Observability and Filter Stability for Partially Observed Markov Processes

“…2.4] [32, Assumption A2]. Similar considerations also inform [19], [33] where N step observability is defined for an HMM. The definition has many attractive features, e.g., it is relatively easier to compute (as compared to stochastic observability) and is useful for filter and control design.…”

Section: Stochastic Models (Hmms)mentioning

confidence: 99%

Duality for Nonlinear Filtering I: Observability

Kim¹,

Mehta²

2022

Preprint

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This paper is concerned with the development and use of duality theory for a hidden Markov model (HMM) with white noise observations. The main contribution of this work is to introduce a backward stochastic differential equation (BSDE) as a dual control system. A key outcome is that stochastic observability (resp. detectability) of the HMM is expressed in dual terms: as controllability (resp. stabilizability) of the dual control system. All aspects of controllability, namely, definition of controllable space and controllability gramian, along with their properties and explicit formulae, are discussed. The proposed duality is shown to be an exact extension of the classical duality in linear systems theory. One can then relate and compare the linear and the nonlinear systems. A side-by-side summary of this relationship is given in a tabular form (Table II).

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Introduction

Yüksel,

Başar

2024

Systems &Amp; Control: Foundations &Amp; Applications

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Observability and Filter Stability for Partially Observed Markov Processes

Cited by 7 publications

References 10 publications

Robustness to Approximations and Model Learning in MDPs and POMDPs

Robustness to Approximations and Model Learning in MDPs and POMDPs

Duality for Nonlinear Filtering I: Observability

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