This technical note derives stochastic realisation and optimal smoothing algorithms for a class of Gaussian Generalised Reciprocal Processes (GGRP). The note exploits the interplay be- tween reciprocal processes and Markov bridges which underpin the GGRP model. A forwards-backwards algorithm for stochastic realisation of GGRP is described. The form on the inverse covari- ance matrix for the GGRP is used, via Cholesky factorisation, to derive a procedure for optimal (MMSE) smoothing of GGRP observed in noise. The note demonstrates 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. A numerical example is provided to illustrate the performance of the MMSE smoother compared to those derived from compatible Markov and Reciprocal model based algorithms.
State Space Realisations and Optimal Smoothing for Gaussian Generalized Reciprocal Processes
Francesco Carravetta
2019
Abstract
This technical note derives stochastic realisation and optimal smoothing algorithms for a class of Gaussian Generalised Reciprocal Processes (GGRP). The note exploits the interplay be- tween reciprocal processes and Markov bridges which underpin the GGRP model. A forwards-backwards algorithm for stochastic realisation of GGRP is described. The form on the inverse covari- ance matrix for the GGRP is used, via Cholesky factorisation, to derive a procedure for optimal (MMSE) smoothing of GGRP observed in noise. The note demonstrates 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. A numerical example is provided to illustrate the performance of the MMSE smoother compared to those derived from compatible Markov and Reciprocal model based algorithms.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.