A low-complexity underwater target motion parameter estimation method
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA SHIP SCIENTIFIC RESEARCH CENTER
- Filing Date
- 2026-04-30
- Publication Date
- 2026-08-04
AI Technical Summary
[0004]本发明为了解决基于传统广义Radon变换的水下目标运动参数估计方法存在计算量大、计算复杂度高、运算效率低的缺陷，导致无法满足水下目标探测的实时性应用需求，提出了一种低计算复杂度的水下目标运动参数估计方法，可以有效降低传统广义Radon变换方法的计算负担，进一步提升目标运动参数估计的运算效率
1.通过引入目标方位信息，推导了方位角与目标运动参数、
、
的变化关系，构建了基于方位测量结果的齐次线性方程组，在此基础上仅需通过求解方程组非零解即可实现目标运动参数的粗略估计。
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Figure CN122507973A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of target motion analysis, and in particular to a method for estimating underwater target motion parameters with low computational complexity. Background Technology
[0002] Underwater target motion parameter estimation has broad application prospects and significant research value in various fields such as underwater exploration and marine resource development. Since target azimuth information is one of the most reliable parameters of a sound source, pure azimuth target motion analysis methods are currently the most widely used type of target motion analysis method. Typical pure azimuth target motion analysis methods can be broadly divided into two categories: recursive methods and batch processing methods. Recursive methods are mainly developed and evolved from Kalman filtering methods. Common recursive methods include extended Kalman filtering, unscented Kalman filtering, and particle filtering. Batch processing methods are target parameter estimation methods that process a batch of time-ordered measurement data simultaneously. Therefore, compared to recursive methods, although batch processing methods have poorer real-time performance, they are more robust and can provide more accurate estimation results, showing great development potential.
[0003] As a typical batch processing method for target motion analysis, the generalized Radon transform does not require prior knowledge of the initial state of the target motion, nor does it require recursive or iterative calculations. Instead, it achieves accurate estimation of target parameters by traversing each measured variable, exhibiting excellent robustness and accuracy. However, in practical applications, since the accurate information of each target parameter cannot be predicted, a large-scale and refined scan of each target parameter can only be performed based on empirical information. This undoubtedly brings a huge computational burden to the generalized Radon transform, greatly limiting the performance of the aforementioned method. Summary of the Invention
[0004] To address the shortcomings of traditional generalized Radon transform-based underwater target motion parameter estimation methods, which suffer from high computational load, high computational complexity, and low computational efficiency, thus failing to meet the real-time application requirements of underwater target detection, this invention proposes a low-computational-complexity underwater target motion parameter estimation method. This method effectively reduces the computational burden of traditional generalized Radon transform methods and further improves the computational efficiency of target motion parameter estimation. The technical solution of this invention is as follows: A method for estimating underwater target motion parameters with low computational complexity includes the following steps: Establish a geometric model of the target's motion and derive the mathematical relationship between the target's azimuth and its motion parameters; Construct a homogeneous linear system of equations about the target motion parameters based on mathematical relationships; Collect target time and azimuth history data, extract the target's measured azimuth angle from it, and substitute it into the homogeneous linear equation system to solve for non-zero solutions, thereby obtaining a rough estimate of the target's motion parameters. Using rough estimates as a reference, the search range for target motion parameters is narrowed down; Perform a generalized Radon transform on the target's time-location history within the narrowed search range to obtain accurate estimates of the target's motion parameters; The target motion parameters include: the azimuth angle of the target relative to the detection platform at the initial moment. Target heading angle Target speed Distance of the target relative to the detection platform at the initial moment ratio .
[0005] A further technical solution is that the mathematical relationship between the target's azimuth and its motion parameters is expressed as follows:
[0006] In the formula, express The azimuth of the target at the time of observation; , They represent The differences in the horizontal and vertical coordinates between the target and the detection platform at the observation time are expressed as follows: .
[0007] Its further technical solution is, for the collected N Group of observation data The homogeneous linear equations concerning the target motion parameters are expressed as follows:
[0008] In the formula: , , , ; ,when It is obtained by transforming mathematical relations; This is a homogeneous linear system of equations to be solved.
