Man Scilab

rpem
Scilab Function

rpem - RPEM estimation

Calling Sequence

[w1,[v]]=rpem(w0,u0,y0,[lambda,[k,[c]]])

Parameters

Description

Recursive estimation of parameters in an ARMAX model. Uses Ljung-Soderstrom recursive prediction error method. Model considered is the following:


y(t)+a(1)*y(t-1)+...+a(n)*y(t-n)=
b(1)*u(t-1)+...+b(n)*u(t-n)+e(t)+c(1)*e(t-1)+...+c(n)*e(t-n)
   
    

The effect of this command is to update the estimation of unknown parameter theta=[a,b,c] with

a=[a(1),...,a(n)], b=[b(1),...,b(n)], c=[c(1),...,c(n)] .

Optional parameters

  • lambda : optional parameter (forgetting constant) choosed close to 1 as convergence occur:

    lambda=[lambda0,alfa,beta] evolves according to :

    
    lambda(t)=alfa*lambda(t-1)+beta 
       
            

    with lambda(0)=lambda0

    k : contraction factor to be chosen close to 1 as convergence occurs.

    k=[k0,mu,nu] evolves according to:

    
    k(t)=mu*k(t-1)+nu 
       
            

    with k(0)=k0 .

    c : large parameter.( c=1000 is the default value).

  • Output parameters:

    w1 : update for w0 .

    v : sum of squared prediction errors on u0, y0 .(optional).

    In particular w1(1) is the new estimate of theta . If a new sample u1, y1 is available the update is obtained by:

    [w2,[v]]=rpem(w1,u1,y1,[lambda,[k,[c]]]) . Arbitrary large series can thus be treated.

    Back