spaxel/docs/research/06-accuracy-and-limits.md

Realistic Accuracy Bounds and Limitations

Localization Accuracy by System Type

System type	Typical accuracy	Conditions
RSSI fingerprinting	2–5 m	Calibrated environment
CSI fingerprinting	0.5–2 m	Controlled environment
CSI model-based (geometric)	0.5–1.5 m	Good geometry, single moving person
SpotFi (MUSIC + subcarrier extension)	~40 cm median	3-antenna AP, calibrated
IndoTrack (Doppler-MUSIC)	~35 cm median	3 antennas, commodity hardware
Widar2.0 (single link)	~75 cm median	Moving target
Widar2.0 (two links)	~63 cm median	Moving target
Multi-link geometric (4–8 nodes)	0.5–1.0 m	Typical indoor room

3D (Z-axis) Accuracy

• Z-axis accuracy is typically worse than XY: 1–3 m with geometric approaches
• Machine learning approaches have achieved 0.4 m vertical RMSE in some studies
• Fundamental limit from wavelength: 2.4 GHz → λ/4 = 3.1 cm minimum theoretical resolution per dimension (unreachable with commodity hardware noise)
• Z accuracy improves significantly with nodes at mixed heights

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The Stillness Problem

This is the most significant practical limitation. When a person is motionless:

• No Doppler shift → DFS-based methods (Widar, IndoTrack) fail entirely
• EMA baseline adapts → person gradually absorbed into background; presence fades
• Variance-based detectors see near-zero variance → interpret as empty room

Mitigations

Mitigation	Mechanism	Limitation
Long EMA time constant (α = 0.999)	Slows background adaptation	Eventually still absorbs stationary person
Motion-gated baseline update	Only update when variance < threshold	Requires quiet periods to capture baseline
Breathing detection (0.1–0.5 Hz)	Chest movement ~5 mm still detectable	Needs 10–30 s averaging; fails with noisy environment
Entry/exit hysteresis	Require exit event before marking absent	Doesn't detect initial entry of already-still person
Static CSI fingerprint comparison	Empty vs. occupied room differ by 3–12 dB on affected links	Requires clean empty-room reference

Breathing at 2.4 GHz: chest displacement ~5 mm → phase change ≈ 2π × 2 × 0.005 / 0.125 ≈ 0.5 rad. Detectable above noise with sufficient averaging.

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Multiple Person Degradation

From WiMANS dataset and related work:

People	Accuracy degradation
1	Baseline (e.g. 35 cm for IndoTrack)
2	~2× increase in error; ambiguity from two reflection sources
3	~3–4× error increase
5	Localization error +15.4%, activity recognition −25.7% vs. single person

Multi-person tracking is an open research problem. Current approaches:

• Track as many simultaneous targets as there are resolvable Doppler sources (limited by angular/frequency resolution)
• Use multiple antennas with MUSIC to spatially separate sources
• Deep learning end-to-end approaches show promise but require large training datasets

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Environmental Sensitivity

Change	Effect	Recovery
Furniture moved	Static multipath changes → fingerprint invalid	Forced baseline reset + slow EMA re-adaptation
Temperature change (AC on/off)	Slight material property and phase shifts	Slow EMA absorbs over hours
High-activity elsewhere in building	Background dynamic CSI from other rooms	Narrow sensing band; spatial filtering
Humidity / rain	Affects building material dielectric properties	Slow EMA absorbs
New large objects added	New permanent multipath components	Forced baseline reset

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ESP32-Specific Limitations

Limitation	Impact	Workaround
Single antenna	No direct AoA from one node	Multi-node mesh provides angular diversity
int8 dynamic range	Saturates near nodes; low SNR far from nodes	Place nodes at 2–5 m from sensing area
No phase coherence across nodes	Cannot directly apply array MUSIC to multi-node data	Use geometric Fresnel method instead
No 5 GHz	Limited to 2.4 GHz (12.5 cm wavelength)	Adequate for body-scale detection
ToF resolution at 20 MHz	c/(2B) = 7.5 m — useless for ranging	Manual node position measurement
Packet rate ~20 Hz	Limits DFS resolution to ±10 Hz	Adequate for walking (16 Hz DFS)

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What Spaxel Can Realistically Achieve

Conservative (safe to claim)

• Presence detection (someone in the room vs. empty): reliable with 2+ nodes on opposite sides
• Approximate 2D position (±0.5–1.0 m): reliable with 4+ well-placed nodes for a moving person
• Motion detection and tracking: reliable with 4+ nodes
• Rough count (0 vs. 1 vs. 2+ people): works in practice, degrades with 3+

Possible with Good Conditions

• Rough 3D position (±1–2 m Z): with nodes at mixed heights
• Stationary person detection: via breathing detection on stable setup
• Velocity estimation: via DFS analysis

Not Achievable with Commodity ESP32-S3

• Sub-10 cm accuracy
• Reliable skeletal pose estimation
• Fine-grained limb position
• Reliable tracking of 5+ simultaneous people
• Through-floor sensing (different frequency needed)