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arsimul
armax simulation
Syntax
[z]=arsimul(a,b,d,sig,u,[up,yp,ep]) [z]=arsimul(ar,u,[up,yp,ep])
Arguments
- ar
an armax process. See armac.
- a
is the matrix
[Id,a1,...,a_r]
of dimension (n,(r+1)*n)- b
is the matrix
[b0,......,b_s]
of dimension (n,(s+1)*m)- d
is the matrix
[Id,d_1,......,d_t]
of dimension (n,(t+1)*n)- u
is a matrix (m,N), which gives the entry u(:,j)=u_j
- sig
is a (n,n) matrix e_{k} is an n-dimensional Gaussian process with variance I
- up, yp
optional parameter which describe the past.
up=[ u_0,u_{-1},...,u_{s-1}]
;yp=[ y_0,y_{-1},...,y_{r-1}];
ep=[ e_0,e_{-1},...,e_{r-1}]
; if they are omitted, the past value are supposed to be zero- z
z=[y(1),....,y(N)]
Description
simulation of an n-dimensional armax process
A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)
A(z)= Id+a1*z+...+a_r*z^r; ( r=0 => A(z)=Id) B(z)= b0+b1*z+...+b_s z^s; ( s=-1 => B(z)=[]) D(z)= Id+d1*z+...+d_t z^t; ( t=0 => D(z)=Id)
z et e are in R^n
et u in R^m
Method
a state-space representation is constructed and an ode with the option
"discrete"
is used to compute z
.
Examples
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