TDOA and AOA moving target positioning method based on RZNN model

Abstract

The invention discloses a TDOA and AOA moving target positioning method based on an RZNN model, and belongs to the technical field of wireless positioning. The method comprises the following steps: establishing a dynamic equation set of TDOA and AOA based on a geometrical relationship; performing linear transformation on the equation and defining an error function; introducing a polynomial noise compensation item and a nonlinear logarithm mapping activation function to construct an RZNN model; solving the linear equation in real time through the model, obtaining a sound source estimation track, and comparing the sound source estimation track with a theoretical track; noise effects are simulated to assess performance. According to the method, an anti-noise item and an activation function are added into the RZNN model, the robustness, the convergence speed and the precision are improved, and high precision and low time delay are kept in time-varying and high-order noise environments.

Description

Technical Field

[0001] This invention relates to the field of positioning technology, and in particular to TDOA and AOA moving target positioning methods based on the RZNN model. Background Technology

[0002] In TDOA positioning estimation, the time difference between the arrival of acoustic emission source signals at different acoustic emission sensors is mainly used for positioning. If multiple receivers are located in a straight line, there are many optimization methods. However, if the receivers are randomly distributed in space, the situation becomes more complex, and nonlinear problems arise when solving the hyperbolic equations. Some literature provides accurate solutions when the number of measurement parameters is the same as the number of source signal coordinates. However, when there is redundancy in the number of measurement parameters, this method cannot fully utilize the statistical information provided by the redundant measurement parameters to improve positioning accuracy. For the case of redundant measurement parameters, some closed-form solutions have been provided in the literature; however, these solutions are not optimal. In AOA positioning estimation, target positioning is mainly achieved by measuring the angle at which the signal arrives at the receiving antenna array. This positioning relies on the receiver's perception of the signal's direction of arrival. However, limitations imposed by multipath propagation leading to false directions of arrival, and the resolution constraints of the receiver's antenna aperture and array layout, mean that small angular deviations can be amplified into significant positional errors at long distances. In scenarios where the target or receiver is moving dynamically, traditional AOA estimation algorithms rely on high-dimensional matrix operations, resulting in high computational complexity and poor real-time performance. Furthermore, issues such as the Doppler effect and antenna array phase mismatch further exacerbate the angle estimation error. Simultaneously, the increased computational cost and significant noise interference make real-time solutions extremely difficult. Summary of the Invention

[0003] To address the aforementioned pain points in the existing technology, this invention provides a TDOA and AOA moving target localization method based on the RZNN model, which mainly solves the technical problems existing in the background technology.

[0004] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0005] This paper presents a method for TDOA and AOA moving target localization based on the RZNN model.

[0006] S1. Based on geometric relationships, establish the dynamic equation sets corresponding to the TDOA algorithm and the AOA algorithm;

[0007] S2. Perform an equivalent linear transformation on the TDOA and AOA positioning equations, and define an error function based on the linear equations of the matrix;

[0008] S3. Based on the ZNN model, a multinomial noise compensation term and a nonlinear logarithmic mapping activation function are introduced to construct the RZNN model;

[0009] S4. Set the initial position and theoretical trajectory equation of the unknown node, solve the linear dynamic equation established by the TDOA and AOA algorithms in real time through the RZNN model, obtain the estimated trajectory of the sound source position, and compare it with the theoretical trajectory.

[0010] S5. Simulate the effects of noise of different orders, solve the problem using the RZNN model under the same positioning conditions, and draw a comparison chart of positioning residual errors under the TDOA and AOA algorithms.

[0011] Furthermore, step S1, establishing the dynamic equation sets for the TDOA and AOA algorithms, includes the following sub-steps:

[0012] The dynamic equations of S11 and TDOA are expressed as follows:

[0013] ;

[0014] Wherein, the coordinates of the anchor node are , The estimated coordinates of the unknown node at time t are: ; Indicates the first The first anchor node is in relation to the first anchor node. Differences in axial coordinates; Indicates the unknown node to the first The distance between each anchor node, and This represents the distance difference between the unknown node and the i-th and 1-th anchor nodes; This is an intermediate variable used to simplify the formula for squared distance, where m is the total number of nodes;

[0015] The dynamic equations of S12 and AOA are expressed as follows:

[0016] ; in, It is the tangent of the angle of arrival of the signal between the unknown node and the i-th anchor node. For the coordinates of the anchor node, , The estimated coordinates of the unknown node at time t.

