Local update filtering method based on adaptive variable step length LMS (Least Mean Square)

Abstract

The invention discloses a local update filtering method based on an adaptive variable step length LMS, and relates to the technical field of electromagnetic filtering methods. The method comprises the following steps: constructing a mixed weight coefficient LMS filter; and filtering a signal transmitted by the signal transmitting device by using the constructed mixed weight coefficient LMS filter, and filtering out an electromagnetic interference signal in the transmitted signal. According to the method provided by the invention, the filter establishes a nonlinear relationship between the step length and the error signal and adopts the mixed weight coefficient for filtering, so that the suppression capability on the interference signal is effectively improved. Simulation and actual measurement results show that the method has high convergence speed and tracking capability under different signal-to-noise ratios, and small steady-state errors can be obtained. According to the method, the calculation complexity is reduced, meanwhile, the convergence speed is increased by at least 12%, and the method is suitable for electromagnetic interference elimination in a complex environment.

Description

Technical Field

[0001] The invention relates to the technical field of electromagnetic filtering methods, and in particular to a local update filtering method based on adaptive variable step size LMS. Background Art

[0002] The traditional LMS filter algorithm has a fixed step size and needs to be manually adjusted. It is not adaptive and therefore cannot meet the requirements of adaptive filtering. The variable step size LMS adaptive filter algorithm is widely used in the fields of echo cancellation, speech enhancement, and system identification due to its small computational complexity, low implementation difficulty, and strong adaptability.

[0003] Researchers have conducted a lot of research on the limitations of the convergence speed, steady-state error and anti-interference of the variable step-size LMS adaptive filtering algorithm. Prior art 1 uses an improved hyperbolic tangent function to adjust the step size, reduces the algorithm's sensitivity to noise, reduces the steady-state error and misalignment at low signal-to-noise ratio, and introduces a compensation term, effectively avoiding the problem of slow convergence caused by adjusting the step size using the error correlation value. Its disadvantages are that many parameters are introduced and the amount of calculation is large. Based on prior art 1, prior art 2 uses the second norm of the step-size feedback factor and the correlation value of the error signal to adjust the step size, overcoming the problems of slow convergence speed and poor anti-noise ability of the fixed step-size algorithm. The disadvantage is also that the amount of calculation is large. Prior art 3 proposes a variable step-size normalized adaptive filtering algorithm of a quasi-spike function, uses a quasi-spike function instead of a Sigmoid function as a step-size iteration formula, introduces a variable step-size adjustment principle based on correlation errors, and enhances the algorithm's stability while improving the algorithm's convergence speed and tracking performance, reducing the algorithm's computational complexity. Prior art 4 uses the inverse hyperbolic tangent function as the basis to establish a nonlinear relationship between step size and error instead of the fixed step size in the traditional LMS algorithm, thereby realizing dynamic adjustment of the step size factor. Prior art 5 proposes a piecewise variable step size LMS adaptive filtering algorithm based on a normal distribution curve, which realizes the adaptive selection of fixed and variable step sizes by setting an error threshold, thereby solving the shortcoming of slow convergence in the initial stage of algorithm iteration. Prior art 6 proposes a variable step size adaptive filtering algorithm with partial update of weight coefficients. The algorithm adopts the periodic partial update of weight coefficients and the variable step size algorithm based on the improved Sigmoid function, which better solves the contradiction between the amount of calculation and the convergence speed in the adaptive interference cancellation algorithm. While effectively reducing the amount of calculation, it still maintains a relatively fast convergence speed. Although the above studies all have their own advantages, there are still deficiencies in the convergence speed, steady-state error, anti-interference performance and system tracking capability of the LMS filtering algorithm, and the filtering performance needs to be further optimized.

[0004] In summary, the existing variable step-size algorithms cannot simultaneously and effectively solve the problems of slow convergence speed, poor system tracking performance, and high steady-state error. Summary of the invention

[0005] The technical problem to be solved by the present invention is how to provide a local update filtering method based on adaptive variable step-size LMS which has faster convergence speed and tracking capability and can obtain smaller steady-state error.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: constructing a mixed weight coefficient LMS filter;

[0007] The constructed mixed weight coefficient LMS filter is used to filter the signal transmitted by the signal transmitting device to filter out the electromagnetic interference signal in the transmitted signal.

[0008] A further technical solution is to establish a nonlinear relationship between the step size and the error signal and to construct a mixed weight coefficient LMS filter using mixed weight coefficients.

