Sinusoidal Frequency Modulation Sparse Recovery for Precession Rate Estimation Using Low-Frequency Long-Range Radar

Low-frequency long-range radars (LFLRRs) are assumed to lack the ability of extracting targets micro motion signature, due to their low and nonuniform track update rate, as well as the weak micro Doppler (m-D) owing to their large wave length. The recently proposed sinusoidal frequency modulated (SFM) Fourier transform can achieve a longer integral period gain, and consequently provides a new perspective for extracting weak m-D signature. However, its direct application is unavailable for LFLRRs, since their track update rate is very low and may not even be constant. This paper derives a new approach, named sinusoidal frequency modulation sparse recovery (SFMSR) for m-D analysis with LFLRR, by exploiting the micro motion spectrum sparsity in SFM signal space. SFMSR employs the Fourier modulation dictionary, which is determined only by the frequency in SFM signal space. Unlike other sparse representation-based methods whose dictionary is discretization of a 3-D space parameterized by the micro motion amplitude, frequency, and initial phase, the SFMSR reduces the m-D analysis to 1-D parameter optimization, and therefore can enhance the precision, stability, and computational efficiency simultaneously. The temporally correlated sparse Bayesian learning in SFM signal space is employed to decompose the signal and produce highly sparse solutions. The simulation results indicate that the proposed method outperforms the existing methods in accuracy and robustness, which can provide satisfactory performance even when the carrier frequency is 430 MHz and the average data rate is 0.5 Hz.