Improvements for Sparse Grid Tiles (STile) Filter

In this paper we present an advanced version of the Sparse-Grid-Tiles (STile) Filter. With increasing calculation power of modern systems, the focus of Stochastic Filtering turns to nonlinear effects. Sophisticated methods have to be investigated in application areas, where linearized methods like the Extended Kalman Filter tend to suboptimality or even divergence and conservative Particle Filters are insufficient due to the curse of dimension. The STile Filter algorithm approximates the probability distribution on an adaptive set of sparse grid tiles. The motivation of sparse grids is to achieve the approximation order of a regular grid by a specific subset of grid points. The numerical improvements of this paper enhance the speed and accuracy of the algorithm. Finally, robustness against measurement errors is achieved by Integrity Monitoring. We compare and analyze three methods in a Monte Carlo setting.