fall into If the value is within the specified range, the fast broadening backtracking filter will take a value of 1 at that position (indicating validity); otherwise, it will take a value of 0 (indicating invalidity).

[0038] Combining the formula in step S30, the width of the fast-expanded backtracking filter can be derived as follows: ; in, This represents the width of the fast-expanding backtracking filter. From the above equation, we can see that: Follow It exhibits superlinear growth, therefore the width of the rapidly widening backtracking filter widens rapidly with the backtracking depth, such as... Figure 3 As shown, this significantly improves robustness to target scanning maneuvers and positioning errors, while also being effective in shallow layers (i.e., (When the size is small) maintain a narrow width to suppress clutter accumulation.

[0039] It is understood that, through the above steps S10 to S40, for a given center velocity, the backtracking depth is calculated based on the radial constant velocity model and the radar system parameters. The mean and standard deviation of the radial distance to the target are calculated. Based on these values ​​and the normal distribution confidence interval theory, the radial distance interval containing the target is determined, and the radial distance interval is mapped to a set of discrete distance cells according to the width of the distance cell. This allows the construction of a corresponding fast-expanding backtracking filter. This fast-expanding backtracking filter can effectively match the quasi-trajectory of a target moving at this center velocity and tolerates a certain degree of maneuvering and positioning errors. In actual detection, firstly, within each scanning cycle, the radar data of each range cell is coherently accumulated to obtain the intra-frame test statistics. Then, for each point, a fast-expanding backtracking filter template corresponding to its radial velocity in the current scan is applied to accumulate the test statistics over multiple scanning cycles. That is, for the current point along the backtracking direction, the intra-frame test statistics are searched within the set of discrete range cells corresponding to each backtracking depth, and the maximum value is selected as the representative test statistics for that backtracking depth. Subsequently, the maximum test statistics for each backtracking depth are accumulated to obtain the multi-frame accumulated test statistics, i.e., the coherent radial velocity spectrum based on the backtracking filter. Finally, the accumulated result is compared with a preset threshold to complete the target determination.

[0040] Furthermore, in a preferred embodiment of the present invention, see [link to previous section]. Figure 2 The method also includes: S50, according to the preset target speed range and a defined velocity sampling interval A set of center velocities is generated, and steps S30 to S40 are repeated to construct fast broadening backtracking filters corresponding to each center velocity in the set of center velocities, so as to form a backtracking filter bank.

[0041] In practical applications, the radial velocity of a target is usually unknown and may vary within a certain range. Therefore, to cover all possible velocities of the target, it is typically necessary to construct a backtracking filter bank consisting of multiple fast-broadening backtracking filters with different center velocities to achieve full coverage of the target velocity range and parallel matched accumulation. The key to constructing this backtracking filter bank lies in determining the velocity sampling interval. This ensures that adjacent fast-expanding backtracking filters overlap at each backtracking depth, preventing energy leakage caused by target velocity mismatch. In this invention, the velocity sampling interval... The method is determined by combining the interval overlap relationship of adjacent fast-expanding backtracking filters at each backtracking depth, the scanning radial velocity resolution, and the double sampling criterion.

[0042] First, by using the radial velocity resolution constraint and the double sampling criterion within the scan, the velocity sampling interval is ensured to be no greater than half of the radial velocity resolution within the scan, thereby reducing the cumulative performance loss caused by velocity mismatch. Specifically, the radial velocity resolution... The number of pulses within the coherent processing interval Pulse repetition interval and operating wavelength Confirmed, specifically: ; To reduce energy loss caused by velocity mismatch, this invention employs an oversampling strategy. In one embodiment of this invention, the velocity sampling interval is adjusted based on a doubling sampling criterion. Set as .

[0043] Secondly, by using interval overlap relationships, it is ensured that there are no uncovered velocity gaps between the backtracking filters corresponding to adjacent velocity channels, in order to avoid missed detections when the target's true radial velocity is located between adjacent filters. ; in, This represents the empty set. Therefore, take... As the velocity sampling interval The upper limit constraint.

[0044] Combining the above two aspects, the velocity sampling interval is determined jointly based on the radial velocity resolution within the scan, the double sampling criterion, and the overlap relationship of adjacent backtracking filter boundary intervals; that is, the velocity sampling interval. Take the minimum of the above two values: ; in, Indicates radial velocity resolution. This represents the standard deviation of random acceleration. Indicates the radar scan period. Indicates the velocity sampling interval. This indicates the minimum value operation.

[0045] It should be noted that in the calculation speed sampling interval The number of pulses required within the coherent processing interval. Pulse repetition interval and operating wavelength All of these can be obtained simultaneously in step S10, and the target speed range Then, the type of target can be set based on experience.

[0046] In one alternative implementation, quadruple oversampling can be used, i.e., the velocity sampling interval. Pick This improves the precision of speed coverage and the matching degree of backtracking accumulation, thereby further enhancing the stability of weak target detection.

[0047] After determining the velocity sampling interval Then, let the central velocity set be: ; in, This indicates the index of the fast-expanding backtracking filter in the backtracking filter bank. , This indicates the rounding up operation.

