Online Bayesian Estimation of Transition Probabilities for Markovian Jump Systems

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link SUMMARYThis paper combines the finite impulse response filtering with the Kalman structure (predictor/corrector) and proposes a fast iterative bias-constrained optimal finite impulse response filtering algorithm for linear discrete time-invariant models. In order to provide filtering without any requirement of the initial state, the property of unbiasedness is employed. We first derive the optimal finite impulse response filter constrained by unbiasedness in the batch form and then find its fast iterative form for finite-horizon and full-horizon computations. The corresponding mean square error is also given in the batch and iterative forms. Extensive simulations are provided to investigate the trade-off with the Kalman filter. We show that the proposed algorithm has much higher immunity against errors in the noise covariances and better robustness against temporary model uncertainties. The full-horizon filter operates almost as fast as the Kalman filter, and its estimate converges with time to the Kalman estimate.

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“…Note that this model is used in moving target tracking [38] and some related results can be found in [7,21,24].…”

Section: Simulationsmentioning

confidence: 99%

Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

Zhao

Shmaliy

et al. 2016

Adaptive Control & Signal

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“…Methods in this category start with an initial representation of the model of the system and updates this model as more data is observed from the environment [16]. After updating the model representation, a new policy is obtained by applying a dynamic programming (DP) algorithm suitable to work in real time, such as asynchronous dynamic programming [14].…”

Section: Adaptive Dynamic Programming (Adp)mentioning

confidence: 99%

Adaptive Planning for Markov Decision Processes with Uncertain Transition Models via Incremental Feature Dependency Discovery

Üre

Geramifard

Chowdhary

et al. 2012

Machine Learning and Knowledge Discovery in Databases

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Abstract. Solving large scale sequential decision making problems without prior knowledge of the state transition model is a key problem in the planning literature. One approach to tackle this problem is to learn the state transition model online using limited observed measurements. We present an adaptive function approximator (incremental Feature Dependency Discovery (iFDD)) that grows the set of features online to approximately represent the transition model. The approach leverages existing feature-dependencies to build a sparse representation of the state transition model. Theoretical analysis and numerical simulations in domains with state space sizes varying from thousands to millions are used to illustrate the benefit of using iFDD for incrementally building transition models in a planning framework.

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“…The off-line design method sets the TPM a priori as a design parameter. In the online method, the TPM is adaptable and is set by the process of quasi Bayesian estimator while filtering for tracking [6]. The existing TPM setting methods perform well when the affect of meteorological environment can be neglect, which is not the case in GA target tracking.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy logic-based multi-factor aided multiple-model filter for general aviation target tracking

Wang

Huang

Huang³

2015

IFS

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Abstract.A fuzzy logic-based multi-factor aided multiple-model filter (FLMAMMF) for General aviation (GA) maneuvering target tracking (MTT) is presented. The target category and meteorological information are introduced into the interacting multiple model (IMM) filter to perform GA target tracking. Fuzzy logic inference is employed in the proposed algorithm to reflect the complicated relationship between these two factors and the transition probability matrix (TPM). Both the number of models in model set and the transition probabilities between models are adjusted through fuzzy inference. Simulation results show that the proposed method is efficient and effective.

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Online Bayesian Estimation of Transition Probabilities for Markovian Jump Systems

Cited by 120 publications

References 29 publications

Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

Adaptive Planning for Markov Decision Processes with Uncertain Transition Models via Incremental Feature Dependency Discovery

Fuzzy logic-based multi-factor aided multiple-model filter for general aviation target tracking

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