[0009] A further technical solution involves calculating a rough estimate of the target motion parameters using the following methods: The nonzero solutions of the homogeneous linear equation system obtained by solving The following formula is used to calculate the result. , , Rough estimate:
[0010]
[0011]
[0012] Its further technical solution is, for parameters In the domain For the case where there are two solutions that differ by 180°, the method also includes: Determine using the measured azimuth of the target at the initial moment The only rough estimate; The measured azimuth of the target at the initial moment is extracted from the target's time-azimuth history data.
[0013] Its further technical solution is, for parameters In the domain For the case where there are two solutions that differ by 180°, the method also includes: According to the unique The quadrant in which the solution is located determines the non-zero solution. A , B The sign of the solution determines the non-zero solution. C , D Positive and negative; Lock the solution from the two solutions. C , D Positive or negative The only rough estimate.
[0014] A further technical solution involves a method for calculating precise estimates of the target motion parameters, including: The parameter estimation formula for the generalized Radon transform is:
[0015] In the formula, A matrix representing the target's time-location history. express The azimuth of the target at the time of observation; N Indicates the total number of observation points; For the shrunken , , The search range is determined by sampling parameters according to a preset discretization scale, traversing the sampled parameters, and accumulating the amplitude values of the time-location history matrix to obtain relevant data. , , The three-dimensional energy matrix is used as the coordinates of each dimension corresponding to the maximum value in the three-dimensional energy matrix. , , The precise estimate.
[0016] A further technical solution involves constructing a northeast-northeast coordinate system for the target motion geometry model, with the location of the detection platform as the origin. x The positive axis points to due north in geodetic coordinates; Define target azimuth angle Connect the target to the origin and... x Clockwise deflection angle in the positive direction of the axis; Define target heading angle For the target motion heading and x Clockwise deflection angle in the positive direction of the axis.
[0017] A further technical solution involves narrowing the search range of the target motion parameters by defining a small, pre-defined interval centered on a rough estimate. , , The search interval is used instead of a full range traversal.
[0018] A further technical solution is that this method is applicable to the estimation of motion parameters of underwater targets traveling at a constant speed in a straight line.
[0019] The beneficial technical effects of this invention are: 1. By introducing target azimuth information, the relationship between azimuth and target motion parameters was derived. , , Based on the changing relationship, a homogeneous linear equation system based on the orientation measurement results was constructed. On this basis, a rough estimate of the target motion parameters can be achieved simply by solving the non-zero solutions of the equation system.
[0020] 2. By using the rough estimate of the target motion parameters as a reference value, the search range of the generalized Radon transform ergodic parameters is significantly reduced. While ensuring the accuracy and robustness of the method, the computational complexity of the method is further reduced and the computational efficiency of the method is improved. Attached Figure Description
[0021] Figure 1 This is a flowchart of a low-computational-complexity underwater target motion parameter estimation method provided in this application; Figure 2 This is a schematic diagram of the target motion geometry model provided in this application; Figure 3 This is a time-location history diagram of the target provided in this application; Figure 4 This application provides a three-dimensional energy matrix obtained by performing a generalized Radon transform within the original search range. Schematic diagram, where: (a) is The maximum value corresponding to - (b) is a schematic diagram of a two-dimensional slice; The maximum value corresponding to - Two-dimensional slice diagram; (c) is The maximum value corresponding to - Schematic diagram of two-dimensional slicing; Figure 5 This is a schematic diagram of the target time and azimuth measurement results at the specified observation time provided in this application; Figure 6 This application provides a three-dimensional energy matrix obtained by performing a generalized Radon transform within a narrowed search range. Schematic diagram, where: (a) is The maximum value corresponding to - (b) is a schematic diagram of a two-dimensional slice; The maximum value corresponding to - Two-dimensional slice diagram; (c) is The maximum value corresponding to - Schematic diagram of two-dimensional slice. Detailed Implementation
[0022] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.
