An analytical method for high-precision ranging measurement with FMCW radar

Accurate range measurement is essential in engineering and sensing applications. Conventional optical, ultrasonic, and laser methods often degrade under fog, dust or temperature fluctuations. Frequency-Modulated Continuous-Wave (FMCW) radar offers advantages such as low power, all-weather operation, and high resolution, making it attractive for structural health monitoring, traffic detection and security surveillance. Existing FMCW ranging techniques, mainly frequency-domain methods or phase interferometry, face limitations from noise sensitivity, spectral leakage or phase-wrapping ambiguities, especially in dense or multi-target scenarios. This study proposes a novel high-precision range estimation method based on beat signal decomposition and a generalised eigenvalue problem formulated with the beat signal and its first-order integral. The approach provides an analytical solution for the beat frequency, thereby eliminating phase unwrapping and improving robustness against noise. In addition, advanced processing techniques are incorporated to enhance integration accuracy and numerical stability. Simulation results show that the proposed method achieves 10 μm accuracy under low sampling rates, small matrix dimensions, varied modulation bandwidths and noise conditions. Indoor experiments further demonstrate its robustness, yielding maximum measurement errors below 120 μm, outperforming conventional approaches. Results confirm that the approach provides high accuracy, efficiency and stability, making it well-suited for complex environments.