Nonlinear estimation of a recursive state variable track: A Gaussian to non-Gaussian transformation as a function of signal to noise ratio.

Recursive tracking filters seek to obtain real time estimates of the target state space vector through a process of prediction and update. For linear, Gaussian system models the filter algorithm quickly reduces to the optimal solution of the well known Kalman filter. When the system involves non-Gaussian or nonlinear behavior, the optimal solution is often intractable due to the nature of the integrals found in the expected value formulations. Since the solution cannot be found analytically, integral approximations lead to sub-optimal variations of the Kalman filter. In this research, I examine the accuracy of two broad groups of filtering methods: the Gaussian noise approximation Kalman filters (or non-particle based filters) and the particle based estimation filters. The effectiveness of these groups of filters is examined through a Gaussian to non-Gaussian transformation of a real world target signal model.