A Real-life Benchmark Study on the Weights of the Symmetric Unscented Kalman-filter

The paper discusses the widely used symmetric Unscented Transformations applied in Kalman-filtering and shows new multiscaled derivations based on the Taylor-series expansion. The methods with different parameters are compared numerically. The results showed that although the scaled and Taylor-series-based methods perform well for polynomial functions, they do not overwhelm the original UT in a real-life localisation problem. Furthermore, the numerical analysis showed how dangerous the methods with negative $W_{0}$ weight are in Kalman-filtering-related computations for functions with more variables.