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.
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