Performance analysis of deterministic sampling filters

This paper deals with a type of nonlinear filters. The deterministic sampling filters (DSFs), including the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF), which use a set of deterministically chosen points to calculated the transformed mean and covariance, are extensions of the Kalman filter to nonlinear systems. The sampling methods coincide with the integration rules and can be seen as a special case of degree 3 integration rules. The stability of the filters is discussed from the integration and covariance perspective. The freedom parameter in the samples is critical to the stability and a strategy of choosing the parameter is given to improve the stability. The proposed strategy is illustrated by a numerical example.