A Method for Solving Dynamic Signal Source Tracking by an Anti-Noise Gradient Neural Network

Abstract

The present invention discloses a method for solving dynamic signal source tracking by an anti-noise gradient neural network, belonging to the fields of matrix equations and intelligent computing. By modeling the dynamic signal source tracking problem, the actual problem is transformed into a problem of solving linear equations. The proposed new model of the gradient neural network is combined with the angle-of-arrival algorithm for solution. A velocity compensation mechanism is added on the basis of the gradient algorithm to enhance the real-time performance of the model. Then, an integral compensation term that can resist noise is added from the perspective of control theory to improve the robustness of the model. Compared with the traditional gradient neural network model, the present invention improves the model that cannot solve dynamic problems into a model that can efficiently solve dynamic problems, greatly improving the generalization of the model, and having a faster convergence speed and convergence accuracy. Considering the difficulty of inversion in the actual industrial environment, the time-consuming and redundant process is replaced by the method of using the mass matrix.

Description

Technical Field

[0001] The present invention relates to the fields of matrix equations and intelligent computing, and particularly to a method for solving dynamic signal source tracking by an anti-noise gradient neural network. Background Art

[0002] In recent years, with the rapid development and increasing maturity of technologies such as wireless communication, integrated circuits, sensors, and microelectronics systems. With the proposal of the Internet of Things concept, sensor technology, as its key technology, has become the core of people's research. As the application of wireless sensor networks gradually penetrates into all aspects of people's lives, the node positioning technology that supports it at the core has also been continuously improved and popularized. Therefore, the demand for research on the problem of dynamic signal source tracking is also increasing day by day, and it is very necessary to provide some simpler and more robust algorithms. In the fields of science and engineering, many problems can be solved by solving dynamic linear matrix equations. Noise is very common in the actual environment. For example, changes in temperature and the speed of wind will have a significant impact. Therefore, it is very important to reduce the impact of noise on system performance and accuracy. To address the challenges brought by periodicity, various methods and techniques have been proposed in industrial engineering, aiming to reduce the adverse effects of noise, such as using filters for anti-noise. However, in the problem of dynamic signal source tracking with particularly strong real-time performance, the method of using traditional filters is no longer applicable. To address this challenge, we use a gradient neural network for solving calculations, and add a velocity compensation term to enhance the real-time performance of the model, and introduce an integral term to reduce the interference caused by noise. In addition, we also use the method of mass matrix to replace the redundant and time-consuming process of matrix inversion. Summary of the Invention

[0003] In view of the above deficiencies in the prior art, the present invention provides a method for solving dynamic signal source tracking by an anti-noise gradient neural network.

[0004] To achieve the above invention purpose, the technical solution adopted by the present invention is as follows:

[0005] A method for solving dynamic signal source tracking by an anti-noise gradient neural network, comprising the following steps:

[0006] S1. Set the dynamic signal source tracking problem, and based on the set dynamic signal tracking problem, collect signal source data according to the actual application scenario;

[0007] S2. Based on the signal source data collected in S1, establish a mathematical model, and transform the established mathematical model into a dynamic linear matrix equation;

[0008] S3. Construct a gradient neural network model, and estimate the state of the dynamic signal source by the gradient descent method to initially optimize the signal tracking accuracy;

[0009] S4. On the basis of the constructed gradient neural network model, introduce a speed compensation mechanism and an anti-noise mechanism to optimize the model, solve the set dynamic signal source tracking problem, and output the optimized dynamic signal source state information.

[0010] Further, the mathematical model of S2 is expressed as:

[0011] ;

[0012] where is the input angle of the dynamic signal source to the th sensor; is the position coordinate of the th sensor, is the position of the dynamic signal source, is the matrix transpose, and then establish the relevant dynamic linear matrix equation as:

[0013] ;

[0014] In the formula, is the output matrix at time, and:

[0015] ;

[0016] is the signal propagation matrix at time, and:

[0017] ;

[0018] is the state matrix at time, and:

[0019] .

[0020] Further, S3 specifically includes the following steps:

[0021] S31. Based on the traditional gradient neural network, construct an error function for the dynamic linear matrix equation;

[0022] S32. Minimize along the negative gradient direction of the constructed error function to obtain the gradient neural network of gradient descent;

[0023] S33. Substitute into the constructed dynamic linear matrix equation and expand to obtain the state information of the initially optimized dynamic signal source.

