Numerical grid-generation algorithms are becoming more critical due to the need for detailed modeling of the geometry of the physical domain and as part of solution-adaptive algorithms. Current planar grid generation algorithms are not robust because they frequently produce skewed or folded grids. These problems can be corrected by trial and error modifications (e.g., to the source term of a Poisson equation), but the procedure is far from automatic. Mathematical analysis will be used to clarify the limitations of current algorithms velocity. The probability density function of the observed aircraft will be propagated between arrivals of new target reports by means of the numerical solutions of a partial differential equation satisfied by the density. The partial differential equation for the density is obtained by applying Kolmogorov's forward equation to the original stochastic differential equation. The resulting non-Gaussian density will be combined with new reports using Bayesian methods to update estimates of aircraft position. In order to perform the tracking function in real time, the algorithm will be designed to work in a parallel computing environment.The potential commercial application as described by the awardee: The greatest potential for commercial use of the proposed process lies in the increased performance of automated detection and tracking systems, in both the commercial and military aviation sectors. Other areas of commercial application include computer simulations in weather prediction, biological modeling, and fluid dynamics.
