Real time detection of object motion is widely used in industrial activities and daily life. The contactless measurement is a flexible way, which has no effect on the state of movement of the object. Compared with the optical, ultrasonic and laser sensors, microwave radar has the advantages of high measurement accuracy and being unaffected by the environment such as smoke, dust, fog, and rain.
The frequency modulated continuous wave (FMCW) radar is a widely used radar system, the echo of which contains abundant information, and there is no blind zone in the range because the transmitter and receiver work at the same time. The algorithm of movement detection of FMCW radar is commonly based on the peak estimation of signal spectrum, in order to achieve high accuracy, it is necessary to increase the frequency and bandwidth, resulting in high hardware complexity, a large amount of calculation, poor real-time response and poor anti-jamming ability. The proposed algorithm is based on the discrete Fourier transform with specific frequency of the beat signal. The real part and imaginary part of discrete Fourier transform are superposed in two perpendicular directions, and the resultant trajectory is approximately elliptical. The relative displacement of the object is proportional to the cumulative phase change of the corresponding points on the ellipse, the phase of each trajectory point can be calculated to restore the motion state of the object. The proposed algorithm does not need Fourier transform for the beat signal of each chirp, so the time complexity is low. The beat signal of the static object is processed into a fixed direct-current signal, which has no influence on the measurement of the moving object, therefore the algorithm has the ability to resist the interference of the static object. The measurement is limited to relative motion, because the phase obtained is relative. It has great potential applications in the fields of measuring relative displacement, such as mechanical vibration frequency, vital signal detection, mechanical arm control, etc..
An experimental setup with a center frequency of 24 GHz, bandwidth of 0.15 GHz and frequency modulation period of 4 ms is used to test the hypothesis. The experimental results are in good agreement with the theoretical results. The displacement measurement accuracy is 0.27 mm, and the linearity is 0.05% with 500 mm as the displacement measurement range. The measurement accuracy of velocity is 1.11 mm/s.
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