Doctoral Dissertations

Date of Award

12-1986

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Electrical Engineering

Major Professor

J. Douglas Birdwell

Committee Members

Suzanne Lenhart, Jack Lawler, Milton Bailey, Joseph Googe

Abstract

This report contains two approaches to nonlinear distributed estimation. The estimator structure is assumed to have a coordinator which contains a correct model of the observed physical process, which is assumed to be Markov, and an arbitrary number of local stations which take measurements of the state of the process and perform local processing. The local stations implement estimation algorithms based upon local models which may be different from the coordinator model and from each other. One-way communication links are assumed to exist from each local station to the coordinator. There is no restriction on the communication link bandwidth. No other communication channel is allowed. The communication links are used to transmit sufficient statistics of the results of the local estimation algorithms to the coordinator.

The objective of this research is to determine under what conditions this estimator structure can be used to implement an algorithm which is functionally equivalent to the centralized estimator. This report defines constraints on the local processing models which guarantee equivalence between the distributed estimator structure and the optimal centralized estimator structure.

Within this framework, the nonlinear distributed estimation problem is solved using two approaches. The first approach (information fusion) combines the local conditional densities to produce the conditional density of the global state of the process, which would have been obtained through a centralized estimation structure using the process (global) model. The second approch (filter inversion) provides conditions which guarantee that each local filter process can be inverted to reconstruct the measurements from the local conditional densities. Using this information a centralized estimation scheme is implemented at the coordinator.

Information fusion requires that the local station implement a locally optimal estimator. Filter inversion does not require this; rather, the local model may be used to preprocess measurement data to reduce the communication requirements. The utility of filter inversion is primarily in the theoretical conditions for nonlinear filter invertibility.

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