Nonlinear robust estimation for tracking of ballistic target using risk sensitive cubature quadrature Kalman filter

Abstract

Abstract In this paper, a risk sensitive estimator based on cubature quadrature Kalman filter is formulated and applied for tracking a ballistic object during its re-entry phase. The formulated algorithm is named here as risk sensitive cubature quadrature Kalman filter. The process model and measurement model for two dimensional ballistic target motion is described. The expression for measurement noise covariance is derived for Cartesian coordinate from polar coordinate. Also expression for initial error covariance is derived. The performance of the risk sensitive cubature quadrature Kalman filter is compared with the cubature quadrature Kalman Filter in terms of root mean square error. The simulation results reveal that for wrongly modeled process noise parameter, the risk sensitive filter performs better than their risk neutral counterpart. Moreover, risk sensitive cubature quadrature Kalman filter performs better than risk sensitive cubature Kalman filter. Since expression for measurement noise covariance as well as initial error covariance for two dimensional ballistic target motion is derived, other Gaussian filters may also be applied for tracking of ballistic objects. Article Highlights The process model for two dimensional ballistic target motion is described comprehensively. The expression for measurement noise covariance matrix for linear measurement model is derived for Cartesian coordinate from polar coordinate. The expression for initial error covariance matrix for the filter initialized from the first two measurements is derived. Risk sensitive filter based on cubature quadrature Kalman filter is applied for tracking of two dimensional ballistic target motion and improvement in performance over its risk neutral counterpart is found. Improvement in performance of risk sensitive filter based on cubature quadrature Kalman filter over risk sensitive filter based on cubature Kalman filter is found.