Linear Optimal Prediction and Innovations Representations of Hidden Markov Models

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Abstract

The topic of this paper is linear optimal prediction of hidden Markov models (HMMs) and innovations representations of HMMs. Our interest in these topics primarily arise from subspace estimation methods, which are intrinsically linked to such representations. For HMMs, derivation of innovations representations is complicated by non-minimality of the corresponding state space representations, and requires the solution of algebraic Riccati equations under non-minimality assumptions.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Control Engineering
  • Probability Theory and Statistics

Keywords

  • Non-minimality, Kalman filter, Hidden Markov model, Innovations representation, Prediction error representation, Riccati equation
Original languageEnglish
Pages (from-to)131-149
JournalStochastic Processes and their Applications
Volume108
Issue number1
Publication statusPublished - 2003
Publication categoryResearch
Peer-reviewedYes