A sparse system identification method and system based on improved adaptive filter

Abstract

The present invention proposes a sparse system identification method and system based on an improved adaptive filter, which belongs to the field of adaptive system identification technology, including: obtaining the current moment input signal; updating the correlation estimation matrix and the cross-correlation estimation vector based on the conjugate gradient method; introducing the nonlinear gradient to update the search direction of the filter; introducing the regularization parameter to obtain the dynamic step size of the filter; updating the tap weight coefficient of the filter; letting the moment be updated to the next moment, updating the weight vector coefficient of the adaptive filter, and when the filter weight coefficient vector is equal to the impulse response of the unknown system, the unknown system identification ends. The present invention can more efficiently realize the identification of sparse unknown systems by modifying the nonlinear gradient update, the regularization parameter and the momentum enhancement update.

Description

Technical Field

[0001] The present invention belongs to the technical field of adaptive system identification, and in particular relates to a sparse system identification method and system based on an improved adaptive filter. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In many applications of adaptive filters, the underlying system impulse response (IRS) to be identified is often sparse or compressible, such as in acoustic echo and feedback cancellation. Therefore, designing adaptive filters that can exploit the sparse structure of the system's IR has always been a research topic of great interest. Not surprisingly, sparse signal recovery (SSR) techniques have been shown to be feasible in learning compact solutions to linear problems, which has promoted the trend of sparse-aware adaptive filtering research. The core principle of adaptive filter system identification technology is to build a speech model based on the input signal and its related characteristics, and continuously adjust the filter coefficients by analyzing the residual between the input signal and the unknown system, so that the estimated value gradually approaches the parameters of the unknown system. However, the high amplitude of impulse noise may be superimposed on the output of the unknown system, causing the coefficients of the adaptive filter to be updated in the direction of a larger error. To this end, how to develop and optimize adaptive filter algorithms with excellent noise immunity has become a challenge in the field of system identification. In the current application of sparse system identification, the following methods are mainly used in the existing technology:

[0004] (1) System identification method based on sparse least mean square (LMS) algorithm. In the paper “Sparse LMS for system identification,” (Y. Chen, Y. Gu, and AO Hero), Proc IEEE Int Conf. Acoust, Speech, Signal Process, (3125–3128), 2009), the complexity of the proposed LMS-type algorithm only scales linearly, but the convergence speed is slow when the signal correlation is strong.

[0005] (2) System identification method based on recursive least squares (RLS) algorithm. In the paper “SPARLS: The sparse RLS algorithm,” (B. Babadi, N. Kalouptsidis, and V. Tarokh), IEEE Trans. Signal Process, (4013–4025), 2010), the proposed RLS algorithm generally has a faster convergence speed than the LMS algorithm, but the computational complexity is greatly increased.

[0006] Therefore, a lot of work has been focused on developing sparse variants of the least mean square (LMS) and recursive least squares (RLS) adaptive filter algorithms based on sparse signal system identification. The complexity of LMS-type algorithms only scales linearly, but converges slowly when the signal correlation is strong. In contrast, RLS-type algorithms usually converge faster, but the computational complexity increases. Summary of the invention

[0007] To overcome the deficiencies of the above-mentioned prior art, the present invention proposes a sparse system identification method and system based on an improved adaptive filter, which uses an S-type function to activate the gradient and introduces a nonlinear response to the gradient update, thereby preventing the system from being overly sensitive to small fluctuations in the signal or noise; the dynamic adjustment of the regularization term can prevent the filter from overfitting in the early stages of learning or in a noisy environment, and the system can better adapt to sparse and dense information; the addition of a momentum term accelerates the convergence speed by allowing the filter to accumulate previous updates, thereby achieving faster and more stable convergence.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0009] In a first aspect, a sparse system identification method based on an improved adaptive filter is disclosed, comprising the following steps:

[0010] Obtaining the input signal at the current moment, and simultaneously inputting the input signal into the improved adaptive filter and the unknown system to be identified, to obtain the filter output signal and the expected signal;

[0011] Based on the conjugate gradient method, the correlation estimation matrix of the input signal and the cross-correlation estimation vector between the input signal and the expected signal are updated;

[0012] Based on the correlation estimation matrix and introducing nonlinear gradient, the search direction of the filter is updated;

[0013] Based on the search direction, a regularization parameter is introduced to obtain the dynamic step size of the filter;

[0014] The tap weight coefficients of the filter are updated based on the dynamic step size;

[0015] Let the time be updated to the next time, and update the weight vector coefficient of the adaptive filter. When the filter weight coefficient vector is equal to the impulse response of the unknown system, the unknown system identification is completed.

