Optimized selection of sigma points in the unscented Kalman filter

The unscented Kalman filter (UKF) is an extension of the Kalman filter for nonlinear systems where a set of weighted sigma points are used to simulate the distribution of the state random variable. The performance of the filter depends heavily on the selection of sigma points, and the computational cost is proportional to the number of sigma points used. It was previously shown that n + 2 (but not fewer) points are able to constitute a well-behaved set of sigma points. In this paper we show that this number can be further reduced to n + 1. Numerical comparison of this optimized sigma point selection strategy with other strategies is also provided.