FMCW radar dynamic demodulation: Enabling accurate vibration measurement

High-accuracy vibration displacement reconstruction and parameter estimation using frequency-modulated continuous-wave (FMCW) radar are essential for non-contact condition monitoring of engineering structures. However, conventional displacement estimation methods (e.g. CZT) suffer from phase jump phenomenon and high computational cost. Moreover, phase-based displacement extraction yields heteroscedastic measurement uncertainty due to additive observation phase noise (AOPN), which reduces the reliability of vibration parameter estimation when using unweighted spectral or least-squares methods. To address these issues, this paper proposes a two-stage framework consisting of a dynamic demodulation algorithm (DDA) and an AOPN-weighted iterative optimization (AWIO) method. The DDA updates the demodulation beat frequency on a sweep-by-sweep basis to suppress phase jump and stabilize slow-time displacement tracking for vibrating targets. The AWIO formulates vibration frequency and amplitude estimation as a weighted optimization problem, where sample-wise weights are derived from the uncertainty induced by observation phase noise, improving robustness to noise and multi-component interference. Simulation and experimental results demonstrate that the proposed methods maintain superior performance under low signal-to-noise ratios and multi-component interference. The displacement estimation error is significantly lower than that of conventional methods, and the amplitude estimation accuracy can reach the micrometer scale. This paper provides a high-accuracy, computationally efficient, and practical non-contact solution for engineering vibration monitoring.