LRKF Revisited- The Smart Sampling Kalman Filter (S²KF)

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1 December 2014
Jannik Steinbring, Uwe D. Hanebeck

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An accurate Linear Regression Kalman Filter (LRKF) for non-linear systems called Smart Sampling Kalman Filter (S2KF) is introduced. In order to get a better understanding of this new filter, a general introduction to Nonlinear Kalman Filters based on statistical linearization and LRKFs is given. The S2KF is based on a new low-discrepancy Dirac mixture approximation of Gaussian densities. This approximation comprises an arbitrary number of optimally and deterministically placed samples in the relevant regions of the state space, so that the filter resolution can be adapted to either achieve high-quality results or to meet computational constraints. The S2KF contains the UKF with equally weighted samples as a special case when using the same amount of samples. With an increasing number of samples, the new filter converges to the (typically unfeasible) exact analytic statistical linearization. Hence, the S2KF can be seen as the ultimate generalization of all LRKFs such as the UKF, sigma-point filters, higher-order variants etc., as it homogeneously covers the state space with a freely chosen number of samples. It is evaluated against state-of-the-art LRKFs by performing nonlinear prediction and extended target tracking.