Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem
نویسندگان
چکیده
This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian problem, (ii) the ensemble Kalman-Bucy filter (EnKBF) which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems, and (iii) the feedback particle filter (FPF) which represents an extension of the EnKBF and furthermore provides for a consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the gain times innovation feedback structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also describes numerical algorithms for gain function approximation in the FPF as well as their relationship to optimal transport and coupling of measures.
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عنوان ژورنال:
- CoRR
دوره abs/1702.07241 شماره
صفحات -
تاریخ انتشار 2017