[0009] A further technical solution is that the hybrid weight coefficient LMS filter constructed is as follows:

[0010] y(n)=W T (n)X(n)

[0011] e(n)=d(n)-W T (n)X(n)

[0012]

[0013] Where x(n) is the input signal. After x(n) passes through the unknown system and the external interference signal v(n) to form the expected signal d(n). After x(n) passes through the adaptive filter, the output signal is y(n). The expected signal d(n) is subtracted from the output signal y(n) to obtain the error signal e(n). X(n) and W(n) are the actual input vector and the filter weight coefficient vector, respectively. u(n) is a variable step size function. β, α, and γ are step size adjustment parameters.

[0014] When e(n)→0, When e(n)→∞, That is, the maximum value of u(n) is β, and the convergence condition of the mixed weight coefficient LMS filter equation is:

[0015] The beneficial effect of adopting the above technical solution is that the filter in the method described in the present application effectively improves the ability to suppress interference signals by establishing a nonlinear relationship between the step size and the error signal and using mixed weight coefficients for filtering. Simulation and actual measurement results show that this method has a faster convergence speed and tracking ability under different signal-to-noise ratios, and can obtain a smaller steady-state error. While reducing the computational complexity, the method increases the convergence speed by at least 12%, and is suitable for eliminating electromagnetic interference in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0017] Figure 1 is a main flow chart of the method described in the embodiment of the present invention;

[0018] Figure 2 is a principle block diagram of an adaptive filter in the prior art in an embodiment of the present invention;

[0019] Figure 3a is a curve diagram showing the influence of parameter β on the step size factor in an embodiment of the present invention;

[0020] Figure 3b is a curve diagram showing the influence of parameter γ on the step size factor in an embodiment of the present invention;

[0021] Figure 3c is a curve diagram showing the influence of parameter α on the step size factor in an embodiment of the present invention;

[0022] Figure 4 is a comparison diagram of simulation convergence for different β values ​​in an embodiment of the present invention;

[0023] Figure 5 is a comparison diagram of simulation convergence for different α values ​​in an embodiment of the present invention;

[0024] Figure 6 is a comparison diagram of simulation convergence for different γ values ​​in an embodiment of the present invention;

[0025] Figure 7 is a comparison diagram of simulation convergence of different filtering methods in an embodiment of the present invention;

[0026] Figure 8a This is the MSE comparison chart of the five algorithms when SNR = 10dB;

[0027] Figure 8b This is the MSE comparison chart of the five algorithms when SNR = 20dB;

[0028] Figure 8c This is the MSE comparison chart of the five algorithms when SNR = 30dB;

[0029] Fig. 9 is a test site diagram of the method described in the embodiment of the present invention;

[0030] Fig.10a is an expected signal diagram in the method described in the embodiment of the present invention;

[0031] Fig.10b is an input signal diagram in the method described in the embodiment of the present invention;

[0032] Fig.11 is a signal diagram after filtering by different algorithms in an embodiment of the present invention;

[0033] Fig.12 It is a comparison of the convergence performance of different algorithms in the embodiments of the present invention. DETAILED DESCRIPTION

[0034] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0036] like Figure 1 As shown, the embodiment of the present invention discloses a local update filtering method based on adaptive variable step size LMS, comprising the following steps:

[0037] S1: construct a mixed weight coefficient LMS filter;

[0038] S2: Use the constructed mixed weight coefficient LMS filter to filter the signal transmitted by the signal transmitting device to filter out the electromagnetic interference signal in the transmitted signal.

[0039] The following is a detailed description of the above steps combined with specific content

[0040] The mixed weight coefficient LMS filter constructed in the present application is a filter based on the mixed weight coefficient variable step size LMS (R-IVSSLMS) algorithm of the Rayleigh distribution curve.

[0041] Based on the Rayleigh distribution curve, the R-IVSSLMS algorithm constructs a nonlinear functional relationship between the step size and the error signal and combines it with the mixed weight coefficient. While adaptively adjusting the step size factor, it reduces the number of iterations of the filter weight coefficient and simplifies the calculation. This ensures that the algorithm can reduce the steady-state error while ensuring rapid convergence and improves the system tracking performance of the algorithm.

