wiener

Scilab Function
Last update : 25/04/2007

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.