The spherical simplex unscented transformation

This paper describes a new and better-behaved sigma point selection strategy for the unscented transformation (UT). The UT approximates the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The UT works by constructing a set of points, referred to as sigma points, which have the same known statistics as the given estimate. This paper describes a sigma point selection strategy that requires, for n dimensions, n+2 sigma points; and n+1 of these points lie on a hypersphere whose radius is proportional to √n. The weights on each point are proportional to 1/n. We illustrate the algorithm through an example which uses simultaneous localisation and map building.