Local Positioning with Parallelepiped Moving Grid

One of the challenges in personal positioning is the efficient numerical solution of the nonlinear filtering equations resulting from the fusion of different measurement sources. One approach to nonlinear filtering is based on approximating probability density functions with piecewise constant functions. In this work, a moving grid filter is outlined and it is applied to the hybrid local positioning problem. Using a linear motion model and a particular uniformly spaced parallelepiped grid design makes the computation load of the method feasible. Numerical test results from a Matlab implementation are presented, and it is found that the grid method is fast enough for real-time implementation.