Steady-state tracking with LFM waveforms

The steady-state gains and error covariance are derived for a two-state Kalman filter (i.e., an α, β filter) for tracking with linear frequency modulated (LFM) waveforms. A procedure is given for calculating the α, β gains from the tracking index Γ, the sample period T, and the range-Doppler coupling coefficient Δt. The steady-state error covariance is found to be a simple function of α, β, Δt, T and the measurement noise variance σ_v². The expressions for the steady-state gains and error covariance were confirmed numerically with the Kalman filtering equations. A gain scheduling technique for α and β during initialization is also given