[0017] Furthermore, step S2 involves performing an equivalent linear transformation on the TDOA and AOA positioning equations, and defining an error function based on this linear matrix equation, including the following sub-steps:

[0018] S21. Transform the TDOA algorithm to convert the dynamic matrix equation into a linear equation: , Let be the coefficient vector, state vector, and constant vector of the corresponding linear equation, respectively. The error function formed by these vectors is: in This represents the error function of the corresponding linear equation;

[0019] S22. Transform the AOA algorithm, changing the dynamic matrix equation into a linear equation: , Let be the coefficient vector, state vector, and constant vector of the corresponding linear equation, respectively. The error function formed by these vectors is: ,in This represents the error function of the corresponding linear equation.

[0020] Furthermore, the expression for the nonlinear logarithmic mapping activation function in step S3 is:

[0021] ;

[0022] In the formula, Let be the error function. Activation function

[0023] The expression for the polynomial noise immunity term is:

[0024] ;

[0025] The specific expression for its parameter is:

[0026] ;

[0027] in, For noise reduction, express The first derivative, express The first derivative, Indicates time substitution, express The points, and These are the state variables used for dynamic noise estimation and compensation. These are the coefficients of the polynomial noise resistance term, used to construct the characteristic equation of a stable system. These are pole placement parameters, which control the convergence speed of the control system. This indicates the order of the polynomial noise-resistance term. Corresponding to the highest order of noise, ;

[0028] The constructed RZNN model is as follows:

[0029] ;

[0030] in, express The first derivative, It is a scale parameter that controls the convergence speed.

[0031] Furthermore, step S4 sets the initial position of the unknown node and the target trajectory equation, and solves the linear dynamic equation established by the TDOA and AOA algorithms in real time using the RZNN model, including the following sub-steps:

[0032] S41. In TDOA, the theoretical trajectory equation for the unknown node is set as follows:

[0033] ;

[0034] in, Corresponding to the coordinate system axis, axis, Theoretical coordinates of the axis This indicates that the trajectory is a three-dimensional real matrix. Based on the RZNN model expression, the error function is specified as follows:

[0035] ;

[0036] in, express The generalized inverse matrix, yes The first derivative, yes The first derivative, yes The first derivative, It is a real number;

[0037] S42. In AOA, the theoretical trajectory equation for the unknown node is defined as follows:

[0038] ;

[0039] in, This indicates that the trajectory is a two-dimensional real matrix. Based on the RZNN model expression, the error function is specified as follows:

[0040] ;

[0041] in, express The generalized inverse matrix, yes The first derivative, yes The first derivative, yes The first derivative.

[0042] The beneficial effects of this invention are as follows: The proposed RZNN-based moving target localization method for TDOA and AOA is based on a multinomial noise compensation term and a logarithmic activation function. This method, based on the traditional ZNN model, incorporates a multinomial noise compensation term and a logarithmic activation function to construct an RZNN model capable of withstanding high-order noise. The RZNN model is used to solve the linear dynamic equations of the localization problem to obtain the moving target's position. The multinomial noise compensation term actively suppresses interference from high-order time-varying noise, ensuring the model maintains superior robustness under complex noise conditions. Simultaneously, the logarithmic activation function enhances the stability of state evolution, accelerates residual convergence, and improves localization accuracy. In high-order noise environments based on TDOA and AOA algorithms, this RZNN model not only achieves global convergence but also exhibits significant advantages in convergence speed, localization accuracy, and noise robustness, demonstrating high accuracy, low latency, and strong stability. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the TDOA and AOA moving target localization methods based on the RZNN model.

[0044] Figure 2 To solve the trajectory overlap map of the localization problem using the RZNN model based on the TDOA algorithm;

[0045] Figure 3 To calculate the residual error convergence map of each direction for solving the localization problem using the RZNN model based on the TDOA algorithm;

[0046] Figure 4 To solve the trajectory overlap map of the localization problem using the RZNN model based on the AOA algorithm;

[0047] Figure 5 To calculate the residual error convergence map of each direction for solving the localization problem using the RZNN model based on the AOA algorithm;

[0048] Figure 6 This is a comparison chart of the residual error convergence accuracy of the RZNN model under different orders of noise, based on the TDOA algorithm.

[0049] Figure 7 This is a comparison chart of the residual error convergence accuracy of the RZNN model based on the AOA algorithm under different orders of noise. Detailed Implementation

[0050] The specific embodiments of the present invention will be described below to enable those skilled in the art to understand the core content of the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. Based on the ideas of the present invention, there will be changes in the specific embodiments and application scope. For those skilled in the art, as long as the various changes are within the scope of the present invention defined and determined by the appended claims, these changes are obvious. In summary, all inventions utilizing the concept of the present invention are protected.

