Cubature Integration Methods in Non-Linear Kalman Filtering and Smoothing
Arno Solin · 2010
Optimal estimation problems arise in various different settings where indirect noisy observations are used to determine the underlying state of a time-varying system. For systems with non-linear dynamics there exist various methods that extend linear filtering and smoothing methods to handle non-linearities. In this thesis the non-linear optimal estimation framework is presented with the help of an assumed density approach. The Gaussian integrals that arise in this setting are solved using two different cubature integration methods. Cubature integration extends the weighted sum approach from univariate quadrature methods to multidimensional cubature methods. In this thesis the focus is put on two methods that use deterministically chosen sigma points to form the desired approximation. The Gauss–Hermite rule uses a simple product rule method to fill the multidimensional space with cubature points, whereas the spherical–radial rule uses invariant theory to diminish the number of points by utilizing symmetries. The