Tracking and Interception of a Ballistic Target on Reentry Using Adaptive Gaussian Sum Quadrature Filters

Abstract

In this work, new nonlinear filtering algorithms based on Gaussian sum framework is formulated and then applied to track a ballistic target on reentry. Other than representing the predicted and updated probability density function of states given measurements as a sum of weighted Gaussian densities, a weight update scheme in time update step is also considered. This weight update scheme is based on a quadratic optimization problem that minimizes the integral square error between the true and the approximated prior density. The Gaussian densities in the weighted sum is realized using various quadrature filters. These filters are applied to track a ballistic target on reentry using measurements from an inbuilt seeker of an interceptor missile, where a 6 degrees of freedom state-dependent coefficient model (SDC) of target–interceptor dynamics is considered. Further, the estimated states are provided to a guidance law for generating interceptor missile accelerations. For performance analysis, root mean square error (RMSE) of relative states and also the range between target and interceptor when they cross each other (miss-distance) are considered. It was found that the miss-distances obtained from the Gaussian filters are smaller than that of the conventional EKF. Further, the Gaussian sum and its weight adaptation scheme with quadrature filter proposals provided far better results, with the weight adaptation filters giving more accurate miss-distances.