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doi:10.1016/0020-0255(74)90002-4 
Copyright © 1974 Published by Elsevier Science Inc.
On optimal nonlinear estimation — Part II: Discrete observation*1
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James Ting-Ho Lo
Received 30 May 1972.
Abstract
A general representation for the joint conditional probability density of an arbitrary random signal process under discrete-time observation is obtained. This representation forms the cornerstone of the paper, and from it all other results are deduced. The conditional densities of prediction and smoothing are expressed in terms of filtering via the application of the general representation. The prediction and smoothing of a random process with linear dynamics and arbitrary a priori distribution are given to illustrate the applicability of the previous results in obtaining effectively computable formulas.
Article Outline
*1 This work was supported in part by the U.S. Army Contract DA-31-124-AR0(D) 394 and NASA Grant NGL 05-020-073 while the author was at Stanford University, and by the U.S. Office of Naval Research under the Joint Services Electronics Program by Contract N00014-67-A-0298-0006 while the author was at Harvard University.
This work was presented at the 1970 IEEE Symp. Adaptive Processes: Decision and Control, Austin, Texas (see [3]).
