Stochastic Realisation and Optimal Smoothing for Gaussian Generalised Reciprocal Processes

This paper derives stochastic realisation algorithms for a class of Gaussian Generalised Reciprocal Processes (GGRP). The paper exploits the interplay between reciprocal processes and Markov bridges which underpin the GGRP model, to derive forwards-backwards state equations for realisation of a GGRP. The form on the inverse covariance matrix for the GGRP is derived, and its Cholesky factorisation can used to also construct the optimal (MMSE) smoother of GGRP observed in noise. The paper claims that the associated smoothing error is also a GGRP with known covariance which may be used to assess the performance of smoothing as a function of the model parameters. Full details are provided in a forthcoming journal paper.