Stable iteration AOA underwater target positioning method

Abstract

The invention provides a stable iteration AOA target positioning iteration method, the model is approximated through a one-dimensional Taylor expansion mode, so that the nonlinearity of the model is eliminated, a linear least square method can be used for target position estimation, and in order to eliminate errors caused by Taylor expansion, an iteration method is adopted, so that the accuracy of target position estimation is improved. And selecting a target position obtained by last iteration as a next Taylor expansion point until a relatively accurate solution is obtained. According to the method, a positioning problem is converted into a linear least square problem, a reasonable initial point is obtained through an iteration method, compared with a convex optimization scheme, the method has the advantages that the calculation amount is remarkably reduced while the same precision is kept, and compared with a least square method and a weighted least square method, the precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of underwater target positioning, in particular to a method for locating an angle of arrival target in a two-dimensional scene, and specifically to a stable AOA (AOA, Angle-of-Arrival) target positioning iteration method. Background Art

[0002] Since the 21st century, countries have continuously strengthened the research and application of marine science and technology to improve their international marine competitiveness, and the maintenance of marine rights and interests has become increasingly important. Underwater Acoustic Sensor Network (UASN) based on acoustic information interaction has the advantages of low cost, strong concealment, good adaptability, and real-time data acquisition, so it has been widely used. In the civilian field, UASN is used to perform common signal processing tasks such as detection, positioning and target tracking; in the military field, UASN-based systems can detect targets farther away, which helps to achieve "first enemy detection and first enemy strike".

[0003] In these tasks, location information is very important for the completion of signal processing tasks. According to the different positioning measurement information obtained by the node, the target positioning methods of wireless sensor networks can be divided into: signal arrival time (TOA, Time of Arrival), signal arrival time difference (TDOA, Time Difference of Arrival), signal arrival angle (AOA, Angle-of-Arrival), signal received signal strength (RSS, Received Signal Strength) and combined multiple measurement methods. TDOA will cause a 3dB performance loss due to the subtraction of TOA measurement; RSS in these measurements is very sensitive to multipath effects and is not suitable for underwater acoustic environments; TOA measurement requires clock synchronization between the target and the node, which is not easy to achieve underwater, especially in non-cooperative target positioning. AOA measurement can usually provide better positioning performance and is more suitable for applications in underwater acoustic environments.

[0004] The AOA-based positioning method requires that each node has directional capability and fuses the position estimate according to the target direction estimated by each node. In the past few years, a variety of AOA-based positioning methods have been proposed, such as triangulation positioning, least squares estimation, and maximum likelihood estimation. However, the triangulation positioning method does not fully utilize information and has large deviations; the maximum likelihood estimation may fall into local optimality; and the least squares method may have significant deviations due to linear approximation when the error is large. Patent CN117686974A proposes a convex optimization target positioning method for AOA, but does not consider the influence of the position error of the sensor node. At the same time, this convex optimization scheme has a large amount of calculation, which will not only result in a longer positioning time, but also waste the limited energy resources of underwater nodes.

[0005] In summary, although the target localization method based on AOA has better performance 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] In order to overcome the shortcomings of the prior art, the present invention provides a stable iterative AOA target positioning iterative method, which approximates the model by means of one-dimensional Taylor expansion, thereby eliminating the nonlinearity of the model, and then the linear least squares method can be used to estimate the target position. In order to eliminate the error caused by Taylor expansion, an iterative method is adopted to select 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 the present invention to solve the technical problem comprises the following steps:

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

[0009] v i =(x i ,y i ) T ,i=1,…,N,

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

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

[0012] Each sensor acquires the AOA measurement value between it and the target in a passive way;

[0013] Step 2: After the target node transmits a signal, the array acquires the measurement;

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

[0015]

[0016] in:

[0017]

[0018] The AOA measurement in step 2 after the final simplified Taylor series approximation It can be expressed approximately as:

[0019]

[0020] in:

[0021]

[0022] Step 4: According to the third step Approximate representation of , using maximum likelihood estimation to locate the target;

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

[0024]

[0025] in Using matrix multiplication and inversion, the estimated target position can be obtained

[0026] Step 6: Calculate the estimated position from step 5 The distance from the position (x0, y0) used for expansion in step 3 And compare it with the pre-determined threshold d0, which is determined according to the required accuracy and device computing power. If the distance d is less than the threshold, then is the final estimated result. If the distance d is greater than the threshold, then As the expansion point (x0, y0) and jump to step 3, the calculation cycle is repeated.

[0027] In step 2, the AOA measurement (target azimuth) obtained by the i-th array is Modeled as:

[0028]

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

[0030] In step 3, the polynomial is expressed as:

[0031]

[0032] in:

[0033]

[0034] The AOA measurement in step 2 after the final simplified Taylor series approximation It can be expressed approximately as:

[0035]

[0036] in:

[0037]

[0038] In step 4, the maximum likelihood estimation is:

[0039]

[0040] in Represents the estimated target position.

[0041] An electronic device comprises: 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 execute the method as described above.

[0042] A computer-readable storage medium stores program codes, and the program codes can be called by a processor to execute the method as described above.

[0043] The beneficial effect of the present invention is that the nonlinearity of the inverse tangent function is eliminated through the method of first-order Taylor expansion, thereby converting the positioning problem into a linear least squares problem, and obtaining a reasonable initial point through an iterative method. Compared with the convex optimization solution, this method significantly reduces the amount of calculation while maintaining the same accuracy. Compared with the least squares method and the weighted least squares method, the accuracy is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is an overall implementation block diagram of the present invention.

