A target positioning method based on a confidence domain broken line method
By constructing the objective function using the trust region piecewise linear method and solving it iteratively, the problems of insufficient prior information and large parameter estimation errors in underwater acoustic localization are solved, and more efficient target localization and tracking are achieved in non-cooperative target localization.
Patent Information
- Application Number
- CN202610512450.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-17
- Publication Date
- 2026-07-10
AI Technical Summary
Existing underwater acoustic localization methods rely on prior information in non-cooperative target localization, leading to divergent localization results. Furthermore, the estimation error of underwater acoustic pulse signal parameters is large, making it difficult to accurately locate targets under noise and nonlinear effects.
The trust region piecewise linear method is adopted to construct the objective function by normalizing the arrival angle and frequency parameters of the underwater acoustic signal, and the target coordinates are solved iteratively using the trust region piecewise linear method, which reduces the dependence on prior information and improves the situation of getting trapped in local optima.
With fewer pulse signals and prior information, the accuracy and robustness of target localization are improved, the sensitivity to noise is reduced, and more efficient target tracking and localization are achieved.
Smart Images
Figure CN122362282A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of underwater acoustic signal target localization, and particularly relates to a target localization method based on the trust region piecewise linear method. Background Technology
[0002] Underwater acoustic positioning technology has always been a hot research topic, with broad application prospects in target search, marine exploration, and fisheries resource exploration. Due to the complexity of the underwater environment, underwater acoustic positioning has always been a challenging and crucial research area. Non-cooperative positioning refers to the method where, due to the non-cooperative nature of the target, the reconnaissance party typically locates the target by intercepting target signals or radiated noise. In this case, the prior characteristics of the target are unknown or incompletely understood. Existing positioning methods usually require some prior information, and the lack or uncertainty of this prior information can easily lead to divergent positioning results. Therefore, non-cooperative positioning has poor accuracy and low effectiveness.
[0003] Underwater acoustic pulse signals are the primary signal targets for underwater acoustic reconnaissance, and their unique characteristics increase the difficulty of target localization. Underwater acoustic pulse signals are typically emitted at a certain period, and the reconnaissance party can only obtain the pulse's parameter information at the moment of arrival. The amount of usable information for localization is limited and discrete. Furthermore, underwater acoustic reconnaissance uses short time windows for pulse signal processing, resulting in low accuracy and large errors in estimating parameters such as signal arrival angle, arrival time, and center frequency. All of these factors contribute to the difficulty of target localization.
[0004] Commonly used initial value estimation algorithms for positioning include pseudolinear methods, auxiliary variable methods, and maximum likelihood methods. The first two methods linearize the pulse signal parameters with respect to the target's motion state and use the least squares method to calculate the target position. These methods have low noise tolerance. The maximum likelihood method, on the other hand, constructs a maximum likelihood function for the pulse signal parameters, transforming the solution for the target position into an extremum problem of a nonlinear likelihood function, which can be solved iteratively using the Gauss-Newton method. The maximum likelihood method can yield estimation results with a small number of observations. Theoretically, as long as the number of observations is greater than or equal to the dimension of the estimated state, an accurate estimation result can be obtained. However, due to the influence of system nonlinearity and noise, this method has a large estimation error when the number of parameters is too small, and it is prone to encountering situations where the Hessian matrix of the likelihood function is not invertible, leading to solution failure or getting trapped in local optima.
[0005] To address the aforementioned problems, this invention proposes a target localization method based on the trust region piecewise linear method. The inputs are the angle of arrival and frequency of arrival of the underwater acoustic signal, and the output is an estimated target coordinate. Simulation and sea trial data processing results show that, compared with traditional target localization methods, this method solves the nonlinearity problem, improves the situation of getting trapped in local optima, and allows for localization using fewer pulse signal parameters and prior information. Summary of the Invention
[0006] The purpose of this invention is to address the problems of limited prior information, large parameter estimation errors, and high nonlinearity in underwater acoustic pulse signals by providing a target localization method based on the trust region piecewise linear method. This method takes the pulse signal's angle of arrival and frequency of arrival as input, along with the vessel's coordinates and velocity. It calculates the mean and standard deviation of the pulse signal's angle of arrival and frequency of arrival, and then normalizes these parameters using the calculated mean and standard deviation. An objective function is constructed using the normalized angle of arrival and frequency of arrival, and the coordinates of the initial iteration point are passed to the objective function. The trust region piecewise linear method is used to solve for the target coordinate estimation and the corresponding objective function. If the maximum gradient of the objective function at the current iteration's estimated coordinates is less than the tolerance or the upper limit of the iteration count is reached, the target coordinate estimation result for the current iteration is given.
