Steady-state tracking with FMCW radars

Kalman filters are typically used for tracking, but they are not convenient for predicting performance and filter design. However, Kalman filters can be approximated with steady-state equivalents like the α-β filter for the nearly constant velocity (NCV) Kalman filter processing measurements of position. Tracking radars often use linear frequency modulated (LFM) waveforms that produce biased measurements of target range due to the range-Doppler coupling in the signal. FMCW radars transmit continuously modulated waveforms that are typically composed of up-chirp and down-chirp LFM segments. However, the measurements produced by the up-chirp and down-chirp waveforms exhibit different properties. Hence, developing the steady-state track filter for an FMCW radar is a challenge. In this paper, the measurements from the up-chirp and down-chirp waveforms are fused to form an pseudo-measurement of range, range rate, and a corresponding covariance. Then, the fused measurements are periodic with a constant covariance and the steady-state filter for an FMCW radar can be developed. The filter gains (α, β, λ, γ) are shown to depend only on the tracking index and the relative or fractional bandwidth of the waveform. Least-squares estimation is used to characterize the estimation performance for a batch of FMCW measurements and develop a gain scheduling scheme for track initiation.