[0045] Figure 2 It is a schematic diagram of the change of the root mean square error of the method of the present invention and the existing weighted least squares method, the existing least squares method and the Cramer-Rao lower bound corresponding to the method of the present invention as the standard deviation of the azimuth measurement noise increases.

[0046] Figure 3 It is a schematic diagram of the change of the root mean square error of the method of the present invention and the existing weighted least squares method, the existing least squares method and the Cramer-Rao lower bound corresponding to the method of the present invention as the number of nodes increases under the condition that the standard deviation of the azimuth measurement noise is 2. DETAILED DESCRIPTION

[0047] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0048] The present invention proposes a stable AOA target positioning iterative method, and its overall implementation block diagram is as follows: Figure 1 As shown, it includes the following steps:

[0049] Step 1: Establish a rectangular coordinate system as a reference coordinate system in the wireless sensor network. There are N arrays and a target with unknown position. 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 acquires the AOA measurement value between it and the target in a passive way.

[0054] Step 2: After the target node transmits a signal, the array acquires the measurement.

[0055] AOA measurement (target azimuth) acquired by the ith array Modeled as:

[0056]

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

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

[0059]

[0060] in:

[0061]

[0062] The AOA measurement in step 2 after the final simplified Taylor series approximation It can be approximately expressed as:

[0063]

[0064] in:

[0065]

[0066] Step 4: According to the third step Approximate representation of , using maximum likelihood estimation to locate the target:

[0067]

[0068] here Represents the estimated target position.

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

[0070]

[0071] in Only matrix multiplication and inversion are needed to find the estimated target position.

[0072] Step 6: Calculate the estimated position from step 5 The distance from the position (x0, y0) used for expansion in step 3 And compare it with the pre-determined threshold d0 (determined according to the required accuracy and device computing power). If it is less than the threshold, then is the final estimated result. If it is greater than the threshold, As the expansion point (x0, y0) and repeat steps 3 to 6.

[0073] The feasibility, effectiveness and positioning performance of the method of the present invention are verified by simulation experiments as follows.

[0074] Assume that there are N=16 sensor nodes and one target in the wireless sensor network, and 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 A schematic diagram of the change of the root mean square error of the method of the present invention and the existing weighted least squares method, the Cramer-Rao lower bound corresponding to the existing least squares method and the method of the present invention as the standard deviation of the azimuth measurement noise increases is given; Figure 2 It can be seen that with the increase of the standard deviation of the azimuth measurement noise, the RMSE of various methods shows an upward trend. The performance of the proposed improved algorithm is always better than other methods. When the measurement error is slightly larger, the performance of the least squares method drops sharply, which shows that the method of the present invention is more robust and has higher positioning accuracy.

[0077] The performance of the method of the present invention is tested as the number of nodes increases.

[0078] Figure 3 A schematic diagram is given of the change in the root mean square error of the method of the present invention and the existing weighted least squares method, the existing least squares method and the Cramer-Rao lower bound corresponding to the method of the present invention 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 the present invention is superior to the existing method and has good stability.

[0080] It can be seen from the above simulation results that the method of the present invention has good performance and can well meet the demand for high-precision positioning.

Claims

1. A stable iterative AOA underwater target positioning method, characterized in that The steps include: Step 1: Establish a rectangular coordinate system as a reference coordinate system in the wireless sensor network; there are N arrays and a target with unknown position, and the position coordinates of the i-th array are: v i =(x i ,y i ) T ,i=1,…,N, The position coordinates of the target to be located are: u 0 =(x 0 ,y 0 ) T , Each sensor acquires the AOA measurement value between it and the target in a passive way; Step 2: After the target node transmits a signal, the array acquires the measurement; Step 3: Since the inverse tangent function is highly nonlinear, it needs to be approximated by Taylor series expansion. The inverse tangent function is expanded by Taylor series at the initial point (x0, y0). The first initial point is (0, 0), and the polynomials of degree one and below are retained, which can be expressed as: in: The AOA measurement in step 2 after the final simplified Taylor series approximation It can be expressed approximately as: in: Step 4: According to the third step Approximate representation of , using maximum likelihood estimation to locate the target; Step 5: The maximum likelihood problem is actually a linear least squares problem. Use the linear least squares method to solve the maximum likelihood problem in step 4: in Using matrix multiplication and inversion, the estimated target position can be obtained Step 6: Calculate the estimated position from step 5 The distance from the position (x0, y0) used for expansion in step 3 And compare it with the pre-determined threshold d0, which is determined according to the required accuracy and device computing power. If the distance d is less than the threshold, then is the final estimated result. If the distance d is greater than the threshold, then As the expansion point (x0, y0) and jump to step 3, the calculation cycle is repeated.

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

3. The stable iterative AOA underwater target positioning method according to claim 2, characterized in that: In step 3, the polynomial is expressed as: in: The AOA measurement in step 2 after the final simplified Taylor series approximation It can be expressed approximately as: in:

4. The stable iterative AOA underwater target positioning method according to claim 3, characterized in that: In step 4, the maximum likelihood estimation is: in Represents the estimated target position.

5. 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, and the one or more programs are configured to execute the method according to any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program codes, and the program codes can be called by a processor to execute the method according to any one of claims 1 to 4.

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