Method for solving dynamic signal source tracking through anti-noise gradient neural network

Abstract

The invention discloses a method for solving dynamic signal source tracking through an anti-noise gradient neural network, belongs to the field of matrix equations and intelligent calculation, and aims at solving the dynamic signal source tracking problem by modeling the dynamic signal source tracking problem and converting the actual problem into a linear equation solving problem. The new gradient neural network model is combined with an arrival angle algorithm for solving, a speed compensation mechanism is added on the basis of a gradient algorithm so as to enhance the real-time performance of the model, then an anti-noise integral compensation item is added from the angle of control science, and the robustness of the model is improved. Compared with a traditional gradient neural network model, a model which cannot solve a dynamic problem is improved into a model which can efficiently solve the dynamic problem, the generalization of the model is greatly improved, the convergence speed and the convergence precision are higher, the difficulty of inversion in an actual industrial environment is considered, and the method is suitable for large-scale popularization and application. The time-consuming and redundant process is replaced by a mass matrix mode.

Description

Technical Field

[0001] The invention relates to the fields of matrix equations and intelligent computing, and in particular to a method for solving dynamic signal source tracking using 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 micro-electric systems. With the introduction of the concept of the Internet of Things, 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, its core supporting node positioning technology has also been continuously improved and promoted. Therefore, the demand for research on the problem of dynamic signal source tracking is also increasing, and it is also 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 actual environments. For example, changes in temperature and wind speed can have a significant impact. Therefore, it is very important to reduce the impact of noise on system performance and accuracy. In order to cope with the challenges brought by periodicity, various methods and techniques have been proposed in industrial engineering to reduce the adverse effects of noise, such as using filters for noise reduction. However, in the problem of dynamic signal source tracking, which is particularly real-time, the use of traditional filters is no longer applicable. In order to meet this challenge, we use gradient neural networks to solve the calculation, add speed compensation terms to enhance the real-time performance of the model, and introduce integral terms to reduce the interference caused by noise. In addition, we also use the mass matrix approach to replace the redundant and time-consuming process of matrix inversion. Summary of the invention

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

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A method for solving dynamic signal source tracking using a noise-resistant gradient neural network comprises the following steps:

[0006] 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;

[0007] 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;

[0008] 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;

[0009] 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.

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

[0011] ; in, For dynamic signal source The input angle of each sensor; For the The position coordinates of the sensors, is the position of the dynamic signal source, Transpose the matrix and then establish the relevant dynamic linear matrix equation as: ; In the formula, for The output matrix at time , and: ; for The signal propagation matrix at time , and: ; for The state matrix at the moment, and: .

[0012] Furthermore, the S3 specifically includes the following steps:

[0013] S31. Based on the traditional gradient neural network, the error function is constructed for the dynamic linear matrix equation;

[0014] S32, minimizing the negative gradient direction of the constructed error function to obtain a gradient descent gradient neural network;

[0015] S33, bringing in the constructed dynamic linear matrix equation and expanding it to obtain the state information of the preliminary optimized dynamic signal source.

[0016] Furthermore, the error function in S31 is expressed as:

[0017] ;

[0018] In the formula, for The error function at time, is the second norm calculation, for The output matrix at time instant, for The signal propagation matrix at time, for The state matrix at the moment.

[0019] Furthermore, the state information of the dynamic signal source preliminarily optimized in S33 is expressed as:

[0020] ;

[0021] In the formula, The state information of the dynamic signal source for preliminary optimization, for The output matrix at time instant, for The signal propagation matrix at time, for The state matrix at time, is the matrix transpose, is a coefficient used to control the convergence of the gradient neural network.

[0022] Furthermore, the speed compensation mechanism in S4 is expressed as:

[0023]

[0024] yes The derivative matrix of The derivative matrix of is a coefficient used to control the convergence of the gradient neural network.

[0025] Furthermore, the anti-noise mechanism in S4 is expressed as:

[0026]

[0027] In the formula, For noise, is the activation function, To replace time t as the integration variable, yes The derivative matrix of The derivative matrix of is a coefficient used to control the convergence of the gradient neural network.

[0028] The present invention has the following beneficial effects:

[0029] 1. The NRGNN model makes good use of the derivative information of the relevant equations, has a certain ability to predict information, and solves the problem of lag error well.

[0030] 2. The integral term designed by the NRGNN model can effectively reduce the interference caused by noise.

[0031] 3. The NRGNN model design requires explicit inversion, but this application uses this feature to allow the mass matrix to replace the tedious and time-consuming process of inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 The present invention is a flow chart of a method for solving dynamic signal source tracking using a noise-resistant gradient neural network.

