Unscented type kalman filter: limitation and combination

This study investigates the shortcomings of existing unscented type Kalman filters (UTKFs) used for state estimation problem of non-linear stochastic dynamic systems. There are three kinds of UTKFs - the traditional unscented Kalman filter, the cubature Kalman filter and the transformed unscented Kalman filter. It was demonstrated in the past that these algorithms could capture the posterior mean and covariance accurately to the second order for any non-linearity when propagated through the true non-linear system. However, they yield different information on the higher order terms. Owing to the dualistic effect of higher order terms on the performance of these algorithms, it is desirable to come up with some solution to preserve the positive effect of this information in a single algorithm. Based on the assumption that the state measurements are Guassian, two methods are proposed in this work as the suitable candidates. The first one is an adaptive method that chooses the UTKF achieving the highest value of the likelihood function. The second method treats these algorithms as sub-filters and uses the partitioning approach to obtain an overall estimate. The numerical simulations show that the proposed methods can have comparable performances as one of the best UTKFs for the problems under consideration.