Generalizing the unscented Kalman filter for state estimation

The recent generalized unscented transform (GenUT) is formulated into a recursive Kalman filter framework. The GenUT constrains 2n + 1 sigma points and their weights to match the first four statistical moments of a probability distribution. The GenUT integrates well into the unscented Kalman filter framework, creating what we call the generalized unscented Kalman filter (GUKF). The measurement update equations for the skewness and kurtosis are derived within. Performance of the GUKF is compared to the UKF under two studies: noise described by a Gaussian distribution and noise described by a uniform distribution. The GUKF achieves lower errors in state estimation when the UKF uses the heuristic tuning parameter κ = 3 − n. It is also stated that when the parameter κ is tuned to an optimal value, the UKF performs identically to the GUKF. The advantage here is that GUKF requires no such tuning.