armax identification
[arc, resid] = armax1(r, s, q, y, u) [arc, resid] = armax1(r, s, q, y, u, b0f)
output signal
input signal
auto regression orders with r >=0, s >=-1.
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
is tlist with type "ar" and fields a, b, d, ny, nu, sig
is the vector [1,a1,...,a_r]
is the vector [b0,......,b_s]
is the vector [1,d1,....,d_q]
resid=[ sig*echap(1),....,];
armax1 is used to identify the coefficients of a 1-dimensional ARX process:
A(z^-1)y= B(z^-1)u + D(z^-1)sig*e(t) e(t) is a 1-dimensional white noise with variance 1. A(z)= 1+a1*z+...+a_r*z^r; ( r=0 => A(z)=1) B(z)= b0+b1*z+...+b_s z^s ( s=-1 => B(z)=0) D(z)= 1+d1*z+...+d_q*z^q ( q=0 => D(z)=1)
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),e(t-1),...,e(t-q)]
and
coef= [-a1,..,-ar,b0,...,b_s,d1,...,d_q]' y(t)= coef'* z(t) + sig*e(t).
a sequential version of the AR estimation where e(t-i) is replaced by an estimated value is used (RLLS). With q=0 this method is exactly a sequential version of armax
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); disp(_("Simulation of an ARMAX process:")); disp(ar); n = 300; u = -prbs_a(n, 1, int([2.5,5,10,17.5,20,22,27,35]*100/12)); zd = narsimul(ar, u); // using now armax1 : colored noise identification // you can test the same example with [arc1, resid] = armax1(3,3,2,zd(1:n),u,1); disp(arc1); | ![]() | ![]() |
In Scilab versions up to 4.1.2 the returned value in
arc.sig
is the square of sig
square. To be conform with the help, the display of arma models
and the armax function, starting from Scilab-5.0 version the
returned arc.sig
is sig
.