[0016] In a second aspect, a sparse system identification system based on an improved adaptive filter is disclosed, comprising:

[0017] A signal acquisition module is configured to: acquire the current input signal and simultaneously input it into the improved adaptive filter and the unknown system to be identified to obtain the filter output signal and the expected signal;

[0018] A signal estimation module, configured to: update a correlation estimation matrix of an input signal and a cross-correlation estimation vector between the input signal and a desired signal based on a conjugate gradient method;

[0019] The filter update module is configured as follows: based on the correlation estimation matrix and introducing nonlinear gradient, update the search direction of the filter; based on the search direction, introduce a regularization parameter to obtain the dynamic step size of the filter; based on the dynamic step size, update the tap weight coefficients of the filter; let the moment be updated to the next moment, update the weight vector coefficients of the adaptive filter, and when the filter weight coefficient vector is equal to the impulse response of the unknown system, the unknown system identification is completed.

[0020] In a third aspect, an electronic device is disclosed, including a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the steps of the above-mentioned sparse system identification method based on the improved adaptive filter are completed.

[0021] In a fourth aspect, a computer-readable storage medium is disclosed for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned sparse system identification method based on the improved adaptive filter are completed.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] The present invention provides a sparse system identification method for an improved adaptive filter, which utilizes a conjugate gradient method improved by nonlinear gradients. By modifying the nonlinear gradient update, regularization parameters, and momentum enhancement update, a more powerful, more adaptable, and more efficient sparse system identification method is obtained, which can handle complex real-world signal processing tasks, including non-Gaussian noise, better than the traditional conjugate gradient method.

[0024] The nonlinear gradient update proposed in the present invention uses the S-type function to activate the gradient, introducing a nonlinear response to the gradient update, making the gradient update very effective in environments with complex or non-Gaussian noise distributions, and helping to avoid being overly sensitive to small fluctuations in signals or noise during sparse system identification.

[0025] The dynamic adjustment of the regularization term proposed in the present invention can prevent the filter from overfitting in the early stages of learning or in noisy environments, and the system can better adapt to sparse and dense information.

[0026] The present invention adds a momentum term to accelerate the convergence speed by allowing the filter to accumulate previous updates, thereby achieving faster and more stable convergence.

[0027] The improved adaptive filter proposed in the present invention has smaller mean square deviation and mean square error compared to the traditional conjugate algorithm; reduces processing delay, supports higher frequency operations, improves efficiency, and expands the possibility of signal processing.

[0028] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0030] Figure 1 This is a flow chart of the sparse system identification method based on the improved adaptive filter described in the first embodiment of the present invention.

[0031] Figure 2 This is a comparison diagram of MSD curves between the sparse system identification method based on the improved adaptive filter described in Example 1 of the present invention and the traditional method.

[0032] Figure 3 This is a comparison chart of EMSE curves between the sparse system identification method based on the improved adaptive filter described in Example 1 of the present invention and the traditional method. DETAILED DESCRIPTION

[0033] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0034] It should be noted that the terms used herein are for describing specific embodiments only and are not intended to be limiting of exemplary embodiments according to the present invention.

[0035] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0036] Embodiment 1

[0037] In one or more embodiments, a sparse system identification method based on an improved adaptive filter is disclosed, comprising the following steps:

[0038] Step S1, obtaining the input signal at the current moment, and simultaneously inputting the input signal into the improved adaptive filter and the unknown system to be identified, to obtain the filter output signal and the expected signal.

[0039] When an adaptive filter performs system identification, the signal input to the filter is generally a known excitation signal, which is used to generate a response by the excitation system, so that the filter can gradually adjust its coefficients to approximate the characteristics of the unknown system. Specifically, the input signal usually has the following types: white noise signal, periodic signal, pulse signal, etc.

