A new finite-time linear smoothing filter
Michael John Grimble · International Journal of Systems Science · 1980
A new time-invariant linear smoothing filter is derived for finite data records. The message generating process is assumed to be represented by constant state equations driven by stationary white noise. The smoothing filter transfer function matrix is obtained by solving the finite-time Wiener-Hopf equation in the ε-domain. The filter has the property that it produces an optimal state estimate [xcirc](T1 |T) at the end of a fixed interval of length [0, T], At other times within the interval the filtor acts as a fixed-lag smoother and gives a sub-optimal state estimate [xcirc](t 1|t). At times t< T the filter has a fixed memory length. The more conventional optimal time-varying smoother may also be calculated using the expression for the time-invariant smoother impulse response matrix. The major advantage of the time-invariant smoother lies in the ease of implementation. The stability of these smoothing filters is discussed and examples are given of the calculation procedure.