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Linear Filtering and State Space Representations of Hidden Markov Models

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Author

Summary, in English

The topic of this paper is linear filtering of hidden Markov models (HMMs) and linear innovation form representations of HMMs. The possibility to represent the widely used HMM as a state space model is interesting in its own respect, but our interest also comes from subspace estimation methods. To be able to fit the HMM into the framework of subspace methods the process needs to be formulated in state space form. This reformulation is complicated by the non-minimality within the state space representation of the HMM. The reformulation involves deriving solutions to algebraic Riccati equations which are usually treated under minimality assumptions.

Publishing year

2002

Language

English

Publication/Series

Preprints in Mathematical Sciences

Issue

2002:5

Document type

Report

Publisher

Center for Mathematical Sceinces, Lund University

Topic

  • Probability Theory and Statistics

Status

Published

Report number

LUTFMS-5019-2002