[0040] Step S101: The input signal is an input vector including M samples that is simultaneously input to the unknown system and the improved adaptive filter. The input signal passes through the unknown system and the improved adaptive filter to obtain two outputs: the filter output signal and the expected signal. The error signal is obtained through the two outputs. The filter weight coefficient vector is updated according to the error signal to continuously approximate the impulse response of the unknown system, thereby identifying the unknown system.

[0041] Step S102: Obtaining the impulse response of the unknown sparse system and the weight coefficient vector of the adaptive filter at time n .

[0042] Step S103: constructing the expected signal model as follows:

[0043] (1)

[0044] in, is the expected signal at time n, which is the output signal of the input signal passing through the unknown system; is the transpose of the input vector; For additional signal.

[0045] Step S2: updating the correlation estimation matrix of the input signal and the cross-correlation estimation vector between the input signal and the expected signal based on the conjugate gradient method.

[0046] Step S201: construct an objective function, and consider the objective function of minimizing the weighted square error at time n as:

[0047] (2)

[0048] in, is the objective function of the weighted square error at time n; n and are n moments and moment; h is the weight coefficient vector of the filter; γ is the forgetting factor, and ; for The square error of the moment; for The expected signal of the unknown system at time T is the transpose; for The input signal at time.

[0049] The accuracy and performance of the filter algorithm estimation are measured by minimizing the square of the error, quantifying the difference between the estimated value and the actual value, and providing a standard for evaluating the filter performance.

[0050] Step S202, minimizing the above formula (2) is equivalent to solving the linear equation:

[0051] (3)

[0052] (4)

[0053] (5)

[0054] in, is the input vector The correlation estimation matrix of is the input vector and expected signal The correlation estimate vector of .

[0055] The update formulas for the two can be obtained as follows:

[0056] (6)

[0057] (7)

[0058] Among them, R n is the correlation estimation matrix at the current time n; b n is the relevant estimation vector at the current time n; R n-1 is the correlation estimation matrix at time n-1; b n-1 is the correlation estimation vector at time n-1.

[0059] Step S3: based on the correlation estimation matrix and introducing nonlinear gradient, update the search direction of the filter.

[0060] Step S301: In order to adjust the filter weight more robustly in non-Gaussian and nonlinear environments, nonlinearity is introduced, and the S-type activation function is used to improve the gradient update to obtain a nonlinear gradient update, which is expressed as:

[0061] (8)

[0062] Among them, g n is the gradient; is a nonlinear factor and is a constant.

[0063] Step S302: Update the search direction of the filter based on the nonlinear gradient.

[0064] Using Markov conjugation, recursively update the search direction, the expression is:

[0065] (9)

[0066] Among them, p n is the search direction at time n; p n-1 is the search direction at time n-1; is the proportional factor. The proportional factor can be obtained by solving formula (10), as shown in formula (11):

[0067] (10)

[0068] (11)

[0069] Step S4: Based on the search direction, a regularization parameter is introduced to obtain a dynamic step size of the filter.

[0070] The dynamic step size satisfies formula (12):

[0071] (12)

[0072] in, is the dynamic step length, i.e. the optimal step length; is the step size, which is a scalar that determines how far to move along the search direction; is the objective function.

[0073] Based on formula (12) Taking the derivative, we can get the dynamic step size as:

[0074] (13)

[0075] in, is the dynamic step length; is the regularization constant, and , is the error signal .

[0076] By introducing a small regularization constant in the dynamic step size , can be adjusted dynamically according to the error signal. When the error increases, overfitting can be prevented by increasing regularization, thereby improving the generalization ability of the filter model under noisy conditions.

[0077] Step S5: Update the tap weight coefficients of the filter based on the dynamic step size.

[0078] Define the momentum factor and calculate the momentum term:

[0079] (14)

[0080] in, is the momentum term at time n; is the momentum factor, which determines the weight of the historical gradient on the update. In this embodiment, it is preferred ; is the momentum term at time n-1.

[0081] After the momentum factor is introduced, the filter tap weight coefficients are updated as follows:

[0082] (15)

[0083] Among them, h n is the weight coefficient vector at time n; h n-1 is the weight coefficient vector at time n-1.

[0084] The introduction of momentum factor allows the filter to accumulate past gradients, which speeds up convergence and helps avoid falling into local minima. The weight coefficient vector of the filter is updated to approximate the impulse response of the unknown system, so as to achieve the purpose of system identification.

