Which ego-velocity estimator should a radar twin choose when the real scene has moving targets?

research/doppler-twin

Radar ego-velocity from Doppler returns: a static-world twin picks least squares, but with moving targets its variance is exactly 1+ετ² times the claim (95% interval covers 48.7% at ε=0.1, τ=10) and the median wins on a band of ε (0.006–0.97 at τ=10; never at τ=1).

8 tests

What it found

Radar ego-velocity from n Doppler returns. In a static-world twin least squares beats the median by exactly π/2, so the twin picks the mean; in a scene where a fraction ε of returns come from moving targets (extra offset sd τσ) the mean’s variance is exactly 1 + ετ² times the twin’s claim and the median’s exact variance is a one-dimensional integral, both matched to simulation. The twin’s choice is wrong on a band of ε (τ=10: 0.006–0.97; τ=3: 0.086–0.83; τ=1: never); at ε=0.1, τ=10 the mean has 5.8× the median’s variance and the twin’s 95% interval covers 48.7% of the time. 2-D least squares scales the same way. A residual-kurtosis test needs about 50 returns to detect it at ε=0.1, τ=10, and hundreds at ε=0.02, τ=3. Stylised: zero-mean Gaussian contamination, no RANSAC, no radar data.

A figure from its own output

Figure produced by research/doppler-twin: mean_vs_median — doppler-twin/experiments/mean_vs_median.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.