Scilab Function

wiener - Wiener estimate

### Calling Sequence

[xs,ps,xf,pf]=wiener(y,x0,p0,f,g,h,q,r)

### Parameters

• f, g, h : system matrices in the interval [t0,tf]
• f =[f0,f1,...,ff], and fk is a nxn matrix
• g =[g0,g1,...,gf], and gk is a nxn matrix
• h =[h0,h1,...,hf], and hk is a mxn matrix
• q, r : covariance matrices of dynamics and observation noise
• q =[q0,q1,...,qf], and qk is a nxn matrix
• r =[r0,r1,...,rf], and gk is a mxm matrix
• x0, p0 : initial state estimate and error variance
• y : observations in the interval [t0,tf]. y=[y0,y1,...,yf], and yk is a column m-vector
• xs : Smoothed state estimate xs= [xs0,xs1,...,xsf], and xsk is a column n-vector
• ps : Error covariance of smoothed estimate ps=[p0,p1,...,pf], and pk is a nxn matrix
• xf : Filtered state estimate xf= [xf0,xf1,...,xff], and xfk is a column n-vector
• pf : Error covariance of filtered estimate pf=[p0,p1,...,pf], and pk is a nxn matrix

### Description

function which gives the Wiener estimate using the forward-backward Kalman filter formulation

C. B.