[0042] Basic principles of LMS algorithm:

[0043] The principle framework of the adaptive filter is as follows Figure 2 As shown in the figure, the input signal x(n) is superimposed by the unknown system and the external interference v(n) to form the expected signal d(n). The output signal of x(n) after passing through the adaptive filter is y(n). The expected signal d(n) is subtracted from the output signal y(n) to obtain the error signal e(n). e(n) is fed back to the adaptive filter to update the weighted coefficient vector of the adaptive filter. The updated output signal is closer to the expected signal, thereby achieving the purpose of adaptive filtering.

[0044] The iterative steps of the LMS algorithm include:

[0045] 1) Initialization parameters: Set the initial value W(0) of the adaptive filter weight coefficient to 0, the order to M, and select an appropriate step value u;

[0046] 2) Calculate the output of the filter estimate: y(n) = W T (n)X(n);

[0047] 3) Calculate the filter error: e(n) = d(n) - y(n);

[0048] 4) The filter weight coefficient update formula is: w(n+1)=w(n)+2ue(n)X(n);

[0049] 5) Repeat the above steps 2) to 4) until the weight coefficients of the filter approach the optimal filtering.

[0050] X(n)=[x(n),x(n-1),...,x(n-L+1)],W(n)=[w(n),w(n-1),...,w(n-L+1)] are the actual input vector and filter weight coefficient vector respectively, L represents the filter length, and u represents the fixed step size. The condition for the algorithm to converge is that the step size factor u satisfies:

[0051]

[0052] Among them, λ max It is the maximum eigenvalue of the autocorrelation matrix of the adaptive filter input signal.

[0053] Mixing weight coefficient variable step size LMS (R-IVSSLMS) algorithm based on Rayleigh distribution curve:

[0054] In order to take into account the convergence speed, steady-state error and tracking performance of the algorithm, this application is based on the characteristics of the Rayleigh distribution curve function. Through the analysis and operation of the function, the function curve changes conform to the adjustment principle of the step size factor of the adaptive filtering algorithm. The Rayleigh distribution curve function expression is:

[0055]

[0056] Based on the Rayleigh distribution curve, the step length is optimized and the β, α, and γ parameters are introduced to jointly control the shape of the step length curve. The relationship between the step length factor and the error function is obtained as follows:

[0057] u(n)=β[1-(1+αe 2 (n))exp(-γe 2 (n))] (3)

[0058] Considering that the designed adaptive filter should have good anti-interference ability, the correlation value of the error function e(n)e(n-1) is used instead of e 2 (n) Reduce the interference of random noise, and improve the bottom characteristics of the step size factor by introducing parameters, which effectively improves the anti-interference performance of the system. The improved variable step size function is:

[0059] u(n)=β[1-(1+αe(n)e(n-1))exp(-γe(n)e(n-1))] (4)

[0060] In the early stage of LMS algorithm filtering, the error e(n) is large, and a larger step size u(n) is required to reduce the error; when the algorithm iterates for a period of time, e(n) gradually converges to 0, while the filter weight coefficient is still iterating. When the sampled data increases, the algorithm will run slower and the computational complexity will increase. To address this problem, a hybrid weight coefficient filtering method is proposed. The error threshold is set to ε. When e(n) is greater than ε, the algorithm iterates; when e(n) is less than ε, the current filter weight coefficient is set to the previous filter weight coefficient. The expression of hybrid weight coefficient filtering is:

[0061]

[0062] Therefore, the LMS algorithm of the mixing weight coefficient based on the Rayleigh distribution curve can be summarized as:

[0063] y(n)=W T (n)X(n) (6)

[0064] e(n)=d(n)-WT (n)X(n) (7)

[0065]

[0066] β, α, γ are step size adjustment parameters. From the analysis of formula (8), we can see that when e(n)→0, When e(n)→∞, That is, the maximum value of u(n) is β. From formula (1), we can get the convergence condition of the improved variable step size LMS algorithm as follows:

[0067]

[0068] Algorithm Analysis

[0069] 1) Parameter selection

[0070] This section analyzes the effect of parameters on step size in the R-IVSSLMS algorithm. The relationship curve is shown in Figure 3a-3c As shown. Among them, Figure 3a The step factor curves are when α=1, γ=1, and β is 0.2, 0.4, 0.6, and 0.8 respectively; Figure 3b The step factor curves are when β = 0.2, α = 600, and γ is 1, 3, 5, and 10 respectively; Figure 3c The step factor curve is when β=0.2, γ=1, and α is 0.1, 0.5, 0.8, and 1 respectively. Figure 3a-3c From the analysis, we can see that the parameter β plays a crucial role in the range of the step length. As the parameter β increases, the step length also becomes larger. That is, when equation (10) is satisfied, a larger β can obtain a larger step length, and the algorithm can obtain a higher convergence speed. The parameters α and γ have a greater influence on the shape of the step length function. Figure 3a-3c It can be seen that when β and α remain unchanged, the larger the γ value, the larger the step factor u(n); when β and γ remain unchanged, the larger the α value, the smaller the step factor u(n). Therefore, in actual engineering applications, it is necessary to compromise the values ​​of α, β, and γ.

