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Quantitative Cramer-Rao Lower Bound analysis for WiFi ranging via both Time-of-Arrival and phase-based methods, with multistatic 4-anchor position-error budget. Headline (20 MHz HT20, 20 dB SNR, 100 averaged frames): - ToA range CRLB: 4.1 cm - Phase (5 deg noise): 0.17 mm - Phase advantage: 240x (after ambiguity resolution) 4-anchor convex-hull room (GDOP 1.5): - ToA position precision: 25 cm (room-pose-quality floor) - Phase position precision: 1 mm (RTK-quality, ambiguity-resolved) This is the strongest architectural lever this loop has surfaced for ADR-029 (multistatic sensing). The current learning-based attention approach has no provable precision floor; an explicit ToA-then-phase pipeline sits within 2x of CRLB by Kay's theory. Composes cleanly with R6: - R6 gives the spatial sensitivity envelope (40 cm Fresnel at 2.4 GHz) - R1 gives the ranging precision within it (1 mm phase, 4 cm ToA averaged) - Independent, additive, together bound full multistatic geometry budget Closes a gap R10 created: foliage drops SNR, which directly worsens ToA CRLB. A 50 m foliage link at 5 dB SNR drops to ~1 m ToA precision. R10's 100 m sparse-foliage range is *detectable* not *localisable*. Honest scope: - CRLB is a lower bound; real estimators sit 1-2x above it - 5 deg phase noise assumes phase_align.rs is applied - Multipath degrades CRLB by 2-5x even with MUSIC super-resolution - Integer-ambiguity (cycle-slip) is unsolved per-subcarrier; needs multi-subcarrier wide-lane unwrap Coordination: ticks/tick-9.md, no PROGRESS.md edit.
2.6 KiB
2.6 KiB
Tick 9 — 2026-05-22 05:34 UTC
Thread: R1 (ToA multistatic CRLB) Verdict: Quantitative precision floor for WiFi multistatic localisation. Phase ranging beats ToA ranging by 238× at WiFi bandwidths — but only after solving the integer-ambiguity (cycle-slip) problem.
What shipped
examples/research-sota/r1_toa_crlb.py— pure-numpy CRLB grid over bandwidth/SNR + phase-noise-vs-precision grid + 4-anchor multistatic geometric dilution.examples/research-sota/r1_toa_crlb_results.json— machine-readable predictions.docs/research/sota-2026-05-22/R1-toa-crlb.md— research note with the math, the headline numbers, the integer-ambiguity catch, ADR-029 architectural implication.
Headline numbers
20 MHz HT20 channel, 20 dB SNR (ESP32-S3 typical):
| Method | Single-shot | 100x averaged |
|---|---|---|
| ToA CRLB | 0.413 m | 0.041 m |
| Phase (single-subcarrier, 5° noise) | 1.73 mm | 0.17 mm |
| Phase advantage | 238× | 240× |
4-anchor multistatic 5×5 m room, GDOP 1.5:
| Method | Position precision |
|---|---|
| ToA | 25.3 cm |
| Phase (ambiguity-resolved) | 1.06 mm |
Why this matters for the loop
- Bounds what's physically possible for any WiFi-localisation feature. 25 cm position precision via ToA-only is the room-pose-quality floor; 1 mm via phase is RTK-quality but ambiguity-resolution-bound.
- Strongest architectural lever for ADR-029: explicit ToA-then-phase pipeline (≤2× from CRLB by Kay's theory) probably outperforms the current learning-based attention. Provable optimality vs flexibility tradeoff.
- Composes cleanly with R6: spatial envelope (R6) × ranging precision (R1) = full multistatic geometry budget. They are independent and additive.
- Closes a gap R10 created: foliage drops SNR, which directly worsens ToA CRLB. A 50 m foliage link at 5 dB SNR → ~1 m ToA precision. The 100 m sparse-foliage number from R10 is not the same as 100 m localisable.
Honest scope landed
- CRLB is a lower bound; real estimators sit 1-2× above it
- 5° phase noise assumes
phase_align.rsis applied; raw ESP32 is 60-180° - Multipath degrades CRLB by 2-5× even with MUSIC super-resolution
- Cycle-slip is unsolved at the WiFi bandwidth level without multi-subcarrier wide-lane unwrap
Coordination
ticks/tick-9.md. No PROGRESS.md edit. Branch research/sota-r1-toa-crlb.
Remaining threads
R2 (subsumed by R6+R12), R3 (cross-room re-ID), R4 (federated learning), R11 (through-bulkhead maritime), R13 (contactless BP), R15 (RF biometric).
~6.4h to cron stop. 9 threads landed.