[0033] Figure 2 Schematic diagram of the principle of the related set of dynamic signal source tracking problems according to an embodiment of the present invention.

[0034] Figure 3 The embodiment of the present invention is in the noise Schematic diagram of the trajectory of the time-dynamic signal source and the trajectory calculated by the model.

[0035] Figure 4 This is a schematic diagram of the residual value generated by the model of the embodiment of the present invention tending to 0.

[0036] Figure 5 Schematic diagram of the error of dynamic signal source tracking on the X and Y axes according to an embodiment of the present invention.

[0037] Figure 6 The noise of the embodiment of the present invention Schematic diagram of the trajectory of the time-dynamic signal source and the trajectory calculated by the model.

[0038] Figure 7 This is a schematic diagram of the residual value generated by the model of the embodiment of the present invention tending to 0.

[0039] Figure 8 Schematic diagram of the error of dynamic signal source tracking on the X and Y axes according to an embodiment of the present invention.

[0040] Fig. 9 This is a schematic diagram of the convergence of the NRGNN model when iterating from four random initial states to solve the linear matrix equation in the absence of noise interference in an embodiment of the present invention.

[0041] Fig.10 The convergence of the values ​​calculated for the two sub-elements of the present invention is implemented.

[0042] Fig.11 In the absence of noise interference, the NRGNN model uses three different activation functions to solve the linear matrix equation, and the four random initial state iterations converge.

[0043] Fig.12This is the convergence of the calculated values ​​of the two sub-elements in the embodiment of the present invention.

[0044] Fig.13 The embodiment of the present invention is in constant noise Under interference, the NRGNN model solves the above linear matrix equations in four different The convergence of the model under the value of .

[0045] Fig.14 The embodiment of the present invention is in constant noise Under interference, the NRGNN model solves the above linear matrix equations in four different The convergence of the model under the value of .

[0046] Fig.15 The linear noise in the embodiment of the present invention Under interference, the NRGNN model solves the above linear matrix equations in four different The convergence of the model under the value of .

[0047] Fig.16 The embodiment of the present invention is in constant noise Under interference, the NRGNN model solves the above linear matrix equations in four different The convergence of the model under the value of . DETAILED DESCRIPTION

[0048] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0049] A noise-resistant gradient neural network method for dynamic signal source tracking, such as Figure 1 As shown, the following steps are included:

[0050] 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;

[0051] In this embodiment, the NRGNN model for solving the dynamic signal source tracking problem can be expressed as:

[0052]

[0053] in, Indicates noise.

[0054] The relevant geometric principle diagram is as follows Figure 2 As shown, 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 and , the geometric relationship is , where i is sensor 1, 2, ….

[0055] 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;

[0056] Through the above geometric relationship, the following deduction can be made:

[0057] ;

[0058] Finally we can use a linear matrix equation To represent. Among them:

[0059] ;

[0060] In the formula, for The output matrix at time , and:

[0061] ;

[0062] for The signal propagation matrix at time , and:

[0063] ;

[0064] for The state matrix at the moment, and:

[0065] ;

[0066] 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;

[0067] In this embodiment, the following steps are specifically included:

[0068] The specific steps include:

[0069] S31. Based on the traditional gradient neural network, the error function is constructed for the dynamic linear matrix equation, which is expressed as:

[0070] ;

[0071] In the formula, for The error function at time, is the second norm calculation, for The output matrix at time instant, for The signal propagation matrix at time, for The state matrix at the moment.

[0072] S32, minimizing the gradient descent of the gradient neural network along the negative gradient direction of the constructed error function, expressed as:

[0073]

[0074] S33, bring in the constructed dynamic linear matrix equation and expand it to obtain the state information of the preliminary optimized dynamic signal source, expressed as:

[0075] ;

[0076] In the formula, The state information of the dynamic signal source for preliminary optimization, for The output matrix at time instant, for The signal propagation matrix at time, for The state matrix at time, is the matrix transpose, is a coefficient used to control the convergence of the gradient neural network.

[0077] 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.

[0078] In this embodiment, the original gradient neural network is added to the speed compensation mechanism:

[0079] ;

[0080] yes The derivative matrix of The derivative matrix of Represents The transpose of .

[0081] Then, from the perspective of control science, an integral term is added to enhance the model's noise resistance:

[0082] ;

[0083] In the formula, For noise, is the activation function. is used to replace time t as the integration variable.

[0084] In this embodiment, three activation functions are given for comparison:

[0085] ;

[0086] ,in ;

[0087] ;

[0088] The parameters of the model are initialized, and the optimized dynamic signal source state information is output for signal source positioning in actual application scenarios.