[0007] To achieve the above objectives, this invention employs a target localization method based on the trust region piecewise linear method, comprising the following steps: Step 1: Initialize positioning processing parameters; Step 2: Read in the arrival angle and frequency parameters of the pulse signal, as well as the coordinates and speed of the ship; Step 3: Calculate the mean and standard deviation of the pulse signal's angle of arrival and frequency of arrival, and use the calculated mean and standard deviation to normalize the signal's angle of arrival and frequency of arrival; Step 4: Construct the objective function using the normalized signal arrival angle and arrival frequency, and pass the coordinates of the starting iteration point into the objective function; Step 5: Use the trust region piecewise linear method to solve for the target coordinate estimation and the corresponding objective function. If the maximum gradient of the objective function on the estimated coordinates in the current iteration is less than the tolerance or reaches the upper limit of the number of iterations, give the target coordinate estimation result for the current iteration.
[0008] Furthermore, step 1 specifically includes the following steps: Initialize positioning processing parameters and set the number of pulse signal groups. Maximum number of iterations The number of iterations is , The initial estimated coordinates of the target are , No. The target estimated coordinates at the next iteration are: .
[0009] Furthermore, step 2 specifically includes the following steps: Read in Group pulse signal detection estimated signal arrival angle Arrival frequency parameters , This is the sequence number of the pulse signal group. ; Read in the ship upon receiving the first The coordinates at the time of each pulse signal are Its velocity in the horizontal and vertical directions is and The coordinate vector of the target signal source is set as follows: Including the x-coordinate of the target signal source and the vertical axis The frequency of its emitted single-frequency signal is Then in the first During the second observation, the target azimuth angle and frequency The theoretical value is calculated using the following formula: .
[0010] Furthermore, step 3 specifically includes the following steps: Step 3.1: Calculate the mean of the pulse signal's angle of arrival and frequency of arrival. , and standard deviation , : ; Step 3.2: Normalize the signal's angle of arrival and frequency of arrival using the calculated mean and standard deviation. Sum the normalized results and use them as the observations in the optimization process. : ; in, and These represent the normalized angle of arrival and frequency of arrival, respectively.
[0011] Furthermore, step 4 specifically includes the following steps: Step 4.1: Using the theoretical model and signal source coordinates The calculated theoretical parameters, weighted according to the mean and standard deviation of the received parameters, are used to obtain the first step in the optimization process. Fitted values of group pulse signal parameters : ; in It is a real number. It is the dimension of the coordinate vector of the target signal source; from this, the first... The residual between the fitted values and observed values of the pulse signal : ; Based on existing Group observation results, residual vector It can be written as: ; Therefore, the objective function is constructed based on the least squares criterion. : ; Step 4.2: Determine the starting point of the iteration for estimating the coordinates of the target signal source. Input the cost function and calculate the corresponding objective function. : .
[0012] Furthermore, step 5 specifically includes the following steps: Step 5.1: Determine a trust region radius. The maximum step size for the current search is initialized to 10; with the th... Secondary coordinate iteration value Centered on, The region with radius is called the trust region; a quadratic approximation model of the objective function is constructed within this trust region. : ; in, It is the transpose symbol of a matrix. It is a tentative step in the search. For the objective function exist gradient at, For the standard function exist Approximate Hessian matrix at: ; in, for Jacobi matrix: ; in, yes about The partial derivative, It is the gradient symbol; The trust region subproblem is constructed based on a quadratic approximation model of the objective function, and its mathematical expression is: ; Step 5.2: Centered on the current search point Solving the trust region subproblem, the proposed steps of the solution The optimal point is denoted as Based on the broken line method, the optimal point Solution by steepest descent method Solution with Gauss-Newton method and trust region radius We obtain the weighted average: ; Among them, coefficient The weighted coefficients are used in the steepest descent solution. Solution with Gauss-Newton method The expression is: ; ; in, It is the inverse of the matrix; Will Record Based on the trust region boundary, obtain information about The equation: ; When solving a quadratic equation, denote the auxiliary variable. , and ; ; thus, and The result is: ; Therefore, the solution is obtained using the steepest descent method. And the solution of Gauss and Newton and weighting coefficients Find the trial step ; Step 5.3: Define a gain ratio function. To determine whether to accept the trial step, the function's expression is: ; Based on the gain ratio function of the current iteration The trust region radius is adjusted in the current iteration as follows: ; in, The maximum trust region radius is set to 0.1 in this invention; while the target state estimate after iterative update... The expression is: ; This completes the first... The next iteration; Step 5.4: Determine whether the iteration should terminate based on the maximum gradient of the objective function and the number of iterations during the iteration process. After the iteration converges, provide a feasible solution for the target position estimation and the corresponding objective function value. The termination condition for the iteration is that the maximum gradient of the objective function is less than a threshold. Or the number of iterations is greater than or equal to the maximum number of iterations. : ; in, This indicates taking the maximum value. This indicates taking the absolute value; if the termination condition is not met, repeat step 5; after the iteration converges, the final target estimate is obtained. At this point, the final estimate of the target's location is obtained, and the output can be further used for tracking and localization.