[0023] One embodiment of this application provides a method for estimating underwater target motion parameters with low computational complexity, referencing... Figure 1 As shown, the method includes the following steps: Step 1: Establish a geometric model of the target's motion and derive the mathematical relationship between the target's azimuth and its motion parameters. The target motion parameters include: the initial azimuth of the target relative to the detection platform. Target heading angle Target speed Distance of the target relative to the detection platform at the initial moment ratio .
[0024] Step 2: Construct a homogeneous linear system of equations about the target motion parameters based on mathematical relationships.
[0025] Step 3: Collect target time-azimuth history data, extract the measured azimuth angle of the target, and substitute it into the homogeneous linear equation system to solve for non-zero solutions, obtaining a rough estimate of the target's motion parameters. In this step, beamforming and spectrum analysis are performed on the array signals collected by the detection platform at different times to obtain the target's time within a certain sampling period. t -position History data, such as Figure 3 As shown.
[0026] Step 4: Using the rough estimate as a reference, narrow down the target motion parameters. , , The search scope.
[0027] Step 5: Perform a generalized Radon transform on the target's time-location history within the narrowed search range to obtain accurate estimates of the target's motion parameters, further improving the real-time performance of the method.
[0028] Before performing generalized Radon transform parameter estimation, a target motion geometry model is first constructed. In one possible implementation, step 1 specifically includes the following: Figure 2 As shown, assuming the target moves at a constant velocity in a straight line, a northeast-northeast coordinate system is constructed with the location of the detection platform as the origin, using a left-handed coordinate system, i.e. x The positive axis points to true north in geodetic coordinates. In this coordinate system... Let be the azimuth angle of the target relative to the detection platform (origin), defined as the angle between the line connecting the target to the origin and . x The clockwise deflection angle along the positive axis (due north), i.e., the angle of north by east; target heading angle. Defined as the target's heading and x Clockwise deflection angle in the positive direction of the axis.
[0029] Depend on Figure 2 Establish the measured azimuth of the target A mathematical model relating to various motion parameters. In this embodiment, because... The periodicity of its values restricts its range to... The principal value interval of can be represented as: (1) In the formula, express The azimuth of the target at the time of observation; , They represent The difference in abscissa between the target and the detection platform at the observation time ( y Axial coordinate), difference between ordinate and longitudinal coordinate ( x Axial coordinates), respectively, are represented as: (2) but / This can be further expressed as: (3) in, , , , , .
[0030] From equations (1)-(3), we can see that the azimuth angle Only with the target , as well as These parameters are related to three motion parameters. Therefore, the generalized Radon transform can be used to estimate these parameters. In this embodiment, the parameter estimation formula for the generalized Radon transform is: (4) In the formula, N This represents the total number of observation points summed. Indicates the first The time corresponding to each sampling point; express The azimuth of the target at the observation time can be obtained by solving equation (1); This represents the target's time-location history matrix. The target's time-location history diagram is shown below. Figure 3 As shown, the target heading angle The initial azimuth angle of the target is 80°. It is 200°. It is 0.3 / min.
[0031] Equation (4) essentially expresses the calculation of taking each moment in the time-location history matrix. Corresponding angle The amplitude values are accumulated to obtain the time-azimuth curve. , , The result of the three-dimensional spatial projection integral is a three-dimensional spatial matrix about the energy distribution. At this point, the coordinates of each dimension corresponding to the maximum value in the three-dimensional spatial matrix are the motion parameters of the target to be measured. Figure 4 (a), (b), and (c) in the figure give the two-dimensional slice results corresponding to the maximum values in the three-dimensional spatial matrix. By reading the coordinates of each dimension corresponding to the maximum values in each two-dimensional plane, the motion parameters of the target can be accurately estimated.
[0032] Because the generalized Radon transform method requires traversing all the measured variables to accurately estimate the target motion parameters, its computational complexity is closely related to the number of sampling points for the measured variables. Figure 4 For example, the target motion parameters in the figure , , The search ranges are respectively , , The discretization scales are 0.01 / min, 1°, and 1°, respectively. It is assumed that for each set of variables traversed... The computational complexity is The total computational complexity of the generalized Radon transform method is then... As the number of sampling points increases, the estimation accuracy of the method improves, but the computational load also increases. Therefore, it is of great practical significance to reasonably select the search range of the variable to be measured and reduce the number of sampling points for the parameters in order to improve the efficiency of the method and reduce the computational burden.