[0071] 2) Algorithm anti-interference analysis

[0072] This application uses the error correlation estimate e(n)e(n-1) to replace e 2 (n), the anti-interference performance of the algorithm is increased, and the theoretical analysis is as follows:

[0073] From formula (7), we can know that:

[0074] d(n)=e(n)+X T (n)W(n) (11)

[0075] according to Figure 2, d(n) can also be written as

[0076] d(n)=v(n)+X T (n)W opt (n) (12)

[0077] Where v(n) has zero mean and variance is σ 2 Gaussian white noise, and is independent of the input signal x(n); W opt is the weight vector of the unknown system and also the optimal weight vector of the adaptive filter.

[0078] Let the weight vector difference be

[0079] ΔW(n)=W(n)-W opt (n) (13)

[0080] From equations (11) to (13), we can get

[0081] e(n)=v(n)-X T (n)ΔW(n) (14)

[0082] e(n-1)=v(n-1)-X T (n-1)ΔW(n-1) (15)

[0083] therefore

[0084]

[0085] Since v(n) is a zero-mean Gaussian white noise and is independent of the input signal x(n), the mathematical expectation of both sides of equation (16) is:

[0086] Ε{e(n)e(n-1)}=Ε{ΔW T (n)X(n)X T (n-1)ΔW(n-1)} (17)

[0087] and

[0088]

[0089] Therefore, the mathematical expectation of both sides of equation (18) is

[0090] Ε{e 2 (n)}=Ε{ΔW T (n)X(n)X T (n)ΔW(n)}+Ε{v 2 (n)} (19)

[0091] From equations (17) and (19), we can see that the expectation of the error e(n)e(n-1) is not affected by the interference v(n) and is only related to the input signal X(n). 2 The expectation of (n) is related to the interference v(n). When v(n) is large, it will seriously affect the stability of the algorithm. Therefore, the step size function of the algorithm described in this application is independent of the interference, that is, it has a certain anti-interference ability.

[0092] Simulation and measurement analysis

[0093] 1) Simulation performance comparison

[0094] The simulations in this application were performed in MATLAB R2019b software. Assume that the order of the adaptive filter is M = 8, assume that the unknown system is a lateral FIR (finite impulse response) structure, and the tap coefficients are [0.8783, -0.5806, 0.6537, -0.3223, 0.6577, -0.0582, 0.2895, -0.2710]. When the number of iterations N = 500, the system mutates, and the tap coefficients are set to [0.3783, -0.2806, 0.3537, -0.1223, 0.3577, -0.2582, 0.1895, -01710].

[0095] Assume that the input signal x(n) and the interference noise v(n) of the adaptive filter are both Gaussian white noise with zero mean, the variance of x(n) is 1, and the variance of v(n) is 0.001. The signal-to-noise ratio is 10dB, 20dB, and 30dB respectively. The number of experimental sampling points of the system is 1000, and each learning curve is the statistical average result of 200 independent simulations.

[0096] Figure 3a-3c The step sizes u(n) of the five existing variable step size algorithms are as follows:

[0097] Variable step size LMS algorithm based on Sigmoid function (SVS-LMS)

[0098]

[0099] Variable step size LMS algorithm based on normal distribution curve (DNC-LMS)

[0100]

[0101] Variable Step-Size LMS Algorithm Based on Inverse Hyperbolic Tangent Function (IHTF-LMS)

[0102]

[0103] Variable Step-Size LMS Algorithm Based on Softsign Function (SS-LMS)

[0104]

[0105] Variable step-size LMS algorithm based on the stalk function (V-LMS)

[0106]

[0107] The simulation parameter settings of different algorithms are shown in Table 1:

[0108] Table 1 - Simulation parameter settings for different algorithms

[0109]

[0110] like Figure 4 The figure shows the simulation convergence comparison of different β values. It can be seen from the figure that when the β value increases, the convergence speed of the algorithm also increases; when β>0.3, the convergence speed of the algorithm slows down, and when β is gradually increased, the convergence performance is similar. After the system mutates, β=0.7 is disturbed and cannot converge to a stable state. Therefore, the best β in this application is 0.5.