[0024] Further, the error function in S31 is expressed as:

[0025] ;

[0026] wherein, is the error function at time the calculation of the two-norm, is the output matrix at time is the signal propagation matrix at time is the state matrix at time

[0027] Furthermore, the state information of the dynamically optimized signal source in S33 is expressed as:

[0028] ;

[0029] wherein, is the state information of the dynamically optimized signal source, is the output matrix at time is the signal propagation matrix at time is the state matrix at time is the matrix transpose, is the coefficient used to control the convergence of the gradient neural network.

[0030] Furthermore, the velocity compensation mechanism in S4 is expressed as:

[0031]

[0032] is the derivative matrix of the derivative matrix of is the coefficient used to control the convergence of the gradient neural network.

[0033] Furthermore, the anti-noise mechanism in S4 is expressed as:

[0034]

[0035] wherein, is the noise, is the activation function, is used to replace time t as the integration variable, is the derivative matrix of the derivative matrix of is the coefficient used to control the convergence of the gradient neural network.

[0036] The present invention has the following beneficial effects:

[0037] 1. The NRGNN model makes good use of the derivative information of relevant equations, has a certain ability to predict information, and well solves the problem of lag error.

[0038] 2. The integral term designed by the NRGNN model well reduces the interference caused by noise.

[0039] 3. The NRGNN model design requires explicit inversion, but this application utilizes this feature to let the mass matrix replace the cumbersome and time-consuming process of inversion. Description of the Drawings

[0040] Figure 1 It is a schematic flow chart of the method for the anti-noise gradient neural network of the present invention to solve the dynamic signal source tracking.

[0041] Figure 2 It is a schematic diagram of the relevant set principle of the dynamic signal source tracking problem in the embodiment of the present invention.

[0042] Figure 3 It is for the embodiment of the present invention in noise Schematic diagram of the trajectory of the dynamic signal source and the trajectory calculated by the model.

[0043] Figure 4 Schematic diagram when the residual value generated by the model of the embodiment of the present invention tends to 0.

[0044] Figure 5 Schematic diagram of the error of the dynamic signal source tracking on the X and Y axes in the embodiment of the present invention.

[0045] Figure 6 It is for the embodiment of the present invention in noise Schematic diagram of the trajectory of the dynamic signal source and the trajectory calculated by the model.

[0046] Figure 7 Schematic diagram when the residual value generated by the model of the embodiment of the present invention tends to 0.

[0047] Figure 8 Schematic diagram of the error of the dynamic signal source tracking on the X and Y axes in the embodiment of the present invention.

[0048] Figure 9 It is a schematic diagram that the NRGNN model converges when iterating from four random initial states in solving the linear matrix equation in the embodiment of the present invention without noise interference.

[0049] Figure 10 It is the convergence situation of the calculated values of two sub-elements in the embodiment of the present invention.

[0050] Figure 11For the embodiment of the present invention, under the condition of no noise interference, the iterative convergence of the NRGNN model with four random initial states when solving linear matrix equations using three different activation functions is shown.

[0051] Figure 12 The convergence of the calculated values of two sub-elements in the embodiment of the present invention is shown.

[0052] Figure 13 For the embodiment of the present invention under constant noise interference, the convergence of the NRGNN model when solving the above linear matrix equation under four different values is shown.

[0053] Figure 14 For the embodiment of the present invention under constant noise interference, the convergence of the NRGNN model when solving the above linear matrix equation under four different values is shown.

[0054] Figure 15 For the embodiment of the present invention under linear noise interference, the convergence of the NRGNN model when solving the above linear matrix equation under four different values is shown.

[0055] Figure 16 For the embodiment of the present invention under constant noise interference, the convergence of the NRGNN model when solving the above linear matrix equation under four different values is shown. Detailed implementation manners

[0056] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0057] A method for an anti-noise gradient neural network to solve dynamic signal source tracking is as Figure 1 shown, including the following steps:

[0058] S1. Set the dynamic signal source tracking problem. Based on the set dynamic signal tracking problem, collect signal source data according to the actual application scenario;

[0059] In this embodiment, the NRGNN model used to solve the dynamic signal source tracking problem can be expressed as:

[0060]

[0061] Among them, represents noise.

