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Ranging using an LFMCW radar (Linear Frequency Modulated Continuous Wave) amounts to estimating frequency from the radar signal. However, the ranging accuracy is nominally limited to a resolution that is equivalent to the frequency resolution of the DFT. In this paper we break this limit using a novel formula for single frequency estimation. This formula is simple yet exact, and is able to handle the damping effect which is prevalent in real-world signals. We validate our formula on simulations and on real radar measurements. Our formula is very fast, and is shown to provide sub-mm ranging accuracy using the frequency estimation, and a micrometer-level accuracy using the associated estimation of the phase difference.

Positioning accuracy better than 0.25 mm when tested with a translation table. A different experiment based on a slowly moving copper reflector demonstrates uncertainty of about 4 micrometers for a distance change of about 10 micrometers.