Kalman filtering in non-Gaussian environment using efficient score function approximation

The authors consider the problem of Kalman filtering in a non-Gaussian environment. It has been shown that a state estimate with a linear prediction corrected by a weighted score function can solve this problem, and the results are nearly optimal. However, the calculation of the score function requires a convolution of two density functions, which is difficult to implement except for simple cases. The authors propose an adaptive normal-expansion-based-distribution approximation for the efficient evaluation of the score function. It is shown that this method is simple and practically feasible. Simulations are also provided to demonstrate the success of the algorithm.