A Sinusoidal Frequency Modulation Fourier Transform for Radar-Based Vehicle Vibration Estimation

The intricate vibration of a working vehicle provides an important signature to the vehicle type. Small vibrations introduce phase modulation in radar echoes, which is referred to as micro-Doppler (m-D) phenomenon and can be modeled as sinusoidal frequency-modulated (SFM) signal. Such phase modulation induced by vibrations consists of multiple frequency components; moreover, the modulation is usually rather weak. Present parametric estimators are difficult to estimate so many parameters of every frequency component, while nonparametric approaches suffer from low precision. This paper considers the analysis of SFM signal with weak and multiple frequency components modulation on phase term. We first define the SFM signal space to bridge a gap between the SFM signal analysis and classical signal processing methods. Based on the defined signal space, a novel m-D analysis method, i.e., the sinusoidal frequency modulation Fourier transform (SFMFT), is presented. With the operations acting directly on the phase term of SFM signal, SFMFT gives the frequency spectrum of vibration traces. Unlike the existing methods, which apply a sliding short-time window to perform an instantaneous approximation, the proposed method makes use of the global data, which can provide a longer integral period gain, and consequently improves the estimation performance significantly. Simulation results indicate that the proposed method outperforms the existing methods in the spectrum accuracy, the range of estimable vibration amplitude/frequency, and the computation complexity.