[0062] The relevant geometric schematic diagram is as shown in Figure 2 . The positions of sensors S1 and S2 are represented as (x1, y1) and (x2, y2) respectively, and the position of the dynamic signal source is represented as T(x, y). For these two sensors, the input angles of the dynamic signal source to the sensors are respectively and , and the geometric relationship is , where i is sensors 1, 2,....

[0063] S2. Establish a mathematical model based on the signal source data collected by S1, and transform the established mathematical model into a dynamic linear matrix equation;

[0064] Based on the above geometric relationship, the following derivation can be carried out:

[0065] ;

[0066] Finally, we can use a linear matrix equation to represent. Where:

[0067] ;

[0068] In the formula, is the output matrix at time, and:

[0069] ;

[0070] is the signal propagation matrix at time, and:

[0071] ;

[0072] is the state matrix at time, and:

[0073] ;

[0074] S3. Construct a gradient neural network model, and estimate the state of the dynamic signal source by the gradient descent method to initially optimize the signal tracking accuracy;

[0075] In this embodiment, it specifically includes the following steps:

[0076] Specifically, it includes the following steps:

[0077] S31. Based on the traditional gradient neural network, construct an error function for the dynamic linear matrix equation, expressed as:

[0078] ;

[0079] In the formula, is the error function at time the calculation of the second norm, is the output matrix at time is the signal propagation matrix at time is the state matrix at time

[0080] S32. Minimize along the negative gradient direction of the constructed error function to obtain the gradient neural network of gradient descent, expressed as:

[0081]

[0082] S33. Substitute into the constructed dynamic linear matrix equation and expand to obtain the state information of the initially optimized dynamic signal source, expressed as:

[0083] ;

[0084] In the formula, is the state information of the initially optimized dynamic signal source, is the output matrix at time is the signal propagation matrix at time is the state matrix at time is the matrix transpose, is the coefficient used to control the convergence of the gradient neural network.

[0085] S4. On the basis of the constructed gradient neural network model, introduce a speed compensation mechanism and a noise resistance mechanism for model optimization, solve the set dynamic signal source tracking problem, and output the state information of the optimized dynamic signal source.

[0086] In this embodiment, add a speed compensation mechanism to the original gradient neural network:

[0087] ;

[0088] is the derivative matrix of the derivative matrix of represents the transpose of

[0089] Then, from the perspective of control theory, an integral term is added to enhance the noise resistance of the model:

[0090] ;

[0091] In the formula, is the noise, is the activation function. is used to replace time t as the integration variable.

[0092] In this embodiment, three activation functions are given for comparison:

[0093] ;

[0094] , where ;

[0095] ;

[0096] Initialize the parameters of the model, and output the optimized dynamic signal source state information for signal source localization in the actual application scenario.

[0097] ① First, input the trajectory of the dynamic signal source, and given the model parameters , then use the proposed NRGNN model for calculation.

[0098] Figure 3 , 4 and 5 are the simulation results of the dynamic signal source tracking experiment under the noise . Figure 3 represents the trajectory of the dynamic signal source and the trajectory calculated by the model. Figure 4 represents that the residual value generated by the model tends to 0. Figure 5 represents the errors of the dynamic signal source tracking on the X and Y axes, both reaching the level of 10 -3 m. It can be seen that the NRGNN model can still maintain excellent robustness when solving the dynamic signal source tracking problem under linear noise interference.

[0099] ② First, input the trajectory of the dynamic signal source, and given the model parameters , then use the proposed NRGNN model for calculation.

[0100] Figure 6 , 7 and 8 are the simulation results of the dynamic signal source tracking experiment under the noise . Figure 6 represents the trajectory of the dynamic signal source and the trajectory calculated by the model.Figure 7 It indicates that the residual values generated by the model tend to 0. Figure 8 It indicates that the errors of the dynamic signal source tracking on the X and Y axes have both reached the level of 10 -3 m. It can be seen that the NRGNN model can still maintain excellent robustness when solving the dynamic signal source tracking problem under constant noise interference.

[0101] First, input the specific problem of the linear matrix equation. The specific matrix is expressed as:

[0102] , .

