Accurate Phase Accumulation Technique Under Vector Cross-Multiplication Framework for High-Accuracy Displacement Motion Sensing

High-accuracy displacement motion sensing via interferometric radar necessitates ultra-accurate phase demodulation. In this article, an accurate phase accumulation (APA) technique is proposed for displacement motion detection. The primary advantage of APA lies in its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm \pi $</tex-math> </inline-formula> phase difference accumulation property, which enhances its performance at low signal-to-noise ratio (SNR) and low sampling rate (SR). Simulations of a 12 mm, 0.5 Hz sinusoidal motion demonstrate that APA achieves a root mean square error (RMSE) of 0.0021 mm at 40 dB and 40 Hz, outperforming the suboptimal reference PCA technique (0.7122 mm). Similarly, at low <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SNR</i>, the RMSE of APA is 0.0666 mm at 10 dB and 100 Hz, surpassing the suboptimal arcsine technique (0.2605 mm). APA also introduces a process for obtaining the initial phase by supplementing the (1, 0) reference point, a step overlooked in previous phase demodulation techniques. Moreover, a vector cross-multiplication analytical framework is proposed to unify and compare numerous linear demodulation techniques, thereby presenting a systematic comparison that highlights the advantages and limitations of these techniques. Under this analytical framework, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SNR</i> and SR serve as the indicators for selecting the optimal technique across heterogeneous application scenarios. Based on a 120 GHz radar, experiments have been conducted to validate the practicality of APA for high-accuracy displacement motion measurement.