[0013] This invention discloses a target localization method based on the trust region piecewise linear method. The method takes the arrival angle and frequency parameters of a pulse signal, as well as the coordinates and speed of the vessel, as input. It calculates the mean and standard deviation of the arrival angle and frequency of the pulse signal, and normalizes these parameters using the calculated mean and standard deviation. An objective function is constructed using the normalized arrival angle and frequency, and the coordinates of the initial iteration point are passed to the objective function. The trust region piecewise linear method is used to solve for the target coordinate estimation and the corresponding objective function. If the maximum gradient of the objective function at the current iteration's estimated coordinates is less than the tolerance or reaches the upper limit of the iteration count, the target coordinate estimation result for the current iteration is given. This achieves more accurate target coordinate estimation even with limited prior information and large parameter estimation errors.
[0014] Compared with existing technologies, the method disclosed in this invention has the following advantages: In passive localization of underwater acoustic pulse signal sources, a cost function is constructed using the normalized pulse signal's angle of arrival and frequency estimation parameters, and the target position parameters are iterated using the trust region piecewise linear method. It also requires a lower number of pulse groups, allowing for more accurate target position estimation with fewer pulse groups. Attached Figure Description
[0015] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a graph showing the localization convergence rate of the method under different numbers of pulses according to the present invention. Detailed Implementation
[0016] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments: This invention utilizes the angle of arrival (AHA) and frequency of arrival (FNA) of underwater acoustic pulse signals to locate targets. The mean and standard deviation of the AHA and FNA are calculated and then normalized using these values. An objective function is constructed based on the normalized AHA and FNA, and the trust region piecewise linear regression method is used to minimize this objective function. The iterative result corresponding to the minimized objective function is the final target position estimate.
[0017] Example 1: The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.
[0018] The parameters are set as follows: using the northeast-central coordinate system, the target is set to remain stationary, located 30km from the origin at 45° east of north. The ship is moving eastward at a constant speed of 6 knots. The pulse signal frequency is 4.5kHz, the signal period is 40s, and the speed of sound in water is... The speed is 1500 m / s. Convergence is considered to occur when the estimated position is within 20% of the actual position, indicating a relatively accurate estimate. The algorithm performance is described using Monte Carlo simulations. The convergence rate is calculated by dividing the number of convergences in the Monte Carlo simulations by the total number of simulations. When comparing the positioning convergence rate of this method with different numbers of pulses, the number of received pulse signal groups was set from 5 to 30, and the standard deviation of the angle noise was 0.5°. The positioning convergence rate results are as follows: Figure 2 As shown.
[0019] A target localization method based on the trust region piecewise linear method, such as Figure 1 As shown, it includes the following steps: Step 1 is as follows: (1.1) Initialize parameters and set the number of pulse signal groups. Maximum number of iterations The value is 100, and the number of iterations is... , The initial estimated coordinates of the target are for , No. The target estimated coordinates at the next iteration are: .
[0020] Step 2 is as follows: (2.1) Reading Group pulse signal detection estimated signal arrival angle Arrival frequency parameters , This is the sequence number of the pulse signal group. Read in the message received by this ship upon receiving the first... The coordinates at the time of each pulse signal are Its velocity in the horizontal and vertical directions is and The coordinate vector of the target signal source is set as follows: Including the x-coordinate of the target signal source and the vertical axis The frequency of its emitted single-frequency signal is Then in the first During the second observation, the target azimuth angle and frequency The theoretical value is calculated using the following formula: Step 3 specifically involves: (3.1) Calculate the mean of the signal arrival angle and arrival frequency of the pulse signal. , and standard deviation , : (3.2) Normalize the signal angle of arrival and frequency of arrival using the calculated mean and standard deviation, and sum the normalized results as the observations in the optimization process. : in, and These represent the normalized angle of arrival and frequency of arrival, respectively.
