Bayesian estimation via sequential Monte Carlo sampling-Constrained dynamic systems.

*(English)*Zbl 1128.93387Summary: Nonlinear and non-Gaussian processes with constraints are commonly encountered in dynamic estimation problems. Methods for solving such problems either ignore the constraints or rely on crude approximations of the model or probability distributions. Such approximations may reduce the accuracy of the estimates since they often fail to capture the variety of probability distributions encountered in constrained linear and nonlinear dynamic systems. This article describes a practical approach that overcomes these shortcomings via a novel extension of sequential Monte Carlo (SMC) sampling or particle filtering. Inequality constraints are imposed by accept/reject steps in the algorithm. The proposed approach provides samples representing the posterior distribution at each time point, and is shown to satisfy the same theoretical properties as unconstrained SMC. Illustrative examples show that results of the proposed approach are at least as accurate as moving horizon estimation, but computationally more efficient and in addition, the approach indicates the uncertainty associated with these estimates.

##### MSC:

93E10 | Estimation and detection in stochastic control theory |

93C10 | Nonlinear systems in control theory |

62L10 | Sequential statistical analysis |

93E11 | Filtering in stochastic control theory |

93C55 | Discrete-time control/observation systems |

##### Keywords:

constrained estimation; extended Kalman filter; particle filter; moving horizon estimation; data rectification
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\textit{L. Lang} et al., Automatica 43, No. 9, 1615--1622 (2007; Zbl 1128.93387)

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