[0089] ①First, the trajectory of the dynamic signal source is passed in, and the model parameters are given ,Then, the proposed NRGNN model is used for calculation.

[0090] Figure 3 , 4 and 5 are both in the noise Simulation results of dynamic signal source tracking experiment. Figure 3 It represents the trajectory of the dynamic signal source and the trajectory calculated by the model. Figure 4 It means that the residual value generated by the model tends to 0. Figure 5 It shows the error of dynamic signal source tracking on X and Y axis, both of which reach 10 -3 It can be seen that the NRGNN model can still maintain excellent robustness when solving dynamic signal source tracking problems under linear noise interference.

[0091] ②First, the trajectory of the dynamic signal source is passed in, and the model parameters are given ,Then, the proposed NRGNN model is used for calculation.

[0092] Figure 6 ,7 and 8 are both in the noise Simulation results of dynamic signal source tracking experiment. Figure 6 It represents the trajectory of the dynamic signal source and the trajectory calculated by the model. Figure 7 It means that the residual value generated by the model tends to 0. Figure 8 It shows the error of dynamic signal source tracking on X and Y axis, both of which reach 10 -3It can be seen that the NRGNN model can still maintain excellent robustness when solving dynamic signal source tracking problems under constant noise interference.

[0093] First, we introduce the specific problem of linear matrix equation. The specific matrix is ​​represented as:

[0094] , .

[0095] The model parameters are given as .

[0096] Fig. 9 It is shown that in the absence of noise interference, the NRGNN model converges to 0 when solving the above linear matrix equations and starting iterations at four random initial states. Fig.10 It shows the convergence of the calculated values ​​of the two sub-elements, both of which can converge to the theoretical value (red) very quickly. Fig.11 It shows that in the absence of noise interference, the NRGNN model converges to 0 when using three different activation functions to solve the above linear matrix equations starting from four random initial states. Fig.12 It shows the convergence of the calculated values ​​of the two sub-elements, both of which can converge to the theoretical value (red) very quickly.

[0097] Fig.13 Shows that at constant noise Under interference, the NRGNN model solves the above linear matrix equations in four different The convergence of the model under the value of . Fig.14 , in constant noise Under interference, the NRGNN model solves the above linear matrix equations in four different The convergence of the model under the value of . Fig.15 Display, linear noise Under interference, the NRGNN model solves the above linear matrix equations in four different The convergence of the model under the value of . Fig.16 , in constant noise Under interference, the NRGNN model solves the above linear matrix equations in four different The results show that The larger the value, the stronger the noise resistance of the model. The above simulation results can show that the proposed NRGNN model has strong robustness and convergence performance in solving time-varying linear matrix equations.

[0098] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0099] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations 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; 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.

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: ； in, For dynamic signal source The input angle of each sensor; For the The position coordinates of the sensors, is the position of the dynamic signal source, Transpose the matrix and then establish the relevant dynamic linear matrix equation as: ； In the formula, for The output matrix at time , and: ； for The signal propagation matrix at time , and: ; for The state matrix at the moment, and: 。 3. The method for solving dynamic signal source tracking using a noise-resistant gradient neural network according to claim 1, characterized in that: The S3 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, bringing in the constructed dynamic linear matrix equation and expanding it to obtain the state information of the preliminary optimized dynamic signal source.

4. The method for solving dynamic signal source tracking using a noise-resistant gradient neural network according to claim 3, characterized in that: The error function in S31 is expressed as: ; In the formula, for The error function at time, is the second norm calculation, for The output matrix at time instant, for The signal propagation matrix at time, for The state matrix at the moment.

5. The method for solving dynamic signal source tracking using a noise-resistant gradient neural network according to claim 3, characterized in that: The state information of the dynamic signal source preliminarily optimized in S33 is expressed as: ; In the formula, The state information of the dynamic signal source for preliminary optimization, for The output matrix at time instant, for The signal propagation matrix at time, for The state matrix at time, is the matrix transpose, is a coefficient used to control the convergence of the gradient neural network.

6. The method for solving dynamic signal source tracking using a noise-resistant gradient neural network according to claim 1, characterized in that: The speed compensation mechanism in S4 is expressed as: ； yes The derivative matrix of The derivative matrix of is a coefficient used to control the convergence of the gradient neural network.

7. The method for solving dynamic signal source tracking using a noise-resistant gradient neural network according to claim 1, characterized in that: The anti-noise mechanism in S4 is expressed as: ； In the formula, For noise, is the activation function, To replace time t as the integration variable, yes The derivative matrix of The derivative matrix of is a coefficient used to control the convergence of the gradient neural network.

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