[0021] Step 4 specifically involves: (4.1) Using theoretical models and signal source coordinates The calculated theoretical parameters, weighted according to the mean and standard deviation of the received parameters, are used to obtain the first step in the optimization process. Fitted values of group pulse signal parameters : in It is a real number. It is the dimension of the coordinate vector of the target signal source. In this invention, The value is 2; therefore, the first... The residual between the fitted values and observed values of the pulse signal : Based on existing Group observation results, residual vector It can be written as: Therefore, the objective function is constructed based on the least squares criterion. : (4.2) The starting point for the iteration of estimating the coordinates of the target signal source. Input the cost function and calculate the corresponding objective function. : Step 5 specifically involves: (5.1) First, determine a trust region radius. The maximum step size for the current search is initialized to 10. Secondary coordinate iteration value Centered on, The region with radius is called the trust region. A quadratic approximation model of the objective function is constructed within this trust region. : in, It is the transpose symbol for a matrix. It's a tentative step in the search. For the objective function exist gradient at, For the standard function exist Approximate Hessian matrix at: in, for Jacobi matrix: in, yes about The partial derivative, It is the gradient symbol.
[0022] The trust region subproblem is constructed based on a quadratic approximation model of the objective function, and its mathematical expression is: (5.2) Centered on the current search point Solving the trust region subproblem, the proposed steps of the solution The optimal point is denoted as Based on the broken line method, the optimal point It can be solved by the steepest descent method. Solution with Gauss-Newton method and trust region radius We obtain the weighted average: Among them, coefficient The weighted coefficients are used in the steepest descent solution. Solution with Gauss-Newton method The expression is: in, It is the inverse of the matrix.
[0023] Will Record Based on the trust region boundary, we obtain information about... The equation: When solving a quadratic equation, denote the auxiliary variable. , and .
[0024] thus, and It can be obtained as follows: Therefore, the solution is obtained using the steepest descent method. And the solution of Gauss and Newton and weighting coefficients The trial step can be calculated. .
[0025] (5.3) Define a gain ratio function To determine whether to accept the trial step, the function's expression is: Based on the gain ratio function of the current iteration The trust region radius is adjusted in the current iteration as follows: in, The maximum trust region radius is set to 0.1 in this invention. The target state estimate after iterative updates... The expression is: This completes the first... The next iteration.
[0026] (5.4) Determine whether the iteration terminates based on the maximum gradient of the objective function and the number of iterations during the iteration process. After the iteration converges, provide a feasible solution for estimating the target position and the corresponding objective function value. The termination condition for the iteration is that the maximum gradient of the objective function is less than a threshold. Or the number of iterations is greater than or equal to the maximum number of iterations. : in, This indicates taking the maximum value. This indicates taking the absolute value. If the termination condition is not met, repeat step 5. After the iteration converges, the final target estimate is obtained. At this point, the final estimate of the target's location is obtained, and the output can be further used for tracking and localization.
[0027] The above embodiments demonstrate that the method of the present invention can effectively locate underwater acoustic pulse signals, achieve effective positioning accuracy with a small number of pulse groups, and is robust to noise, which is beneficial for subsequent target tracking and positioning.
[0028] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.
Claims
1. A target localization method based on the trust region piecewise linear method, characterized in that... It includes the following steps: Step 1: Initialize positioning processing parameters; Step 2: Read in the arrival angle and frequency parameters of the pulse signal, as well as the coordinates and speed of the ship; Step 3: Calculate the mean and standard deviation of the pulse signal's angle of arrival and frequency of arrival, and use the calculated mean and standard deviation to normalize the signal's angle of arrival and frequency of arrival; Step 4: Construct the objective function using the normalized signal arrival angle and arrival frequency, and pass the coordinates of the starting iteration point into the objective function; Step 5: Use the trust region piecewise linear method to solve for the target coordinate estimation and the corresponding objective function. If the maximum gradient of the objective function on the estimated coordinates in the current iteration is less than the tolerance or reaches the upper limit of the number of iterations, give the target coordinate estimation result for the current iteration.
