采用最小平均平方算法进行非线性系统辨识Matlab代码.rar

%% System Identification Using Voltera Least Mean Square (VLMS) algorithm % Plant identification simulation % Author: SHUJAAT KHAN (shujaat123@gmail.com) %% Start clc; clear all; close all; %% signal and system parameters N = 1e5; % Number of samples noise_var = 1e-2; % Noise level h = [-0.76 -1.0 1.0 0.5 0 2.0 -1.6 0.8 1.2]; % system coefficients order = 2; % delay elements power = 2; % highest polynomial power memory = order+1; % memory elements (current value + order) x = sqrt(0.1)*rand(1,N); % random signal uniformly distributed x = filter([1 -0.95],1,x); % all-pole filter x = [zeros(1,memory) x]; % Zero padding for i=1:N % Input passed trought system(h) r(i)=h(1)*x(i+1)+h(2)*x(i+2)+h(3)*x(i+3)+h(4)*x(i+1)^2+h(5)*x(i+1)*x(i+2)+h(6)*x(i+1)*x(i+3)+h(7)*x(i+2)^2+h(8)*x(i+2)*x(i+3)+h(9)*x(i+3)^2; end x= x((memory+1):end); % Removing Zero padding SNR = 10*log10(1/noise_var); % SNR calculation d = awgn(r, SNR); % Addition of white Gaussian noise of SNR value defined above %% VLMS parameter eta1 = 2e-0; % Learning rate1 for VLMS eta2 = 2e-0; % Learning rate2 for VLMS Wvlms = zeros(1,length(h)); % Initial weights of VLMS Uv1 = zeros(1,memory); % Input frame1 length of VLMS Uv2 = zeros(1,length(Wvlms)-memory); % Input frame2 length of VLMS for n = 1 : N %% VLMS Uv1(1,1:end-1) = Uv1(1,2:end); % Shifting of frame window % Input of VLMS Uv1(1,end) = x(n); Uv2 = [Uv1(1)^2 Uv1(1)*Uv1(2) Uv1(1)*Uv1(3) Uv1(2)^2 Uv1(2)*Uv1(3) Uv1(3)^2]; ys = (Wvlms)*[Uv1 Uv2]'; % Output of VLMS es = d(n) - ys; % Instantaneous error of VLMS Wvlms = Wvlms + es * [eta1*Uv1 eta2*Uv2]; % Weight update rule of VLMS %% Normalized weight difference (NWD) NWD_VLMS(n) = norm(h-Wvlms)./norm(h); % Normalized weight difference of VLMS end % %% Cost function plots figure plot(20*log10(NWD_VLMS),'','linewidth',2) hold on line ([0 N],[-SNR -SNR],'linewidth',2,'color','r') xlabel('Iterations'); ylabel('Normalized Weight Deviation (dB)'); grid minor legend('VLMS','Noise Level'); [h;Wvlms]