## I-A Stochastic Filtering Theory............... 2

### BibTeX

@MISC{Chen_i-astochastic,

author = {Zhe Chen},

title = {I-A Stochastic Filtering Theory............... 2},

year = {}

}

### OpenURL

### Abstract

Abstract — In this self-contained survey/review paper, we systematically investigate the roots of Bayesian filtering as well as its rich leaves in the literature. Stochastic filtering theory is briefly reviewed with emphasis on nonlinear and non-Gaussian filtering. Following the Bayesian statistics, different Bayesian filtering techniques are developed given different scenarios. Under linear quadratic Gaussian circumstance, the celebrated Kalman filter can be derived within the Bayesian framework. Optimal/suboptimal nonlinear filtering techniques are extensively investigated. In particular, we focus our attention on the Bayesian filtering approach based on sequential Monte Carlo sampling, the so-called particle filters. Many variants of the particle filter as well as their features (strengths and weaknesses) are discussed. Related theoretical and practical issues are addressed in detail. In addition, some other (new) directions on Bayesian filtering are also explored.

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(Show Context)
Citation Context ... accurate degree by a sufficiently large number of Gaussian mixture densities, which admits tractable solution by calculating individual first and second order moments. The Gaussian sum filter [421], =-=[8]-=-, essentially uses this idea and runs a bank of EKFs in parallel to obtain the suboptimal estimate. The following theorem reads the underlying principle: Theorem 2: [12] Suppose in equations (2a)(2b) ... |

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Citation Context ...ails can be found in the thesis of Brigo [55]. C. Interacting Multiple Models One of important Bayesian filtering methods in literature is the multiple models, e.g., generalized pseudo-Bayesian (GPB) =-=[1]-=-, interacting multiple models (IMM) [27], which are widely used in the data association and target tracking [501], [28]. The intuition of using multiple models is to tackle the multiple hypotheses pro... |

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(Show Context)
Citation Context ...cated, weighted, and propagated recursively according to the Bayesian rule. In retrospect, the earliest idea of Monte Carlo method used in statistical inference is found in [200], [201], and later in =-=[5]-=-, [6], [506], [433], [258], but the formal establishment of particle filter seems fair to be due to Gordon, Salmond and Smith [193], who introduced certain novel resampling technique to the formulatio... |

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Citation Context ...ntion is deserved. Though theoretically attractive, the implementation of partitioned sampling is quite complicated, the de58 It was also called the localization sampling or local multiple imputation =-=[3]-=-. tails are left for the interested reader and not discussed here. H. Data Augmentation The data augmentation idea arises from the missing data problem, it is referred to a scheme of augmenting the ob... |

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(Show Context)
Citation Context ..., weighted, and propagated recursively according to the Bayesian rule. In retrospect, the earliest idea of Monte Carlo method used in statistical inference is found in [200], [201], and later in [5], =-=[6]-=-, [506], [433], [258], but the formal establishment of particle filter seems fair to be due to Gordon, Salmond and Smith [193], who introduced certain novel resampling technique to the formulation. Al... |