State estimation of manoeuvring targets from noisy radar measurements

Analytical results for tracking manoeuvring targets from noisy radar measurements are presented. A three-dimensional mathematical model based on the Kalman filtering technique is discussed for the tracking of a manoeuvring aircraft using noisy measurements obtained from a three-dimensional radar. The measurement uncertainties and the manoeuvre characteristics are assumed to be known in polar co-ordinates, and are also assumed to be white Gaussian with zero mean and constant variance. These are coupled to the cartesian co-ordinate system selected for tracking operation. The elements of the covariance and Kalman gain matrices are expressed in terms of those which apply for tracking in polar co-ordinates. The steady-state results are expressed in compact form by appropriately partitioning the covariance matrices. The numerical computations of the steady-state filter parameters of the model are in excellent agreement with those obtained from the recursive Kalman filter matrix equations. Hence these results are of practical interest in developing trackers for tracking manoeuvring aircraft and to eliminate the real-time execution of the complete filter equations.