[0111] like Figure 5 The influence of different α values ​​on the convergence of the algorithm simulation is analyzed. It can be seen from the figure that different α values ​​have little influence on the convergence speed of the algorithm. Before and after the system mutation, different α values ​​can converge to a stable state. Therefore, the best α value for this application is 0.1.

[0112] like Figure 6 The figure shows the effect of different γ values ​​on the convergence of the algorithm simulation. It can be seen from the figure that when γ = 10, the convergence performance of the system is optimal. When the γ value increases, the convergence speed of the algorithm also increases; when γ>3, the convergence speed of the algorithm slows down. Before and after the system mutation, different γ values ​​show the same convergence trend.

[0113] like Figure 7 The simulation convergence of different filtering methods is compared. It can be seen from the figure that after the error threshold ε is used to control the filter coefficient W(n), the algorithm converges significantly faster than the traditional filtering method. After the system undergoes a sudden change, it can also quickly converge to a stable state. The advantage of selecting mixed weight coefficient filtering is that it reduces iterative calculations and improves convergence speed.

[0114] The traditional filtering method needs to update W(n) and u(n) after each iteration, which increases the computational complexity. The mixed weight coefficient filter proposed in this application realizes the update of local weight coefficients by setting an error threshold. When e(n)>ε, W(n) and u(n) are updated once; when e(n)≤ε, W(n) and u(n) do not need to be updated, and the previous value can be used. The effectiveness of the algorithm proposed in this application is verified through simulation analysis.

[0115] Depend on Figure 8a It can be seen that when the signal-to-noise ratio (SNR) is 10dB, the convergence speed and steady-state error performance of the R-IVSSLMS algorithm are significantly higher than those of the other five variable-step-size LMS algorithms. Among them, the SS-LMS algorithm has the worst convergence performance and cannot reach a stable state in a short time. The other four algorithms have comparable convergence performance and can converge to a stable state in a short time, and their steady-state errors are also relatively small. Before and after a sudden change in the system, it can maintain the same convergence trend and can quickly converge to a stable state, demonstrating good system tracking capabilities. The algorithm of this application improves the convergence speed, steady-state error, and system tracking capabilities of the algorithm on the basis of simplifying the amount of computation. Figure 8b As shown in Figure 1, the SNR is further increased to 20 dB. Before and after the system mutation occurs, the convergence speed and steady-state error of the algorithm in this application are significantly higher than those of the five existing variable step-size algorithms. Figure 8c As shown, if the SNR is further increased to 30dB, the convergence speed of the existing five algorithms is significantly slower than that of the algorithm in this application, and the steady-state error is also lower than that of the algorithm in this application. Through the above comparative analysis, it can be seen that under the background of high and low signal-to-noise ratios, compared with the existing five variable-step LMS algorithms, the R-IVSSLMS algorithm has obvious advantages in convergence speed, lower steady-state error, and stronger adaptability to external systems. Table 1 compares the number of convergence iterations of the six algorithms under different signal-to-noise ratios. It can be seen that the number of convergence iterations of the method in this application is within 100, and the convergence speed is increased by at least 18%. From the perspective of simulation, the effectiveness of the algorithm in this application is verified.

[0116] Measured performance comparison

[0117] The filtering performance of the R-IVSSLMS algorithm proposed in this application is verified by actual measurement. The receiving antenna adopts the self-developed Vivaldi miniaturized antenna, whose operating frequency range is 30MHz to 12GHz and the gain range is 1dBi to 11dBi. The signal transmitting antenna adopts a hybrid log-periodic antenna of model 3142E, and the test frequency range is 30MHz to 6GHz. The distance between the receiving antenna and the EUT transmitting antenna is 1m. The signal generator model is 1435D, the frequency range is 9KHz to 6GHz, and the maximum output power is 20dBm. The data acquisition device is implemented by a four-channel oscilloscope of model MSO8104, with a test bandwidth of 2GHz and a signal sampling frequency of 10GHz / s. The two antennas are located on the same horizontal line, and the electromagnetic interference is mainly the surrounding environmental interference.

