Target Tracking using Kalman Filter

Abstract

Target tracking is an important field of research in current decade. In target tracking we basically estimate future state of a target depending on its past records. So we require an estimator which is based on sequential state estimation. Kalman filter is the linear minimum variance estimator which is based on sequential state estimation. So for linear model Kalman Filter (KF) is used and for non linear model Extended Kalman Filter (EKF) is used. Here KF and EKF are used for tracking of targets. Kalman filter basically combines two random quantities to reduce the variance of the final combination. As the purpose of every estimator is to accurately estimate the parameter under consideration and accuracy will be more if variance is less, so Kalman filter is optimal in mean square error sense. Kalman filter is an optimal filter if the noise covariances are known to the filter before its operation. If those values are taken wrongly then Kalman filter may diverge. So it is very required to know the value of those parameters for which mean square error will be minimized.
Particle Swarm Optimization (PSO) is a technique which is used to optimize function. Here PSO is used to optimize mean square error of estimation by finding appropriate values of both process noise covariance and measurement noise covariance. Both the values of noise covariances are found by PSO and they are used in Kalman filter to minimize actual estimate error for better accuracy.