[0033] In one possible implementation, step 2 specifically includes the following: when Then, equation (1) can be expressed in the following form: (5) Substituting equation (3) into equation (5) yields a result regarding... A , B , C , D The linear equation is expressed as follows: (6) For the collected N Group of observation data Based on the form of equation (6), the following homogeneous linear equation system can be obtained: (7) In the formula, This is a system of homogeneous linear equations to be solved. When the solution is non-zero, it should satisfy the following mathematical relationship: (8) In one possible implementation, step 3 specifically includes the following: solving the non-zero solutions of the homogeneous linear equation system... Substituting into equation (8) yields the following results: , , A rough estimate. Wherein, since the tan function is... A periodic function with periodicity, therefore the parameters and In the domain There will be two solutions that differ by 180°, which can be further expressed as: (9) In the formula, mod represents the modulo operation, preventing... and Greater than Or less than 0.
[0034] To address the situation where there are two possible solutions for the parameters, this embodiment first determines the azimuth angle of the target relative to the detection platform at the initial moment in the observation time-azimuth history. The only rough estimate. Based on this, according to the only... The quadrant in which the solution is located can determine the non-zero solution. A , B The positive and negative, that is, through , Determine the sign, and then determine the non-zero solutions. C , D The positive and negative, ultimately from The two solutions satisfy the locking condition. C , D It is a single, rough estimate, either positive or negative. The principle of this method can be referenced from all non-zero solutions of a homogeneous linear system of equations, which are proportional to each other. A , B , C , D The pattern of sign changes can be found; it can also be determined by combining the physical laws governing changes in the target's orientation. C , D symbol.
[0035] In this embodiment, Figure 5 Given t =Target azimuth measurement results at four time points: 0 min, 2 min, 4 min, and 8 min (200°, 165°, 132°, and 105° respectively). Substituting the above measurement results into equations (5)-(7) respectively, a set of non-zero solutions to the homogeneous linear equation system can be obtained as follows: Based on this, equation (8) can be solved to obtain the following results: =0.302 / min, =19.988°, 199.988° =80.700°, 260.700°. Among them, by t The target's initial azimuth angle can be determined by the azimuth measurement results at time =0 min. =199.988°, and calculate , All are negative numbers. Combined with the known non-zero solutions...x The change of sign in can be used to determine , All are positive numbers, only This condition is met when the value is 80.700.
[0036] In one possible implementation, step 4 specifically includes the following: narrowing the search range of the target motion parameters by defining a pre-defined small interval centered on a rough estimate. , , The search interval is defined to replace a full range traversal. Parameters are defined in this embodiment. , , The search ranges are respectively , , The discretization scales are 0.01 / min, 1°, and 1°, respectively. Therefore, the total computational complexity of the method is... This represents a decrease of nearly one-eightieth compared to before.
[0037] In one possible implementation, step 5 specifically includes the following: using equation (4) to reduce the size of the sample. , , The search range is determined by sampling parameters according to a preset discretization scale, traversing the sampled parameters, and accumulating the amplitude values of the time-location history matrix to obtain relevant data. , , The three-dimensional energy matrix (i.e., the three-dimensional space matrix) The coordinates of each dimension corresponding to the maximum value in the three-dimensional energy matrix are used as... , , The precise estimate. Figure 6 (a), (b), and (c) in the figure give the three-dimensional space matrix. The results of each two-dimensional slice corresponding to the maximum value in each two-dimensional plane are obtained. Accurate estimation of the target motion parameters can be achieved by reading the coordinates of each dimension corresponding to the maximum value in each two-dimensional plane. Compared with directly performing the generalized Radon transform, the method provided in this embodiment can significantly reduce the search range of parameters, thereby reducing the computational complexity of the method.
