Scilab Function
Last update : 12/01/2004

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

### Author

C. B.