A polynomial-adaptive scheme for Bayesian tracking

A grid-based Bayesian tracking approach is presented in which the traditional piecewise-constant model of the probability over a grid cell is replaced with a polynomial model of higher order. This method extends p-adaptive finite element methods to Bayesian target tracking and state estimation. Through a passive sonar tracking example, the computational efficiency of moving to higher order models instead of increasing grid cell resolution is demonstrated. Comparisons are made between increases in global grid resolution, global polynomial order, and local polynomial order around detailed features of the probability surface.