MODELING AND ESTIMATION OF DISCRETE-TIME GAUSSIAN RECIPROCAL PROCESSES

In this paper, discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. It is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. Finally, it is shown that the smoothing error is itself a reciprocal process. © 1990 IEEE