[0051] like Figure 1 As shown, the TDOA and AOA moving target localization method based on the RZNN model includes the following steps:

[0052] S1. Based on geometric relationships, establish the dynamic equation sets corresponding to the TDOA algorithm and the AOA algorithm;

[0053] S11, In the TDOA algorithm, the state vector of the unknown node and the position matrix of the m anchor nodes are defined as follows:

[0054] ;

[0055] in, It is the three-dimensional state vector of the unknown node. , , The unknown nodes in the three-dimensional coordinate system are respectively axis, axis, Axis coordinate estimation. This is the anchor node position matrix. It is the first Anchor nodes Axis coordinates yes Anchor nodes Axis coordinates yes Anchor nodes Axis coordinates.

[0056] Indicates the unknown node to the first The square of the distance between each anchor node:

[0057] ;

[0058] in, It is the anchor cable. It is an intermediate variable used to simplify the formula for squared distance, and it is defined as follows: Similarly, we can conclude that... From the expansion of the difference of squares, we can derive:

[0059] ;

[0060] Combining the two equations, we can obtain the dynamic equation:

[0061] ;

[0062] Rearranged into matrix equations:

[0063] ;

[0064] S12, In the AOA algorithm, the state vector of the unknown node and the position matrix of the m anchor nodes are defined as follows:

[0065] ;

[0066] in, It is a two-dimensional state vector of the location node. , The unknown nodes are in a two-dimensional coordinate system. axis, Axis coordinate estimation. This is the anchor node position matrix. It is the first Anchor nodes Axis coordinates yes Anchor nodes Axis coordinates.

[0067] No. The azimuth angle of the signal received by each anchor node , defined as the direction of signal propagation relative to the anchor node reference direction (e.g. The angle is clockwise (in the positive direction of the axis). This angle is determined by the difference in horizontal coordinates between the unknown node and the anchor node.

[0068] Unknown node and the first Anchor nodes Axis coordinate difference: ;

[0069] Unknown node and the first Anchor nodes Axis coordinate difference: ;

[0070] Therefore, the tangent of the azimuth angle satisfies:

[0071] ;

[0072] in, It is the anchor cable.

[0073] Transforming the tangent of the azimuth angle into a linear equation yields:

[0074] ;

[0075] The linear equations are integrated into matrix equations, as defined below:

[0076] ;

[0077] S2. Perform an equivalent linear transformation on the TDOA and AOA positioning equations, and define an error function based on the linear equations of the matrix;

[0078] S21, Transform the TDOA algorithm, Represented as ,Will Represented as ,Will Represented as Therefore, the resulting linear equation is:

[0079] ;

[0080] The resulting error function is: in Let represent the error function of the aforementioned linear equation.

[0081] S22, transform the AOA algorithm, and Represented as , Represented as , Represented as Therefore, the resulting linear equation is:

[0082] ;

[0083] The resulting error function is: ,in Let represent the error function of the aforementioned linear equation.

[0084] S3. Based on the ZNN model, a multinomial noise compensation term and a nonlinear logarithmic mapping activation function are introduced to construct the RZNN model. The expression for the new nonlinear logarithmic mapping activation function is as follows:

[0085] ;

[0086] The expression for the polynomial noise immunity term is:

[0087] ;

[0088] The specific expression for its parameter is:

[0089] ;

[0090] in, express The first derivative, express The first derivative, Indicates time substitution, Indicates to definite integral, and These are the state variables used for dynamic noise estimation and compensation. These are the coefficients of the polynomial noise resistance term, used to construct the characteristic equation of a stable system. These are pole placement parameters, which control the convergence speed of the control system. This indicates the order of the polynomial noise-resistance term. Corresponding to the highest order of noise, .

[0091] The constructed RZNN model is as follows:

[0092] ;

[0093] in, express The first derivative, It is a scale parameter that controls the convergence speed.

[0094] S4. Set the initial position and theoretical trajectory equation of the predicted sound source, solve the linear dynamic equation established by the TDOA and AOA algorithms in real time through the RZNN model, obtain the calculated trajectory of the sound source position, and compare it with the target trajectory.

[0095] S41, in TDOA, the theoretical trajectory equation for the unknown node is set as follows:

[0096] ;

[0097] And set the initial position of the unknown node as Based on the RZNN model expression, the error function is specified as follows:

[0098] ;

[0099] in, express The generalized inverse matrix, yes The first derivative, yes The first derivative, yes The first derivative.

[0100] S42, in AOA, the theoretical trajectory equation for the unknown node is defined as follows:

[0101] ;

[0102] And set the initial position of the unknown node as Based on the RZNN model expression, the error function is specified as follows:

[0103] ;

[0104] in, express The generalized inverse matrix, yes The first derivative, yes The first derivative, yes The first derivative.

