Analytical Results for the x, y Kalman Tracking Filter

A two-dimensional x, y Kalman tracking filter is analyzed for a track-while-scan (TWS) operation when the radar sensor measures range and bearing (r, θ) at uniform sampling intervals T seconds apart. This development explicitly considers the coupling between the quantities measured by the sensor (r, θ) and the Cartesian x, y coordinate system selected for the tracking operation. The steadystate components of the gain and error covariance matrixes are analytically determined under the assumption of a white noise maneuver acceleration model in two dimensions. These results are verified by computer calculation of the Kalman filter matrix equations.