Steady-State Filter Design for Radar Tracking with Up-Chirp-Down-Chirp Waveforms

The up-chirp (UC) LFM waveform is known to give better radar tracking than a monotone waveform or a down-chirp LFM waveform. However, the question of the value of other LFM waveforms to tracking is raised. In this paper, the value of an up-chirp-down-chirp (UCDC) waveform to radar tracking is considered. The optimal steady-state filter for tracking a nearly constant velocity target with an UCDC waveform is investigated and compared to that for a standard UC LFM waveform. The filter gains and state covariance are shown to be defined by Discrete White Noise Acceleration (DWNA) tracking index, the sample period, normalized pulse length, and the normalized range-doppler coupling coefficient. After developing the steady-state gain and covariance relationships for tracking with an UCDC waveform, tracking performances with UCDC and UC waveforms are compared. The UCDC waveform is shown to give a decrease in track filter covariance.