[0085] Step S6: set time Repeat steps S1-S5 to update the weight vector of the adaptive filter at time n in sequence The coefficient of , that is, the weight coefficient vector is equal to the impulse response vector of the unknown system to be identified, and the identification of the unknown system is completed.

[0086] When the adaptive filter is used to perform system identification in this embodiment, the final result is usually a model that can approximately or accurately describe the dynamic behavior of the unknown system to be identified.

[0087] The model obtained by identifying the unknown sparse system can be used for prediction and control: predicting the future behavior of the system, or designing a control system to guide the system to achieve the desired performance; it can be used for simulation and analysis: simulating and analyzing the response of the system under different input conditions, which is very useful for system design and optimization; it can be used for fault diagnosis: by comparing the actual system behavior with the model prediction, anomalies or faults in the system can be detected and diagnosed; it can be used for optimization: helping to optimize the operating conditions of the system to reduce energy consumption, improve efficiency or meet specific performance indicators.

[0088] This embodiment realizes the identification of sparse systems to improve production efficiency. In industrial control systems, accurate system models can be used to optimize production processes, reduce waste, and improve product quality and output. Cost savings: through model prediction and optimization, energy consumption and material waste can be reduced, thereby reducing operating costs. Enhanced security: in critical systems such as aerospace, nuclear energy and other fields, accurate system models are essential to ensure the safe operation of the system. Improved user experience: in consumer electronics, system models can be used to improve user experience, such as in audio processing, image recognition and other fields.

[0089] Simulation experiment

[0090] In order to verify the effectiveness of the method of the present invention, experiments were conducted and the performance was compared with the traditional conjugate gradient algorithm.

[0091] In the simulation experiment, the adaptive filter order is 8, the forgetting factor is 0.6, and the momentum factor is 0.5.

[0092] The input signal is a white noise signal generated by a function in the matlab software. The advantage of using a white noise signal is that it contains all frequency components, which helps the filter identify the dynamic characteristics of the system.

[0093] like Figure 2 As shown, both curves gradually converge with the increase of the number of iterations. In the initial stage, the two curves drop rapidly, but the system identification method proposed in the present invention tends to stabilize faster. In steady state, the system identification method proposed in the present invention is about 5dB lower than the MSD of the traditional conjugate gradient algorithm for unknown system identification. In steady state, the traditional conjugate gradient algorithm curve has obvious fluctuations, while the identification method proposed in the present invention is smoother, indicating that the sparse system identification method of the improved adaptive filter proposed in the present invention is not only more accurate, but also more stable.

[0094] like Figure 3As shown, the excess mean square error of the two algorithms can be analyzed from the figure, showing the performance comparison of the method proposed by the present invention and the traditional conjugate gradient algorithm in error suppression. Throughout the process, the EMSE of the method proposed by the present invention is lower than that of the traditional conjugate gradient algorithm, showing a better error suppression effect. In steady state, the EMSE of the algorithm proposed by the present invention is about 5dB lower than that of the traditional conjugate gradient algorithm. Obviously, the curve of the method proposed by the present invention is smoother and the fluctuation amplitude is small, indicating that the error control of the method in a steady state is more stable.

[0095] Embodiment 2

[0096] In one or more embodiments, a sparse system identification system based on an improved adaptive filter is disclosed, specifically comprising:

[0097] A signal acquisition module is configured to: acquire the current input signal and simultaneously input it into the improved adaptive filter and the unknown system to be identified to obtain the filter output signal and the expected signal;

[0098] A signal estimation module, configured to: update a correlation estimation matrix of an input signal and a cross-correlation estimation vector between the input signal and a desired signal based on a conjugate gradient method;

[0099] The filter update module is configured as follows: based on the correlation estimation matrix and introducing nonlinear gradient, update the search direction of the filter; based on the search direction, introduce a regularization parameter to obtain the dynamic step size of the filter; based on the dynamic step size, update the tap weight coefficients of the filter; let the moment be updated to the next moment, update the weight vector coefficients of the adaptive filter, and when the filter weight coefficient vector is equal to the impulse response of the unknown system, the unknown system identification is completed.

