Steady-state tracking with LFM waveforms

The steady-state gains and error covariance are derived for a two-state Kalman filter (i.e., an /spl alpha/, /spl beta/ filter) for tracking with linear frequency modulated (LFM) waveforms. A procedure is given for calculating the /spl alpha/, /spl beta/ gains from the tracking index /spl Gamma/, the sample period T, and the range-Doppler coupling coefficient /spl Delta/t. The steady-state error covariance is found to be a simple function of /spl alpha/, /spl beta/, /spl Delta/t, T and the measurement noise variance /spl sigma//sub v//sup 2/. The expressions for the steady-state gains and error covariance were confirmed numerically with the Kalman filtering equations. A gain scheduling technique for /spl alpha/ and /spl beta/ during initialization is also given.