Noncontact High-Linear Motion Sensing Based on A Modified Differentiate and Cross-Multiply Algorithm

The interferometric radar sensor can wirelessly detect the relative displacement motions, owing to its inherent nature of high sensitivity to the moving objects. To overcome the phase ambiguity and discontinuity caused by non-linear phase modulation, approaches such as differentiate and cross-multiply (DACM) were proposed for linear demodulation of the vibration motions. However, the existing DACM algorithm is strongly dependent on the calibration of I/Q output signals, resulting in low tolerance to noise and inaccuracy in detecting motions of large linear displacement. Based on the differentiation and the geometrical theorem of the trigonometric functions, this paper proposes a modified DACM algorithm with simplified expression but much improved performance for high-linear motion detection. Theoretical analysis was presented to introduce the proposed algorithm. Both simulation and experimental results demonstrate that the proposed algorithm is not only free from phase ambiguity, but also superior in several aspects: the stability under a signal to noise ratio (SNR) of 25 dB has been improved by 9 dB and the linearity of measuring large displacement motion has been improved by 32 dB, comparing to the existing DACM algorithm. Moreover, the simplified expression would greatly reduce the computational resources needed for linear phase demodulation.