What does a radar twin with unlimited unambiguous velocity over-certify?

research/aliasing-twin

What a radar twin with unlimited unambiguous velocity over-certifies: exact wrapped-Gaussian bias (−V at μ=V) and MSE with a bias² floor so averaging widens the gap (7.9× → 2.1×10³ at μ=0.8V, n=1→10⁴), safe speed ≈V+sΦ⁻¹(tol/2V), and prior-unwrapping failure 2Φ(−V/√(s²+s_p²)) needing prior error ≤ 0.26V.

9 tests

What it found

A pulsed Doppler radar reports radial velocity modulo 2V; a twin that renders velocity as a real number never aliases. The real bias of a wrapped return is an exact Gaussian tail series (−V at speed V, −2V beyond) and the real MSE has a bias² floor, so averaging widens the gap to the twin's claim s²/n: at V=10, s=1 and speed 8 the real/claimed MSE is 7.9× for one return and 2.1×10³ for 10⁴. Speeds with |bias| ≤ 0.1 reach only 87%, 74% and 48% of V for noise 0.5, 1, 2. Unwrapping against a prior has exact failure probability 2Φ(−V/√(s²+s_p²)) and stays within 10% of the twin's claim only for prior error ≤ 0.26V. Stylised: one radial channel, Gaussian noise, simulated radar.

A figure from its own output

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

Paper, code and results

More in Digital twins & sim-to-real

Which rungs of a ladder of digital twins are worth running?Which rungs of a multi-fidelity twin ladder to run: exact nested-estimator variance, a cheaper rung pays iff ρ₂/ρ₁ > 2√r/(1+r) (step correlation, 0.943 for halved cost), using all rungs can be worse than none (1.41× real-only at q=0.9) while the best subset gets 0.83, and a timestep-ladder plant shows 0.156 of real-only variance (0.204 single twin) collapsing to the cheapest twin when disturbance replay is only 90%.
A heartbeat twin that drops packets independently: how often does the real bursty link trip a missed-beat watchdog, and what timeout is safe?I.i.d.-loss heartbeat twin vs a bursty Gilbert link: a 5-missed-beat watchdog false-trips every 3.4e6 ticks in the twin but every 235–990 on the real link, worst at burst length ≈ m (mean time to trip ≈ e·m/p), and a 1e6-tick target needs m = 16–154 instead of the twin's 5. Stylised.
A twin whose sensor never produces outliers: does an innovation gate help or hurt the real estimator, and what does it do after a jump?Gaussian-sensor twin vs a real sensor with outliers under an innovation gate: the twin says the gate costs 8.5% MSE, the real sensor gains 3.0× from it, the worst outlier scale for a gated filter is finite (κ≈4) while ungated error grows as κ², and a gate locks out recovery from a jump for ≈76·D² steps. Stylised.
A twin without ground effect: where does a landing altitude loop go wrong?Rotorcraft altitude twin without ground effect vs real thrust gain 1/(1−(R/4z)²): hover sits 18 mm high at one rotor radius (twin: 0), and a delayed loop with 28% twin headroom goes unstable at 0.54 rotor radii. Stylised.
What does a linear photon-counter twin of a SPAD lidar miss about dead time?Linear photon-counter twin of a SPAD lidar vs dead time: half the flux reported at nτ=1, a paralyzable-detector ambiguity (one reading, two fluxes, 12.7× apart at mτ=0.2), first-photon range bias −N/(2√π)σ saturating near −2σ (−22.6 cm at N=10, σ=1 ns) that does not average out, and a Coates correction that removes it. Stylised.
What ghost ranges does a single-ray lidar twin never produce at a depth edge?Single-ray lidar twin vs a finite beam with merged pulses at a depth edge: ghost-range band exactly 2Φ⁻¹(1−ε/D) beam widths (2.56 at ε/D=0.1, none at ε≥D/2), shifts and narrows for unequal brightness, matches a scan simulation to 0.3%, and a 3-of-5 persistence filter still passes 80–99% of ghosts.

All 164 Digital twins & sim-to-real projects →

Other research topics

Proper scoring & elicitation28 Effort & peer prediction9 Verification games & slashing19 Detection & tolerances14 Markets as routers13 Prediction-market design9 Paying contributors8 Decentralised training systems23 Digital twins & sim-to-real164 LLM chip design loops40 Robot manufacturing loops53 Ambient AI assistant46 Self-replicating manufacturing34 Simulation-first design64 Engineered clothing45 Task-specific AI accelerators40 Algorithmic chip-design loops42 Open-source purpose-built robots44 The software-engineering loop43 Adversarial human imitation41 Open-source residential construction41 Autonomous multi-angle capture34 Sensing, imaging and 3D31 Energy supply and dense energy storage39 Robot societies among people31 Agentic co-design of low-cost robots27 Laundry-hanging robots25 Machine learning on qualitative data23 Robots on the building site27 Civilizations & group psychology1 History & human sciences1

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.