A stable iterative AOA underwater target localization method

Abstract

This invention provides a stable iterative method for AOA target localization. It approximates the model using a one-dimensional Taylor expansion, thereby eliminating model nonlinearity. This allows for target position estimation using linear least squares. To eliminate errors caused by Taylor expansion, an iterative approach is employed, selecting the target position obtained in the previous iteration as the Taylor expansion point for the next iteration, until a relatively accurate solution is obtained. This invention transforms the localization problem into a linear least squares problem and obtains a reasonable initial point through iteration. Compared to convex optimization schemes, this method significantly reduces computational cost while maintaining the same accuracy. Compared to least squares and weighted least squares methods, it offers improved accuracy.

Description

Technical Field

[0001] This invention relates to the field of underwater target localization, and in particular to a method for locating targets at an angle of arrival in a two-dimensional scene, specifically a stable iterative method for AOA (Angle-of-Arrival) target localization. Background Technology

[0002] Since the beginning of the 21st century, countries have continuously strengthened their research and application of marine science and technology to enhance their international maritime competitiveness, and the protection of maritime rights has become increasingly important. Underwater Acoustic Sensor Networks (UASNs) based on acoustic information interaction have gained widespread application due to their advantages of low cost, strong concealment, good adaptability, and real-time data acquisition. In the civilian sector, UASNs are used to perform common signal processing tasks such as detection, localization, and target tracking; in the military sector, UASN-based systems can detect targets at greater distances, contributing to the ability to "detect and strike first."

[0003] In these tasks, location information is crucial for signal processing. Based on the different measurement information acquired by nodes for positioning, wireless sensor network target localization methods can be categorized as: Time of Arrival (TOA), Time Difference of Arrival (TDOA), Angle of Arrival (AOA), Received Signal Strength (RSS), and methods combining multiple measurements. TDOA incurs a 3dB performance loss due to the subtraction of TOA measurements; among these measurements, RSS is highly sensitive to multipath effects and is unsuitable for underwater acoustic environments; TOA measurements require clock synchronization between the target and nodes, which is difficult to achieve underwater, especially in non-cooperative target localization. AOA measurements, on the other hand, typically provide better positioning performance and are more suitable for applications in underwater acoustic environments.

[0004] AOA-based positioning methods require each node to have orientation capabilities and fuse position estimates based on the target directions estimated by each node. In recent years, various AOA-based positioning methods have been proposed, such as triangulation, least squares estimation, and maximum likelihood estimation. However, triangulation methods do not fully utilize information and have significant biases; maximum likelihood estimation may get trapped in local optima; and least squares methods may exhibit significant biases due to linearization approximation when errors are large. Patent CN117686974A proposes a convex optimization target positioning method for AOA, but it does not consider the impact of sensor node position errors. Furthermore, this convex optimization scheme involves high computational costs, leading to longer positioning times and wasting the limited energy resources of underwater nodes.

[0005] In summary, although the target localization method based on AOA performs better than other methods, the existing methods still have many shortcomings. Therefore, it is necessary to conduct in-depth research on the target localization technology based on AOA. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a stable iterative AOA target localization method. The model is approximated by a one-dimensional Taylor expansion, thereby eliminating the nonlinearity of the model. Then, the target position can be estimated using the linear least squares method. In order to eliminate the error caused by the Taylor expansion, an iterative method is adopted, selecting the target position obtained in the previous iteration as the Taylor expansion point for the next iteration, until a more accurate solution is obtained.

[0007] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0008] Step 1: Establish a Cartesian coordinate system as the reference coordinate system in the wireless sensor network; there are N arrays and one target with an unknown location. The position coordinates of the i-th array are:

[0009] v i =(x i ,y i ) T i = 1, ..., N

[0010] The coordinates of the target to be located are:

[0011] u 0 =(x 0 ,y 0 ) T ,

[0012] Each sensor passively acquires the AOA measurement value between itself and the target.

[0013] Step 2: The array acquires measurements after the target node transmits a signal;

[0014] Step 3: Since the arctangent function is highly nonlinear, it needs to be approximated by a Taylor series expansion. The arctangent function is expanded using a Taylor series at the initial point (x0, y0), with the first initial point set to (0, 0). The polynomials of degree one and below are retained, and expressed as:

[0015]

[0016] in:

[0017]

[0018] After the final simplification and Taylor series approximation, the AOA measurement in step two... Approximately expressed as:

[0019]

[0020] in:

[0021]

[0022] Step 4: According to step 3 An approximate representation of the target is obtained, and the target is located using maximum likelihood estimation.

