Optimal Estimation for Hidden Markov and Hidden Reciprocal Processes
| SPEAKER: | Prof. L.B. White |
| DATE: | Monday, 9th November 2009 |
| TIME: | 2:10pm |
| VENUE: | EM316 Directions |
- Abstract:
This presentation will outline some important new results associated with optimal estimation of finite state random processes. In particular, we prove, by choosing appropriate state and observation spaces, in the manner of Elliott and Moore, that an optimal linear estimator is itself optimal. Thus we establish an a priori lower bound on the mean square estimation error for any finite state process. This is a significant result. Recursive optimal fixed-interval smoothers are derived for both hidden Markov processes and hidden Reciprocal processes with finite state and observation spaces. These estimators are linear. Reciprocal processes are non-causal generalisations of Markov processes and correspond to one-dimensional Markov random fields (although they are not Markov). We also derive associated models for the error processes and show that the optimal smoothers may be interpreted as a "copy" of the signal model driven by the estimation error. Thus we can emulate many of the nice properties associated with the estimation of Gauss-Markov and Gaussian reciprocal processes which have been previously derived (eg Levy, Frezza, Krener 1990). We indicate several possible generalisations including to two dimensional Markov random fields as used in image processing, and general nearest-neighbour models for processes defined on a graph.
- Biography:
Lang White graduated from the University of Queenland, Brisbane Australia with degrees in Mathematics (1984), Electrical Engineering (1985) and Ph D (1989). From 1986 to 1999, he worked with the Defence Science and Technology Organisation Australia until taking up a Chair at the University of Adelaide, where he is now Professor of Telecommunications Engineering. Prof White's research interests are broadly in the areas of signal processing, control and artificial intelligence and applications.