[0105] Then, we initialize the parameters for the final solution based on the two localization algorithms: The ODE solver is used to solve the equations of the RZNN model based on TDOA and AOA algorithms. During the solution process, the polynomial compensation term, based on the Taylor expansion principle, achieves noise cancellation by actively learning noise features. This mechanism significantly reduces the model's dependence on noise information, and the RZNN model can maintain excellent convergence even when noise increases significantly over time. Simultaneously, the nonlinear logarithmic mapping activation function can selectively adjust the error direction, avoiding model divergence caused by drastic error fluctuations under sudden noise or large disturbances, and can adaptively adjust the convergence speed according to different error magnitudes, achieving precise zeroing of residual errors.

[0106] Through the above detailed solution process, the predicted trajectory information of the sound source is finally obtained, and a comparison and overlap diagram of the estimated trajectory and theoretical trajectory of the sound source motion is generated, as well as a diagram of the convergence of residuals in each direction.

[0107] Figure 2 This image shows the trajectory overlap generated by the RZNN model based on the TDOA algorithm for solving the localization problem. The blue circles represent the anchor node positions, the solid black line represents the theoretical trajectory of the moving target, and the dashed red line represents the estimated trajectory obtained by the RZNN model. We can see that the estimated trajectory highly overlaps with the theoretical trajectory, indicating that the RZNN model based on the TDOA algorithm has high 3D localization accuracy.

[0108] Figure 3This displays the residual error convergence graph for solving the localization problem using the RZNN model based on the TDOA algorithm, in each direction. The blue solid line represents... The residual error convergence logarithmic curve of the axis, the pink solid line is The logarithmic curve of the residual error convergence of the axis, the solid yellow line is The logarithmic convergence curve of the residual error on the axis. As can be seen from the figure, the RZNN model based on the TDOA algorithm solves in... , , The system exhibits efficient convergence capabilities in all directions, and the positioning errors in all three dimensions converge and remain stable. This demonstrates the accuracy of RZNN in 3D dynamic localization tasks.

[0109] Figure 4 This image shows the trajectory overlap generated by the RZNN model based on the AOA algorithm for solving the localization problem. In the image, blue circles represent anchor node positions, the solid black line represents the theoretical trajectory of the moving target, and the dashed red line represents the estimated trajectory obtained by the RZNN model. As can be seen from the image, in a two-dimensional scene, the theoretical trajectory of the moving target and the estimated trajectory obtained by the RZNN model show a high degree of overlap. This indicates that the RZNN model based on the AOA algorithm can efficiently and accurately approximate the theoretical solution in two-dimensional space.

[0110] Figure 5 This displays the residual error convergence graph for solving the localization problem using the RZNN model based on the AOA algorithm, showing the convergence of errors in each direction. The blue solid line represents... The residual error convergence logarithmic curve of the axis, the pink solid line is The logarithmic convergence curve of the residual error along the axis. From the graph, we can see that within 3 seconds, the residual convergence accuracy in all directions reaches a stable level, and the convergence accuracy remains at a certain level. The accuracy is around the meter level. This confirms the accuracy of RZNN in two-dimensional dynamic localization tasks.

[0111] S5. Simulate the effects of noise of different orders, solve the problem using the RZNN model under the same positioning conditions, and make a comparison of the positioning residuals under the TDOA and AOA algorithms.

[0112] Define the polynomial noise as:

[0113] ;

[0114] The RZNN model expression based on the TDOA algorithm under noise interference is as follows:

[0115] ;

[0116] The RZNN model expression based on the AOA algorithm under noise interference is as follows:

[0117] ;

[0118] Figure 6 The graph shows the results of applying noise interference to the sound source localization of the RZNN model based on the TDOA algorithm, and compares the residual errors for different noise orders. The noise order ranges from 0 to 3, represented by the blue, pink, yellow, and gray curves in the graph, respectively. It is clearly observed from the graph that regardless of the noise order, the convergence accuracy of the RZNN model can reach [percentage missing]. The residual error decreases rapidly and tends to stabilize, fully demonstrating its efficient convergence capability. In summary, the RZNN model consistently exhibits superior noise handling capabilities and stable error control performance in noise scenarios of different orders based on the TDOA algorithm. This result effectively verifies its applicability and reliability in complex noise environments.

[0119] Figure 7 The results show the effects of applying noise interference to the sound source localization of the RZNN model based on the AOA algorithm, and a comparison of the residual errors for different noise orders. The experimental results correspond to a gradual increase in noise order from 0 to 3. As can be observed from the figure, the error decreases rapidly and stabilizes at a low level for all set noise orders. Further analysis shows that even in higher-order noise environments, the model based on the AOA algorithm maintains stability and superiority in error convergence. This experimental result further demonstrates that the RZNN model consistently possesses excellent localization capabilities when faced with noise interference of different orders.

