armax1

armax identification

Calling Sequence

[arc,resid]=armax1(r,s,q,y,u [,b0f])

Arguments

:y output signal : :u input signal : :r,s,q auto regression orders with r >=0, 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

: :arc is tlist with type “ar” and fields a, b, d, ny, nu, sig

:a is the vector [1,a1,...,a_r] : :b is the vector [b0,......,b_s] : :d is the vector [1,d1,....,d_q] : :sig resid=[ sig*echap(1),....,]; :

:

Description

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

Important notice

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.