[0048] Therefore, for each central velocity in the set of central velocities (Right now Repeat steps S30 to S40 to construct the corresponding fast broadening backtracking filter, thereby generating a filter that covers the target velocity range. of A fast-expanded backtracking filter is used to obtain a backtracking filter bank.

[0049] It should be noted that this invention incorporates the overlap between the radial velocity resolution within the scan and the boundary intervals of adjacent backtracking filters into the calculation, providing a regularized method for determining the velocity sampling interval. This design principle, while ensuring sufficient overlap between adjacent templates to prevent target velocity mismatch, effectively controls the number of filter banks and the overall computational load. It avoids the tedious process of relying on repeated trials and manual adjustment of velocity intervals in traditional methods, achieving a more stable and controllable trade-off between detection performance, robustness, and computational complexity.

[0050] In actual detection, firstly, within each scan cycle, the radar data of each range cell is coherently accumulated to obtain the intra-frame test statistics. Then, for each point, a fast-expanding backtracking filter template corresponding to its radial velocity in the current scan is used (i.e., based on the radial velocity of the current scan, the center velocity closest to the radial velocity is selected to construct the backtracking filter), and the test statistics are accumulated over multiple scan cycles. That is, for the current point along the backtracking direction, the intra-frame test statistics are searched within the set of discrete range cells corresponding to each backtracking depth, and the maximum value is selected as the representative test statistics for that backtracking depth. Subsequently, the maximum test statistics of each backtracking depth are accumulated to obtain the multi-frame accumulated test statistics, i.e., the coherent radial velocity spectrum based on the backtracking filter. Finally, the accumulated result is compared with a preset threshold to complete the target decision. Finally, the decision results of different radial velocity channels of each range cell are fused to output the final target detection result.

[0051] See Figure 4 , Figure 4 This diagram illustrates target tracking using a single fast-stretching backtracking filter according to an embodiment of the present invention. The horizontal axis represents the discrete range unit (i.e., the range gate in the diagram), the vertical axis represents the scan time, the starting detection position-time coordinate is (0, 0), and the dashed line in the diagram represents the center velocity. The trajectory is shown, with the red solid line representing the broadening range of the fast-broadening backtracking filter. For example... Figure 4 As shown, at each scan time, the distance interval between the two red solid lines is the detection interval, and target detection is performed within this detection interval at each scan time. Figure 4 middle Indicates the current backtracking depth The standard deviation of the target radial distance. See [reference needed]. Figure 5 , Figure 5 This is a schematic diagram of a backtracking filter bank provided in an embodiment of the present invention. The backtracking filter bank consists of nine fast-expanding backtracking filters. Figure 5 middle This represents the index of the backtracking filter. The horizontal axis of each fast-expanding backtracking filter is a discrete distance unit, and the vertical axis is the number of backtracking frames (i.e., backtracking depth). Each fast-expanding backtracking filter corresponds to a different center velocity. Thus, the backtracking filter can traverse all possible motion scenarios of the target, achieving full coverage of the target's velocity range and parallel matching accumulation.

[0052] The backtracking filter construction method based on the radial constant velocity model provided by this invention has the following advantages compared with the prior art: First, the construction of the fast-expanding backtracking filter has clear physical interpretability. This invention establishes a radial constant velocity model incorporating random acceleration perturbations, describing the target's motion between scans as a superposition of constant velocity motion and random perturbations. Based on this model, the mean and variance of the target's radial distance at each backtracking depth are calculated. Furthermore, based on the normal distribution confidence interval theory, the high-probability radial distance interval of the target is determined, thereby deriving the template broadening amount at each backtracking depth. This technical approach directly correlates the broadening characteristics of the fast-expanding backtracking filter with physical quantities such as target maneuvering intensity and radar scan cycle, changing the traditional design mode that relies solely on experience to set the broadening width. This provides a clear physical basis for selecting the parameters of the fast-expanding backtracking filter, significantly improving the portability of the technical solution under different radar platforms and sea states.

[0053] Secondly, this invention achieves a better balance between detection performance and false alarm suppression. Based on the normal distribution signal interval theory, this invention determines the template broadening amount at each backtracking depth, enabling the fast-broadening backtracking filter to adaptively envelop the target's path deviation caused by inter-scan maneuvering and positioning errors with a preset probability. This design avoids missed detections due to target energy leakage caused by insufficient broadening, and also prevents increased false alarms due to excessive clutter introduced by excessive broadening. It fundamentally solves the inherent contradiction in existing technologies where insufficient broadening leads to missed detections or excessive broadening leads to increased false alarms, achieving robust suppression of false alarms while effectively accumulating target energy.

[0054] Third, this invention provides a standardized design criterion for velocity sampling intervals. Furthermore, this invention incorporates the overlap between the radial velocity resolution within the scan and the boundary intervals of adjacent backtracking filters into the calculation, providing a standardized method for determining the velocity sampling interval. This design criterion, while ensuring sufficient overlap between adjacent templates to prevent target velocity mismatch, effectively controls the number of filter banks and the overall computational load. It avoids the tedious process of relying on repeated trials and manual adjustment of velocity intervals in traditional methods, achieving a more stable and controllable trade-off between detection performance, robustness, and computational complexity.

