armax armax identification [arc,la,lb,sig,resid]=armax(r,s,y,u,[b0f,prf]) y output process y(ny,n); ( ny: dimension of y , n : sample size) u input process u(nu,n); ( nu: dimension of u , n : sample size) r and s auto-regression orders r >=0 et s >=-1 b0f optional parameter. Its default value is 0 and it means that the coefficient b0 must be identified. if bof=1 the b0 is supposed to be zero and is not identified prf optional parameter for display control. If prf =1, the default value, a display of the identified Arma is given. arc a Scilab arma object (see armac) la is the list(a,a+eta,a-eta) ( la = a in dimension 1) ; where eta is the estimated standard deviation. , a=[Id,a1,a2,...,ar] where each ai is a matrix of size (ny,ny) lb is the list(b,b+etb,b-etb) (lb =b in dimension 1) ; where etb is the estimated standard deviation. b=[b0,.....,b_s] where each bi is a matrix of size (nu,nu) sig is the estimated standard deviation of the noise and resid=[ sig*e(t0),....] ( armax is used to identify the coefficients of a n-dimensional ARX process where e(t) is a n-dimensional white noise with variance I. sig an nxn matrix and A(z) and B(z): A(z)=1) B(z) = b0+b1*z+...+b_s z^s ( s=-1 => B(z)=0) ]]> for the method see Eykhoff in trends and progress in system identification, page 96. with z(t)=[y(t-1),..,y(t-r),u(t),...,u(t-s)] and coef= [-a1,..,-ar,b0,...,b_s] we can write y(t)= coef* z(t) + sig*e(t) and the algorithm minimises sum_{t=1}^N ( [y(t)- coef'z(t)]^2) where t0=max(max(r,s)+1,1))). a = [1, -2.851, 2.717, -0.865]; b = [0, 1, 1, 1]; d = [1, 0.7, 0.2]; ar = armac(a, b, d, 1, 1, 1); n = 300; u = -prbs_a(n, 1, int([2.5,5,10,17.5,20,22,27,35]*100/12)); zd = narsimul(ar, u); plot2d(1:n,[zd',1000*u'],style=[1,3]);curves = gce(); legend(["Simulated output";"Input [scaled]"]); imrep2ss time_id arl2 armax frep2tf