I am interested in the theoretical limit of parameter and state estimation under the measurement origin uncertainty. As a tradition in estimation theory, one often uses the lower bound of the estimation error covariance, e.g., the well-known Cramer-Rao lower bound (CRLB) to quantify the best performance that an algorithm can achieve. The approach has been extended to the state estimation problem with a recursive formula to compute the posterior CRLB. Due to the measurement origin uncertainty, the CRLB is shown to increase with the Fisher information matrix being multiplied by a scalar information reduction factor (IRF). When the target also has motion uncertainty being modeled by a set of different dynamic equations, the system is hybrid, i.e., it contains both continuously and discretely distributed parameters which in general do not satisfy the regularity conditions hence the CRLB can not be applied. A more general lower bound, namely, the Weiss-Weinstein lower bound (WWLB) is free from the regularity conditions and it covers both the CRLB and the Bobrovsky-Zakai lower bound as its special cases.

In order to use the WWLB, one has to know the joint distribution of both continuously and discretely distributed parameters. Unfortunately, the computation of this joint distribution is very cumbersome in a hybrid system. In viewing this and the available recursive formula to compute the posterior CRLB, I would like to develop a recursive algorithm that only uses the transitional state distribution to compute the WWLB. Such a lower bound should incorporate both target motion and measurement origin uncertainties so that it quantifies the best performance among all practical algorithms. Preliminary study indicates that the information reduction due to both measurement origin uncertainty and target motion uncertainty can not be summarized by a scalar. Surprisingly, the information reduction term can be decomposed into two matrices being pre-multiplied and post-multiplied to the inverse of WWLB of the target-motion-certain and measurement-origin-certain case. I plan to study the tightness of the WWLB and the practical algorithms to compute the information reduction terms efficiently for various clutter densities. My research has been supported in part by ARO and an SBIR subcontract.

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People working in Estimation and Signal Processing area with online publications

Alfred Hero at UMich, Jose M.F. Moura at CMU, Lang Tong at Cornell, Yonina Eldar at Technion, Ali H Sayed at UCLA

People working in Information Theory and Communication area with online publications

P R Kumar at UIUC, S Verdu at Princeton, David Tse at UC Berkeley, M. K Varanasi at UColorado, J M Cioffi at Stanford

N Merhav at Technion, B Hassibi at Caltech, David MacKay at Cambridge, J A O’Sullivan at Washington Univ. in St Louis

G B Giannakis at U Minnesota, A Goldsmith at Stanford