Closed optimal dimension reduction for skew-filtering

Skewed Kalman filtering is a powerful tool for statistical inference of measurements with asymmetric noise. However, it suffers from the problem of increasing dimensionality during recursive estimation, which can present a numerical computational barrier. Although a number of techniques exist to provide solutions, these methods are usually too complex for multidimensional problems. In this paper, a new optimisation scheme is proposed to reduce the dimensionality of the skewness of the closed skew normal distribution, and the solution of this optimisation scheme is analytical, which greatly improves the computational efficiency. The effectiveness of the proposed method is then shown through numerical examples. The results show that the method facilitates recursive state estimation in the presence of skewed noise.