[0055] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0056] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0057] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0058] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method of constructing a backtracking filter based on a radial constant- speed model, characterized in that, include: Acquire radar system parameters; the radar system parameters include radar scanning period and range cell width; A radial constant velocity model of the target is established, which describes the motion of the target between scans as an overlay of constant velocity motion and random acceleration perturbations that are subject to a zero-mean Gaussian distribution, resulting in a retro-depth of the target at a time t; wherein, , denotes a maximum retro-depth; For a given center velocity, the backtracking depth is calculated based on the radial constant velocity model and the radar system parameters. The mean and standard deviation of the radial distance to the target are calculated. Based on the mean and standard deviation of the radial distance to the target, the radial distance interval where the target is located is determined according to the normal distribution confidence interval theory, and the radial distance interval is mapped to a set of discrete distance cells according to the width of the distance cell. A fast-spread retrocausal filter corresponding to the central velocity is constructed from the set of discrete range cells; the fast-spread retrocausal filter has an effective range cell at a retrocausal depth determined from the set of discrete range cells.

2. The radial constant-speed model based backtracking filter construction method of claim 1, wherein, The radial constant velocity model describes the backtracking process in a recursive form: ； ； ； ； in, Indicates the backtracking depth The radial distance of the target at that time Indicates the backtracking depth radial velocity at time Indicates the radial distance of the target currently being scanned. Indicates the radial velocity of the current scan. Indicates the radar scan period. Indicates the backtracking depth Random acceleration at time, This indicates that the mean is 0 and the variance is 0. The normal distribution This represents the standard deviation of random acceleration. This indicates that they are independent and identically distributed.

3. The radial constant-speed model based backtracking filter construction method of claim 1, wherein, The determination of the radial distance interval of the target based on the mean and standard deviation of the radial distance, using the normal distribution confidence interval theory, specifically includes: The radial distance interval is determined as follows: ； in, This represents the mean radial distance from the target. The standard deviation of the radial distance of the target is represented by the following: The expansion coefficient is determined based on a preset coverage probability. Indicates the radial distance range.

4. The method for constructing a backtracking filter based on a radial constant velocity model according to claim 3, characterized in that, The expansion coefficient is either 2 or 3.

5. The radial constant-speed model based backtracking filter construction method of claim 1, wherein, The step of mapping the radial distance interval to a set of discrete distance cells according to the width of the distance cell includes: Based on the width of the distance cell, calculate the lower and upper bounds of the index of the discrete distance cells corresponding to the radial distance interval to obtain the set of discrete distance cells: ； ； ； in, Indicates the index of a discrete distance cell. This represents the lower bound of the index of the discrete distance cell corresponding to the lower bound of the radial distance interval. This represents the upper bound of the index of the discrete distance cell corresponding to the upper bound of the radial distance interval. Represents a set of discrete distance cells. This represents the floor function. This represents the floor function. This represents the mean radial distance from the target. The standard deviation of the radial distance of the target is represented by the following: The expansion coefficient is determined based on a preset coverage probability. Indicates the width of the distance unit.

6. The radial constant-speed model based backtracking filter construction method of claim 1, wherein, The fast broadening backtracking filter is a two-dimensional binary mask acting on the distance-scan time plane. It takes a value of 1 when the index of the discrete distance cell falls into the set of discrete distance cells, and 0 otherwise.

7. The radial constant-speed model based backtracking filter construction method of claim 1, wherein, The method further includes: Based on the preset target speed range and the determined speed sampling interval, a set of center speeds is generated, and fast broadening backtracking filters corresponding to each center speed in the set of center speeds are constructed to form a backtracking filter group.

8. The radial constant-speed model based backtracking filter construction method of claim 7, wherein, The velocity sampling interval is jointly determined based on the interval overlap relationship of adjacent fast-expanding backtracking filters at each backtracking depth, the radial velocity resolution within the scan, and the double sampling criterion. Specifically, the interval overlap relationship ensures that there are no uncovered velocity gaps between backtracking filters corresponding to adjacent velocity channels, thus avoiding missed detections when the target's true radial velocity lies between adjacent filters. The radial velocity resolution constraint within the scan and the double sampling criterion ensure that the velocity sampling interval is no greater than half of the radial velocity resolution within the scan, reducing the cumulative performance loss caused by velocity mismatch. The velocity sampling interval is jointly determined based on the radial velocity resolution within the scan, the double sampling criterion, and the overlap relationship of the boundary intervals of adjacent backtracking filters. ； in, Indicates radial velocity resolution. This represents the standard deviation of random acceleration. Indicates the radar scan period. Indicates the velocity sampling interval. This indicates the minimum value operation.

9. The method for constructing a backtracking filter based on a radial constant velocity model according to claim 8, characterized in that, The radial velocity resolution is determined by the number of pulses within the coherent processing interval, the pulse repetition interval, and the operating wavelength.

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