[0120] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for TDOA and AOA moving target localization based on the RZNN model, characterized in that, The method includes the following steps: S1. Based on geometric relationships, establish the dynamic equation sets corresponding to the TDOA algorithm and the AOA algorithm; S2. Perform an equivalent linear transformation on the TDOA and AOA positioning equations, and define an error function based on the linear equations of the matrix; S3. Based on the ZNN model, a multinomial noise compensation term and a nonlinear logarithmic mapping activation function are introduced to construct the RZNN model; S4. Set the initial position and theoretical trajectory equation of the unknown node, solve the linear dynamic equation established by the TDOA and AOA algorithms in real time through the RZNN model, obtain the estimated trajectory of the sound source position, and compare it with the theoretical trajectory. S5. Simulate the effects of noise of different orders, solve the problem using the RZNN model under the same positioning conditions, and draw a comparison chart of positioning residual errors under the TDOA and AOA algorithms.

2. The method for TDOA and AOA moving target localization based on the RZNN model according to claim 1, characterized in that, Step S1, establishing the dynamic equation sets for the TDOA and AOA algorithms, includes the following sub-steps: The dynamic equations of S11 and TDOA are expressed as follows: ； Wherein, the coordinates of the anchor node are , The estimated coordinates of the unknown node at time t are: ; Indicates the first The first anchor node is in relation to the first anchor node. Differences in axial coordinates; Indicates the unknown node to the first The distance between each anchor node, and This represents the distance difference between the unknown node and the i-th and 1-th anchor nodes; This is an intermediate variable used to simplify the formula for squared distance, where m is the total number of nodes; The dynamic equations of S12 and AOA are expressed as follows: ； in, It is the tangent of the angle of arrival of the signal between the unknown node and the i-th anchor node. For the coordinates of the anchor node, , The estimated coordinates of the unknown node at time t.

3. The TDOA and AOA moving target localization method based on the RZNN model according to claim 2, characterized in that, Step S2 involves performing an equivalent linear transformation on the TDOA and AOA positioning equations, and defining an error function based on this linear equation, including the following sub-steps: S21. Transform the TDOA algorithm to convert the dynamic matrix equation into a linear equation: , Let be the coefficient vector, state vector, and constant vector of the corresponding linear equation, respectively. The error function formed by these vectors is: in This represents the error function of the corresponding linear equation; S22. Transform the AOA algorithm, changing the dynamic matrix equation into a linear equation: , Let be the coefficient vector, state vector, and constant vector of the corresponding linear equation, respectively. The error function formed by these vectors is: ,in This represents the error function of the corresponding linear equation.

4. The TDOA and AOA moving target localization method based on the RZNN model according to claim 3, characterized in that, The expression for the nonlinear logarithmic mapping activation function in step S3 is: ； In the formula, Let be the error function. For activation functions; The expression for the polynomial noise immunity term is: ; The specific expression for its parameter is: ； in, For noise reduction, express The first derivative, express The first derivative, Indicates time substitution, express The points, and These are the state variables used for dynamic noise estimation and compensation. These are the coefficients of the polynomial noise resistance term, used to construct the characteristic equation of a stable system. These are pole placement parameters, which control the convergence speed of the control system. This indicates the order of the polynomial noise-resistance term. Corresponding to the highest order of noise, ; The constructed RZNN model is as follows: ; in, express The first derivative, It is a scale parameter that controls the convergence speed.

5. The TDOA and AOA moving target localization method based on the RZNN model according to claim 4, characterized in that, Step S4 sets the initial position of the unknown node and the target trajectory equation, and solves the linear dynamic equation established by the TDOA and AOA algorithms in real time using the RZNN model, including the following sub-steps: S41. In TDOA, the theoretical trajectory equation for the unknown node is set as follows: ； in, Corresponding to the coordinate system axis, axis, Theoretical coordinates of the axis This indicates that the trajectory is a three-dimensional real matrix. Based on the RZNN model expression, the error function is specified as follows: ； in, express The generalized inverse matrix, yes The first derivative, yes The first derivative, yes The first derivative, It is a real number; S42. In AOA, the theoretical trajectory equation for the unknown node is defined as follows: ； in, This indicates that the trajectory is a two-dimensional real matrix. Based on the RZNN model expression, the error function is specified as follows: ； in, express The generalized inverse matrix, yes The first derivative, yes The first derivative, yes The first derivative.

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