Nonlinear projection filter for target tracking using range sensor & optical tracker

Target tracking filters have a variety of applications in various areas. Typically, a radar provides the range measurement and an optical sensor measures the orientation of a target. The measurements provided by the sensors have very strong nonlinearities with the states of the target given in the Cartesian coordinates while its dynamics is linear parameter time-varying. The time-varying component exists because of the unknown acceleration input in the target. Nonlinear projection filter provides a solution to the nonlinear estimation problem by approximating the solution as a linear combination of orthogonal basis functions. The analytic expression for propagating the joint probability density function is derived for the target tacking problem and this reduces large amount of computation times, where the filter equations are normally obtained numerically. The effectiveness of the filter is demonstrated by a numerical simulation.