S2KF: The Smart Sampling Kalman Filter

An accurate Linear Regression Kalman Filter (LRKF) for nonlinear systems called Smart Sampling Kalman Filter (S²KF) is introduced. It is based on a new low-discrepancy Dirac Mixture approximation of Gaussian densities. The approximation comprises an arbitrary number of optimally and deterministically placed samples in the entire state space, so that the filter resolution can be adapted to either achieve high-quality results or meet computational constraints. For two samples per dimension, the S²KF comprises the UKF as a special case. With an increasing number of samples, the new filter quickly converges to the (typically infeasible) exact analytic LRKF. The S²KF can be seen as the ultimate generalization of all sample-based LRKFs such as the UKF, sigma-point filters, higher-order variants etc., as it homogeneously covers the state space with an arbitrary number of samples. It is evaluated by performing extended target tracking.