[0103] The model parameters are given as .

[0104] Figure 9 It shows that, in the case of no noise interference, when the NRGNN model solves the above linear matrix equation, starting from four random initial states, the iterations all converge to 0. Figure 10 It shows the convergence of the calculated values of the two sub-elements, and they can all converge to the theoretical value (red) very quickly. Figure 11 It shows that, in the case of no noise interference, when the NRGNN model solves the above linear matrix equation using three different activation functions, starting from four random initial states, the iterations all converge to 0. Figure 12 It shows the convergence of the calculated values of the two sub-elements, and they can all converge to the theoretical value (red) very quickly.

[0105] Figure 13 It shows that, under the interference of constant noise , when the NRGNN model solves the above linear matrix equation, the convergence of the model under four different values. Figure 14 , under the interference of constant noise , when the NRGNN model solves the above linear matrix equation, the convergence of the model under four different values. Figure 15 It shows that, under the interference of linear noise , when the NRGNN model solves the above linear matrix equation, the convergence of the model under four different values. Figure 16 , under the interference of constant noise , when the NRGNN model solves the above linear matrix equation, the convergence of the model under four different values. The results show that The larger the value is, the stronger the anti-noise ability of the model is, and the above simulation results can all show that the proposed NRGNN model has very strong robustness and convergence performance in solving time-varying linear matrix equations.

[0106] In the present invention, specific embodiments are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0107] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principle of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A method for tracking dynamic signal sources using a noise-resistant gradient neural network, characterized in that: The steps include: S1. Setting a dynamic signal source tracking problem, based on the set dynamic signal tracking problem, collecting signal source data according to an actual application scenario; S2, establishing a mathematical model based on the signal source data collected by S1, and converting the established mathematical model into a dynamic linear matrix equation; S3, construct a gradient neural network model, and estimate the state of the dynamic signal source through the gradient descent method to preliminarily optimize the signal tracking accuracy, which specifically includes the following steps: S31. Based on the traditional gradient neural network, the error function is constructed for the dynamic linear matrix equation; S32, minimizing the negative gradient direction of the constructed error function to obtain a gradient descent gradient neural network; S33, bring in the constructed dynamic linear matrix equation and expand it to obtain the state information of the preliminary optimized dynamic signal source. The state information of the preliminary optimized dynamic signal source is expressed as: In the formula, is the state information of the dynamic signal source for preliminary optimization, Q(t) is the output matrix at time t, P(t) is the signal propagation matrix at time t, X(t) is the state matrix at time t, T is the matrix transpose, and α is the coefficient used to control the convergence of the gradient neural network; S4. Based on the constructed gradient neural network model, a speed compensation mechanism and an anti-noise mechanism are introduced to optimize the model, solve the set dynamic signal source tracking problem, and output the optimized dynamic signal source state information, wherein the speed compensation mechanism is expressed as: is the derivative matrix of Q(t), is the derivative matrix of P(t), α is the coefficient used to control the convergence of the gradient neural network; The anti-noise mechanism is expressed as: Where N(t) is the noise, Π(·) is the activation function, and l is the integral variable instead of time t. is the derivative matrix of Q(t), is the derivative matrix of P(t), and α is the coefficient used to control the convergence of the gradient neural network.

2. The method for solving dynamic signal source tracking using a noise-resistant gradient neural network according to claim 1, characterized in that: The mathematical model of S2 is expressed as: Among them, θ i is the input angle of the dynamic signal source to the i-th sensor; (x i ,y i ) is the position coordinate of the i-th sensor, (x, y) is the position of the dynamic signal source, T is the matrix transpose, and then the relevant dynamic linear matrix equation is established as follows: Q(t)=P(t)X(t); Where Q(t) is the output matrix at time t, and: P(t) is the signal propagation matrix at time t, and: X(t) is the state matrix at time t, and: X(t)=[x y] T 。 3. The method for solving dynamic signal source tracking using a noise-resistant gradient neural network according to claim 1, characterized in that: The error function in S31 is expressed as: Where Θ(t) is the error function at time t, is the two-norm calculation, Q(t) is the output matrix at time t, P(t) is the signal propagation matrix at time t, and X(t) is the state matrix at time t.

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