Recursive filtering and smoothing for reciprocal Gaussian processes-pinned boundary case

The least square estimation problem for pinned-to-zero discrete-index reciprocal Gaussian processes in additive white noise is solved, thus completing and extending some previous results available in the literature. In particular, following the innovations approach a (finite) set of recursive equations is obtained for the filter and for the three standard classes of smoothers (fixed-point, fixed-interval, fixed-lag). Recursive expressions for the mean square performance of the proposed estimators are also given