A new perspective on Gaussian sigma-point Kalman filters

There are a variety of Gaussian sigma-point Kalman filters (GSPKF) existing in the literature which are based on different quadrature rules. Their performances are always compared with each other on accuracy and robustness from the numerical-integration perspective, where the number of the sigma points and their corresponding weights are the main reasons resulting in the different accuracy. A new perspective on the GSPKF is proposed in this paper, which is the Mahalanobis distance ellipsoid (MDE). From the MDE perspective, GSPKFs differ from each other on accuracy and robustness mainly because they enclose different probability concentrations. This characteristic is evident when using the high-degree GSPKFs to filter the low-dimensional nonlinear systems. Two classical nonlinear system examples are used to demonstrate the proposed point of this paper. Moreover, some suggestions are given on how to select an appropriate GSPKF for a given nonlinear system.