[0023] Step 5: The maximum likelihood problem is actually a linear least squares problem. We use the general method of linear least squares to solve the maximum likelihood problem in Step 4:

[0024]

[0025] in The estimated position of the target can be obtained by using matrix multiplication and inversion.

[0026] Step Six: Calculate the position estimated in Step Five Distance between the position (x0, y0) used for expansion in step three It is then compared with a pre-determined threshold d0, which is determined based on the required precision and the device's computing power. If the distance d is less than the threshold, then at this point... For the final estimation result, if the distance d is greater than the threshold, then at this point... Use (x0, y0) as the expansion point and jump to step three to recalculate.

[0027] In step two, the AOA measurement (target azimuth angle) acquired by the i-th array... The model is as follows:

[0028]

[0029] In the formula, θ represents the AOA measurement value obtained by the array. i The true angle of the target relative to the i-th array, ε i The AOA measurement error is modeled as a zero-mean, zero-variance error. Gaussian white noise.

[0030] In step three, the polynomial is expressed as:

[0031]

[0032] in:

[0033]

[0034] After the final simplification and Taylor series approximation, the AOA measurement in step two... Approximately expressed as:

[0035]

[0036] in:

[0037]

[0038] In step four, the maximum likelihood estimation is used as follows:

[0039]

[0040] in This represents the estimated target location.

[0041] An electronic device includes: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to perform the methods described above.

[0042] A computer-readable storage medium storing program code that can be invoked by a processor to perform the method described above.

[0043] The beneficial effect of this invention is that it eliminates the nonlinearity of the arctangent function by using the first-order Taylor expansion method, thereby transforming the localization problem into a linear least squares problem. It also obtains a reasonable initial point through an iterative method. Compared with convex optimization schemes, this method significantly reduces the amount of computation while maintaining the same accuracy. Compared with least squares method and weighted least squares method, the accuracy is improved. Attached Figure Description

[0044] Figure 1 This is a general implementation block diagram of the present invention.

[0045] Figure 2 This diagram illustrates how the root mean square error changes as the standard deviation of the azimuth measurement noise increases, along with the lower bound of the Cramer-Rao method of the present invention and existing weighted least squares methods, existing least squares methods, and the method of the present invention.

[0046] Figure 3 This diagram illustrates how the root mean square error of the method of the present invention, the existing weighted least squares method, the existing least squares method, and the corresponding Cramer-Rao lower bound of the method of the present invention changes with the increase of the number of nodes, under the condition that the standard deviation of the azimuth measurement noise is 2. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0048] The present invention proposes a stable AOA target localization iterative method, the overall implementation block diagram of which is shown below. Figure 1 As shown, it includes the following steps:

[0049] Step 1: Establish a Cartesian coordinate system as the reference coordinate system in the wireless sensor network. There are N arrays and one target with an unknown location. The position coordinates of the i-th array are...

[0050] v i =(x i ,y i ) T i = 1, ..., N

[0051] The position coordinates of the target to be located are

[0052] u 0 =(x 0 ,y 0 ) T ,

[0053] Each sensor passively acquires the AOA measurement value between itself and the target.

[0054] Step 2: The array acquires measurements after the target node transmits a signal.

[0055] The AOA measurement (target azimuth) acquired by the i-th array. The model is as follows:

[0056]

[0057] In the formula, θ represents the AOA measurement value obtained by the array. i The true angle of the target relative to the i-th array, ε i The AOA measurement error is modeled as a zero-mean, zero-variance error. Gaussian white noise.

[0058] Step 3: Since the arctangent function is highly nonlinear, it needs to be approximated by a Taylor series expansion. The arctangent function is expanded using a Taylor series at the initial point (x0, y0) (the first initial point is (0, 0)). The polynomials of degree one and below are retained, and expressed as:

[0059]

[0060] in:

[0061]

[0062] After the final simplification and Taylor series approximation, the AOA measurement in step two... It can be approximated as:

[0063]

[0064] in:

[0065]

[0066] Step 4: According to step 3 An approximate representation of the target is obtained, and the target is located using maximum likelihood estimation:

[0067]

[0068] here This represents the estimated target location.

[0069] Step 5: The maximum likelihood problem is actually a linear least squares problem. We use the general solution of linear least squares to solve the maximum likelihood problem in Step 4.

