hi, I simulated TRLS algorithm with leading DCD, but the coefficients didn't converge,would you help me?please
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clear all close all clc
global N Ts format long % ============================= system model ============================ % % continuous model
num = [0.004104 , 380]; den = [0.0000000213 , 0.0000586 , 1];
G = tf(num,den) pole(G); zero(G); syms z;
% discrete model Ts = 20e-06; % Ts = 0.1; Gd = c2d(G,Ts) pole(Gd); zero(Gd);
b = Gd.num{1,1}; a = Gd.den{1,1}; %step responce
% identification parameters teta = [a(2:3),b(2:3)]' N = 800;
% ======================== RLS with step input ========================== %
Rand_signal = [0.91*randn(1,N/8) -0.91*randn(1,N/8) zeros(1, 3*(N/4)) ] ; % Rand_signal = [0.85*randn(1,N/2) zeros(1,N/2) ] ; x = [0.91*rand(1,N/8) -0.91*rand(1,N/8) zeros(1, 3*(N/4)) ]; S = var(x); %signal Power SNR = 30; Noise_amp = sqrt(S/(10^(SNR/10))); Noise_sample = Noise_amp*rand(1,length(x)); % figure(1) % plot([0:N-1]*Ts,Noise_sample)
u = 0.126*ones(1,N) + Noise_sample ; % figure(2) % plot([0:N-1]*Ts,u)
y = system_equation(a,b,u);
teta_hat(:,2) = zeros(4,1); % 4 parameters should be identified M=16; H=1; landa= 0.965; L=4; R=1e-1*eye(4,4);
r = zeros(4,1); %Rh=z h=zeros(L,N); %solution vector alpha=H; %step size m=1;
for t = 3:N for w=1:4 phi = [-y(t-1) -y(t-2) u(t-1) u(t-2)]';
R(:,w) = landa*R(:,w)+ phi(w)*phi ;
y_hat (t) = phi'*teta_hat(:,t-1);
error(t) = y(t) - phi'*teta_hat(:,t-1);
z = landa*r+error(t)*phi;
r = z; %residual vector
[~,p]=(max(abs(r)));
for k=1:1:N %itrations while abs(r(p))<=alpha/2*R(p,p) && m<=M m=m+1; alpha=alpha/2; end if m>M % number of bits coeffiecient break end h(p,t)=h(p,t)+sign(r(p))*alpha; r=r-sign(r(p))*alpha*R(:,p);
end
% [r , h] = DCDReal(R,z,L,M,N,H);
SNRi = 10*log10(var(phi)/var(error));
% disp([num2str(SNRi) 'dB SNR Improvement']);
teta_hat(:,t) = teta_hat(:,t-1) + h(:,t);
end
end
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