[0038] The above descriptions are merely preferred embodiments of this application, and the present invention is not limited to the above embodiments. It is understood that other improvements and variations directly derived or conceived by those skilled in the art without departing from the spirit and concept of the present invention should be considered to be included within the protection scope of the present invention.
Claims
1. A method for estimating underwater target motion parameters with low computational complexity, characterized in that, The method includes: Establish a geometric model of the target's motion and derive the mathematical relationship between the target's azimuth and its motion parameters; Based on the aforementioned mathematical relationships, a homogeneous linear system of equations concerning the target motion parameters is constructed; Collect target time and azimuth history data, extract the target's measured azimuth angle from it, and substitute it into the homogeneous linear equation system to solve for non-zero solutions, thereby obtaining a rough estimate of the target's motion parameters. Using the rough estimate as a reference, the search range for the target motion parameters is narrowed down; Perform a generalized Radon transform on the target's time-location history within the narrowed search range to obtain accurate estimates of the target's motion parameters; The target motion parameters include: the azimuth angle of the target relative to the detection platform at the initial moment. Target heading angle Target speed Distance of the target relative to the detection platform at the initial moment ratio .
2. The underwater target motion parameter estimation method according to claim 1, characterized in that, The mathematical relationship between the target's azimuth and its motion parameters is expressed as follows: In the formula, express The azimuth of the target at the time of observation; , They represent The differences in the horizontal and vertical coordinates between the target and the detection platform at the observation time are expressed as follows: 。 3. The underwater target motion parameter estimation method according to claim 2, characterized in that, For the collection N Group of observation data The homogeneous linear equations concerning the target motion parameters are expressed as follows: In the formula: , , , ; ,when It is obtained by transforming mathematical relations; The solution to the homogeneous linear system of equations is to be found.
4. The underwater target motion parameter estimation method according to claim 1, characterized in that, The method for calculating the rough estimate of the target motion parameters includes: The nonzero solutions of the homogeneous linear equation system obtained by solving The following formula is used to calculate the result. , , Rough estimate: 。 5. The underwater target motion parameter estimation method according to claim 4, characterized in that, For parameters In the domain The method further includes the following for the case where there are two solutions that differ by 180°: Determine using the measured azimuth of the target at the initial moment The only rough estimate; The measured azimuth angle of the target at the initial moment is extracted from the target's time-azimuth history data.
6. The underwater target motion parameter estimation method according to claim 5, characterized in that, For parameters In the domain The method further includes the following for the case where there are two solutions that differ by 180°: According to the unique The quadrant in which the solution is located determines the non-zero solution. A , B The sign of the solution determines the non-zero solution. C , D Positive and negative; Lock the solution from the two solutions. C , D Positive or negative The only rough estimate.
7. The underwater target motion parameter estimation method according to claim 1, characterized in that, The method for calculating the accurate estimate of the target motion parameters includes: The parameter estimation formula for the generalized Radon transform is as follows: In the formula, A matrix representing the target's time-location history. express The azimuth of the target at the time of observation; N Indicates the total number of observation points; For the shrunken , , The search range is determined by sampling parameters according to a preset discretization scale, traversing the sampled parameters, and accumulating the amplitude values of the time-location history matrix to obtain relevant data. , , The three-dimensional energy matrix is used as the coordinates of each dimension corresponding to the maximum value in the three-dimensional energy matrix. , , The precise estimate.
8. The underwater target motion parameter estimation method according to claim 1, characterized in that, The target motion geometry model constructs a northeast coordinate system with the location of the detection platform as the origin. x The positive axis points to due north in geodetic coordinates; Define target azimuth angle Connect the target to the origin and the... x Clockwise deflection angle in the positive direction of the axis; Define target heading angle For the target motion heading and the said x Clockwise deflection angle in the positive direction of the axis.
9. The underwater target motion parameter estimation method according to claim 1, characterized in that, The process of narrowing the search range for the target motion parameters involves defining a small interval centered on the rough estimate. , , The search interval is used instead of a full range traversal.
10. The method for estimating underwater target motion parameters according to any one of claims 1-9, characterized in that, The method is applicable to the estimation of motion parameters of underwater targets traveling at a constant speed in a straight line.