[0118] exist Fig. 9 The signal generator transmits a sinusoidal signal with a frequency of 50MHz and a signal power of 0dB. The environmental interference mainly includes interference signals generated by radio communications such as radio stations, high-voltage transmission lines, and mobile phone base stations. The receiving antenna collects the expected signal and environmental interference as x(n). The expected signal is obtained through testing in an anechoic chamber as d(n). The parameter settings of different algorithms during the experimental test are shown in Table 2.

[0119] Table 2 Parameter settings of different algorithms

[0120]

[0121] like Figure 10a-Figure 10b The signal is measured. The purpose of the experiment is to extract the expected signal d(n) from the input signal x(n) through an adaptive filtering algorithm. Fig.11 The following are some output signal result diagrams after the signal x(n) is filtered by different variable step-size LMS algorithms. It can be seen that the error of the filtered signal of the R-IVSSLMS algorithm proposed in this application is smaller, and it has a smaller error at the beginning of the iteration. The signal after sampling point 150 reaches a stable state, which meets the actual filtering requirements.

[0122] like Fig.12The figure shows a comparison of the filtering convergence performance of different algorithms for the complete measured signal. It can be seen that the convergence error of the R-IVSSLMS algorithm proposed in this application is significantly smaller than the existing five algorithms, and there is no mutation after convergence and stabilization. Compared with the SS-LMS algorithm, the convergence speed is increased by 25%, and the MSE is increased by 0.04dB; compared with the IHTF-LMS algorithm, the convergence speed is increased by 24%, and the MSE is increased by 0.039dB; compared with the V-LMS algorithm, the convergence speed is increased by 20%, and the MSE is increased by 0.036dB; compared with the SVS-LMS algorithm, the convergence speed is increased by 15%, and the MSE is increased by 0.02dB; compared with the NDC-LMS algorithm, the convergence speed is increased by 12%, and the MSE is increased by 0.01dB; This section verifies the effectiveness of the signal filtering algorithm proposed in this application from the perspective of experimental testing.

[0123] In summary, the filter constructed in this application overcomes the shortcomings of the existing variable step-size LMS algorithm that cannot take into account the convergence speed, tracking speed and steady-state performance. The algorithm adopted by the filter uses error correlation estimation to adjust the step size, which enhances the anti-interference ability of the variable step-size LMS algorithm, thereby reducing the steady-state error and steady-state imbalance of the algorithm at low signal-to-noise ratios. It is combined with the filtering method of mixed weight coefficients, and the iterative update of W(n) and u(n) is controlled by setting an error threshold, which simplifies the filtering iteration process and improves the convergence speed. Simulation and actual measurement show that the algorithm has a faster convergence speed and tracking ability under different signal-to-noise ratios, and can obtain a small steady-state error. Compared with the existing 5 variable step-size LMS algorithms, on the basis of simplifying the amount of calculation, the convergence speed is increased by at least 12%, which is suitable for electromagnetic interference elimination in complex environments.

Claims

1. A local update filtering method based on adaptive variable step size LMS, characterized in that The steps include: Construct a mixed weight coefficient LMS filter; The constructed mixed weight coefficient LMS filter is used to filter the signal transmitted by the signal transmitting device to filter out the electromagnetic interference signal in the transmitted signal.

2. The local update filtering method based on adaptive variable step size LMS as claimed in claim 1 is characterized in that: A nonlinear relationship between the step size and the error signal is established and a mixed weight coefficient LMS filter is constructed using the mixed weight coefficient.

3. The local update filtering method based on adaptive variable step size LMS as claimed in claim 1 is characterized in that: The constructed mixed weight coefficient LMS filter is as follows: y(n)=W T (n)X(n) e(n)=d(n)-W T (n)X(n) Where x(n) is the input signal. After x(n) passes through the unknown system and the external interference signal v(n) to form the expected signal d(n). After x(n) passes through the adaptive filter, the output signal is y(n). The expected signal d(n) is subtracted from the output signal y(n) to obtain the error signal e(n). X(n) and W(n) are the actual input vector and the filter weight coefficient vector, respectively. u(n) is a variable step size function. β, α, and γ are step size adjustment parameters. When e(n)→0, When e(n)→∞, That is, the maximum value of u(n) is β, and the convergence condition of the mixed weight coefficient LMS filter equation is:

4. The local update filtering method based on adaptive variable step size LMS as claimed in claim 1 is characterized in that: The parameters β=0.5, α=0.1, and γ=10.

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