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armax1(1) Scilab Function armax1(1)
NAME
armax1 - armax identification
CALLING SEQUENCE
[a,b,d,sig,resid]=armax1(r,s,q,y,u,[b0f])
PARAMETERS
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 sup-
posed to be zero and is not identified
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 identifica-
tion) 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 sequen-
tial version of armax
AUTHOR
J.-Ph.C
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