[0100] Embodiment 3

[0101] This embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps of the above-mentioned sparse system identification method based on the improved adaptive filter are completed.

[0102] Embodiment 4

[0103] This embodiment provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned sparse system identification method based on the improved adaptive filter are completed.

[0104] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0105] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0106] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0107] The description of each embodiment in the above embodiments has different emphases. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0108] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A sparse system identification method based on an improved adaptive filter, characterized in that: The following steps are involved: Obtaining the input signal at the current moment, and simultaneously inputting the input signal into the improved adaptive filter and the unknown system to be identified, to obtain the filter output signal and the expected signal; Based on the conjugate gradient method, the correlation estimation matrix of the input signal and the cross-correlation estimation vector between the input signal and the expected signal are updated; Based on the correlation estimation matrix and introducing nonlinear gradient, the search direction of the filter is updated; Based on the search direction, a regularization parameter is introduced to obtain the dynamic step size of the filter; The tap weight coefficients of the filter are updated based on the dynamic step size; Let the time update be the next time, update the weight vector coefficient of the adaptive filter, and when the filter weight coefficient vector is equal to the impulse response of the unknown system, the unknown system identification is completed; The updating formula of the nonlinear gradient is: Among them, g n is the gradient; is a nonlinear factor; Based on the search direction of the nonlinear gradient update filter, the expression is: Among them, p n is the search direction at time n; p n-1 is the search direction at time n-1; is the scale factor; The dynamic step length expression is: in, is the dynamic step length; is the regularization constant, and ,in is the error signal, ; R n is the correlation estimation matrix at the current n moment; The updating of the tap weight coefficients of the filter based on the dynamic step size includes: Define the momentum factor and calculate the momentum term: in, is the momentum term at time n; is the momentum factor, which determines the weight of the impact of historical gradients on the update; is the momentum term at time n-1; Update the filter tap weight coefficients after introducing the momentum factor: Among them, h n is the weight coefficient vector at time n; h n-1 is the weight coefficient vector at time n-1.

2. A sparse system identification method based on an improved adaptive filter as claimed in claim 1, characterized in that: The expected signal model is constructed based on the input signal and the impulse response of the unknown sparse system. The expected signal expression is: in, d n is the expected signal; is the transpose of the input vector; is the impulse response of the unknown sparse system; For additional signal.

3. A sparse system identification system based on an improved adaptive filter, characterized in that: include: A signal acquisition module is configured to: acquire the current input signal and simultaneously input it into the improved adaptive filter and the unknown system to be identified to obtain the filter output signal and the expected signal; A signal estimation module, configured to: update a correlation estimation matrix of an input signal and a cross-correlation estimation vector between the input signal and a desired signal based on a conjugate gradient method; A filter update module is configured to: update the search direction of the filter based on the correlation estimation matrix and introduce a nonlinear gradient; introduce a regularization parameter based on the search direction to obtain a dynamic step size of the filter; and update the tap weight coefficients of the filter based on the dynamic step size; Let the time update be the next time, update the weight vector coefficient of the adaptive filter, and when the filter weight coefficient vector is equal to the impulse response of the unknown system, the unknown system identification is completed; The updating formula of the nonlinear gradient is: Among them, g n is the gradient; is a nonlinear factor; Based on the search direction of the nonlinear gradient update filter, the expression is: Among them, p n is the search direction at time n; p n-1 is the search direction at time n-1; is the scale factor; The dynamic step length expression is: in, is the dynamic step length; is the regularization constant, and ,in is the error signal, ; R n is the correlation estimation matrix at the current n moment; The updating of the tap weight coefficients of the filter based on the dynamic step size includes: Define the momentum factor and calculate the momentum term: in, is the momentum term at time n; is the momentum factor, which determines the weight of the impact of historical gradients on the update; is the momentum term at time n-1; Update the filter tap weight coefficients after introducing the momentum factor: Among them, h n is the weight coefficient vector at time n; h n-1 is the weight coefficient vector at time n-1.

4. An electronic device, characterized in that: The invention comprises a memory and a processor and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the sparse system identification method based on the improved adaptive filter as described in any one of claims 1 to 2 is completed.

5. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the sparse system identification method based on an improved adaptive filter as described in any one of claims 1-2.

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