[0070]

[0071] in The estimated position of the target can be obtained simply by using matrix multiplication and inversion.

[0072] Step Six: Calculate the position estimated in Step Five Distance between the position (x0, y0) used for expansion in step three And compare it with a predetermined threshold d0 (determined based on required precision and device computing power). If it is less than the threshold, then at this time... The final estimated result, if greater than the threshold, will then be... As the expansion point (x0, y0), repeat steps three through six.

[0073] The following simulation experiments are used to verify the feasibility, effectiveness, and positioning performance of the method of the present invention.

[0074] Assume there are N=16 sensor nodes and one target in the wireless sensor network. All nodes (including anchor nodes and target nodes) are randomly deployed in a two-dimensional space of 40×40 square meters.

[0075] The performance of the method of the present invention was tested as the standard deviation of the azimuth measurement noise increased.

[0076] Figure 2 The following diagrams illustrate the changes in the root mean square error (RMSE) of the method of this invention, the existing weighted least squares method, the existing least squares method, and the Cramer-Rao lower bound corresponding to the method of this invention as the standard deviation of the azimuth measurement noise increases; from Figure 2 It can be seen that as the standard deviation of azimuth measurement noise increases, the RMSE of all methods shows an upward trend. The performance of the proposed improved algorithm is always better than other methods. When the measurement error is slightly large, the performance of the least squares method drops sharply. This shows that the method of the present invention is more robust and has higher positioning accuracy.

[0077] The performance of the method of this invention was tested to see how it changes with the number of nodes.

[0078] Figure 3 The diagram shows the changes in the root mean square error of the proposed method, the existing weighted least squares method, the existing least squares method, and the Cramer-Rao lower bound corresponding to the proposed method as the number of nodes increases, under the condition that the standard deviation of the azimuth measurement noise is 2. As the number of nodes increases, the positioning accuracy of all methods increases.

[0079] In summary, the algorithm proposed in this invention is superior to existing methods and has good stability.

[0080] As can be seen from the simulation results above, the method of the present invention has good performance and can well meet the requirements of high positioning accuracy.

Claims

1. A stable iterative AOA underwater target localization method, characterized in that... Includes the following steps: Step 1: Establish a Cartesian coordinate system as the reference coordinate system in the wireless sensor network; there are N arrays and one target with an unknown location. The position coordinates of the i-th array are: v i =(x i ,y i ) T ,i=1,…,N, The coordinates of the target to be located are: u 0 =(x 0 ,y 0 ) T , Each sensor passively acquires the AOA measurement value between itself and the target. Step 2: The array acquires measurements after the target node transmits a signal; Step 3: Since the arctangent function is highly nonlinear, it needs to be approximated by a Taylor series expansion. The arctangent function is expanded using a Taylor series at the initial point (x0, y0), with the first initial point set to (0, 0). The polynomials of degree one and below are retained, and expressed as: in: After the final simplification and Taylor series approximation, the AOA measurement in step two... Approximately expressed as: in: Step 4: According to step 3 An approximate representation of the target is obtained, and the target is located using maximum likelihood estimation. Step 5: The maximum likelihood problem is actually a linear least squares problem. We use the linear least squares method to solve the maximum likelihood problem in Step 4: in The estimated position of the target can be obtained by using matrix multiplication and inversion. Step Six: Calculate the position estimated in Step Five Distance between the position (x0, y0) used for expansion in step three It is then compared with a pre-determined threshold d0, which is determined based on the required precision and the device's computing power. If the distance d is less than the threshold, then at this point... For the final estimation result, if the distance d is greater than the threshold, then at this point... Use (x0, y0) as the expansion point and jump to step three to recalculate.

2. The stable iterative AOA underwater target localization method according to claim 1, characterized in that: In step two, the AOA measurement acquired by the i-th array The model is as follows: In the formula, θ represents the AOA measurement value obtained by the array. i Let ε be the true angle of the target relative to the i-th array. i The AOA measurement error is modeled as a value with zero mean and variance of . Gaussian white noise.

3. The stable iterative AOA underwater target localization method according to claim 1, characterized in that: In step four, the maximum likelihood estimation is used as follows: in This represents the estimated target location.

4. An electronic device, characterized in that, include: One or more processors; Memory; One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs being configured to perform the method as described in any one of claims 1-3.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program code that can be invoked by a processor to execute the method as described in any one of claims 1-3.

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