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An effective method for joint estimation of chirp rates, initial frequencies and DOAs of multiple LFM signals with sub-Nyquist spatial-temporal sampling

GRCRT(Generalized Robust Chinese Remainder Theorem) allows to reconstruct multiple numbers when all the moduli have a common factor and all residue sets have errors. In this paper, we propose a new approach based on GRCRT to joint estimation of chirp rates, initial frequencies and DOAs (direction of arrivals) for multiple LFM(linear frequency modulation) signals with sub-Nyquist spatial-temporal sampling. We first obtain the condition for ignoring the cross-terms for the convenience of estimating parameters of LFM signals. On the premise of ignoring the cross-terms, we then use GRCRT to estimate chirp rates, initial frequencies when multiple LFM signals are undersampled for multiple times in time domain and DOAs when multiple LFM signals are received at array where the distance between adjacent array elements is larger than half of the signal wavelength. Finally, the simulation results show that the newly approach based on GRCRT for multiple numbers can estimate chirp rates, initial frequencies and DOAs of multiple LFM signals accurately and robustly.