Nonlinear Bayesian state filtering with missing measurements and bounded noise and its application to vehicle position estimation

Lenka Pavelková

Kybernetika (2011)

  • Volume: 47, Issue: 3, page 370-384
  • ISSN: 0023-5954

Abstract

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The paper deals with parameter and state estimation and focuses on two problems that frequently occur in many practical applications: (i) bounded uncertainty and (ii) missing measurement data. An algorithm for the state estimation of the discrete-time non-linear state space model whose uncertainties are bounded is proposed. The algorithm also copes with situations when some measurements are missing. It uses Bayesian approach and evaluates maximum a posteriori probability (MAP) estimates of states and parameters. As the model uncertainties are supposed to have a bounded support, the searched estimates lie within an area that is described by the system of inequalities. In consequence, the problem of MAP estimation becomes the problem of nonlinear mathematical programming (NLP). The estimation with missing data reduces to the omission of corresponding inequalities in NLP formulation. The proposed estimation algorithm is applied to the estimation of a moving vehicle position when incomplete data from global positioning system (GPS) together with complete data from vehicle sensors are at disposal.

How to cite

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Pavelková, Lenka. "Nonlinear Bayesian state filtering with missing measurements and bounded noise and its application to vehicle position estimation." Kybernetika 47.3 (2011): 370-384. <http://eudml.org/doc/197181>.

@article{Pavelková2011,
abstract = {The paper deals with parameter and state estimation and focuses on two problems that frequently occur in many practical applications: (i) bounded uncertainty and (ii) missing measurement data. An algorithm for the state estimation of the discrete-time non-linear state space model whose uncertainties are bounded is proposed. The algorithm also copes with situations when some measurements are missing. It uses Bayesian approach and evaluates maximum a posteriori probability (MAP) estimates of states and parameters. As the model uncertainties are supposed to have a bounded support, the searched estimates lie within an area that is described by the system of inequalities. In consequence, the problem of MAP estimation becomes the problem of nonlinear mathematical programming (NLP). The estimation with missing data reduces to the omission of corresponding inequalities in NLP formulation. The proposed estimation algorithm is applied to the estimation of a moving vehicle position when incomplete data from global positioning system (GPS) together with complete data from vehicle sensors are at disposal.},
author = {Pavelková, Lenka},
journal = {Kybernetika},
keywords = {non-linear state space model; bounded uncertainty; missing measurements; state filtering; vehicle position estimation; non-linear state space model; bounded uncertainty; missing measurements; state filtering; vehicle position estimation},
language = {eng},
number = {3},
pages = {370-384},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nonlinear Bayesian state filtering with missing measurements and bounded noise and its application to vehicle position estimation},
url = {http://eudml.org/doc/197181},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Pavelková, Lenka
TI - Nonlinear Bayesian state filtering with missing measurements and bounded noise and its application to vehicle position estimation
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 3
SP - 370
EP - 384
AB - The paper deals with parameter and state estimation and focuses on two problems that frequently occur in many practical applications: (i) bounded uncertainty and (ii) missing measurement data. An algorithm for the state estimation of the discrete-time non-linear state space model whose uncertainties are bounded is proposed. The algorithm also copes with situations when some measurements are missing. It uses Bayesian approach and evaluates maximum a posteriori probability (MAP) estimates of states and parameters. As the model uncertainties are supposed to have a bounded support, the searched estimates lie within an area that is described by the system of inequalities. In consequence, the problem of MAP estimation becomes the problem of nonlinear mathematical programming (NLP). The estimation with missing data reduces to the omission of corresponding inequalities in NLP formulation. The proposed estimation algorithm is applied to the estimation of a moving vehicle position when incomplete data from global positioning system (GPS) together with complete data from vehicle sensors are at disposal.
LA - eng
KW - non-linear state space model; bounded uncertainty; missing measurements; state filtering; vehicle position estimation; non-linear state space model; bounded uncertainty; missing measurements; state filtering; vehicle position estimation
UR - http://eudml.org/doc/197181
ER -

References

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