2. The target localization method based on the trust region piecewise linear method according to claim 1, characterized in that, Step 1 specifically includes the following steps: Initialize positioning processing parameters and set the number of pulse signal groups. Maximum number of iterations The number of iterations is , The initial estimated coordinates of the target are , No. The target estimated coordinates at the next iteration are: .
3. The target localization method based on the trust region piecewise linear method according to claim 2, characterized in that, Step 2 specifically includes the following steps: Read in Group pulse signal detection estimated signal arrival angle Arrival frequency parameters , This is the sequence number of the pulse signal group. ; Read into the ship upon receipt of the first The coordinates at the time of each pulse signal are Its velocity in the horizontal and vertical directions is and ; Set the coordinate vector of the target signal source as Including the x-coordinate of the target signal source with the vertical axis The frequency of its emitted single-frequency signal is Then in the first During the second observation, the target azimuth angle and frequency The theoretical value is calculated using the following formula: 。 4. The target localization method based on the trust region piecewise linear method according to claim 3, characterized in that, Step 3 specifically includes the following steps: Step 3.1: Calculate the mean of the pulse signal's angle of arrival and frequency of arrival. , and standard deviation , : ； Step 3.2: Normalize the signal's angle of arrival and frequency of arrival using the calculated mean and standard deviation. Sum the normalized results and use them as the observations in the optimization process. : ； in, and These represent the normalized angle of arrival and frequency of arrival, respectively.
5. The target localization method based on the trust region piecewise linear method according to claim 1, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Using the theoretical model and signal source coordinates The calculated theoretical parameters, weighted according to the mean and standard deviation of the received parameters, are used to obtain the first step in the optimization process. Fitted values of group pulse signal parameters : ； in It is a real number. It is the dimension of the coordinate vector of the target signal source; from this, the first... The residual between the fitted values and observed values of the pulse signal : ； Based on existing Group observation results, residual vector Written as: ； Therefore, the objective function is constructed based on the least squares criterion. : ； Step 4.2: Determine the starting point of the iteration for estimating the coordinates of the target signal source. Input the cost function and calculate the corresponding objective function. : 。 6. The target localization method based on the trust region piecewise linear method according to claim 5, characterized in that, Step 5 specifically includes the following steps: Step 5.1: Determine a trust region radius. The maximum step size for the current search is initialized to 10. With the first Secondary coordinate iteration value Centered on, The region with radius is called the trust region; a quadratic approximation model of the objective function is constructed within this trust region. : ； in, It is the transpose symbol of a matrix. It is a tentative step in the search. For the objective function exist gradient at, For the standard function exist Approximate Hessian matrix at: ； in, for Jacobi matrix: ； in, yes about The partial derivative, It is the gradient symbol; The trust region subproblem is constructed based on a quadratic approximation model of the objective function, and its mathematical expression is: ； Step 5.2: Centered on the current search point Solving the trust region subproblem, the proposed steps of the solution The optimal point is denoted as Based on the broken line method, the optimal point Solution by steepest descent method Solution with Gauss-Newton method and trust region radius We obtain the weighted average: ； Among them, coefficient The weighted coefficients are used in the steepest descent solution. Solution with Gauss-Newton method The expression is: ； ； in, It is the inverse of the matrix; Will Record Based on the trust region boundary, we obtain information about The equation: ； When solving a quadratic equation, denote the auxiliary variable. , and ; ； thus, and The result is: ； Therefore, the solution is obtained using the steepest descent method. And the solution of Gauss and Newton and weighting coefficients Find the trial step ; Step 5.3: Define a gain ratio function. To determine whether to accept the trial step, the function's expression is: ； Based on the gain ratio function of the current iteration The trust region radius is adjusted in the current iteration as follows: ； in, It is the set maximum trust region radius; while the target state estimate after iterative update is... The expression is: ； This completes the first... The next iteration; Step 5.4: Determine whether the iteration should terminate based on the maximum gradient of the objective function and the number of iterations during the iteration process. After the iteration converges, provide a feasible solution for the target position estimation and the corresponding objective function value. The termination condition for the iteration is that the maximum gradient of the objective function is less than a threshold. Or the number of iterations is greater than or equal to the maximum number of iterations. : ； in, This indicates taking the maximum value. This indicates taking the absolute value; if the termination condition is not met, repeat step 5; after the iteration converges, the final target estimate is obtained. .