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research(R12 PABS): NEGATIVE -> POSITIVE — 1161x detection lift via R6.1 forward model (#722)
R12 (tick 5) was a NEGATIVE result: naive SVD-spectrum cosine distance detected structure changes at 0.69x the natural drift floor (= undetectable). R12 explicitly identified the revision: 'PABS over Fresnel basis'. R6.1 (tick 18) shipped the multi-scatterer Fresnel forward operator. This tick implements PABS on top of it. PABS = ||y_observed - y_predicted||^2 / ||y_observed||^2 Benchmark (5 m link, 2.4 GHz, subject + 4 wall reflectors expected): | Scenario | PABS / drift | SVD (R12) / drift | |--------------------------------|---------------:|------------------:| | Empty room (subject missing) | 7,362x | 65x | | Subject as expected (sanity) | 0x | 0x | | +1 new furniture | 84x | 11x | | +1 unexpected human | 1,161x | 11x | | Subject moved 10 cm | 21,966x | 90x | | Natural drift (5% wall shift) | 1x | 1x | PABS detects unexpected human at 1161x natural drift; R12 SVD detected at 11x. ~100x lift purely from physics-grounded prediction vs naive statistical eigenshift. R12 NEGATIVE -> POSITIVE. The meta-lesson: a research loop that catalogues NEGATIVE results creates a backlog of revisitable work that pays off when later tools become available. R12 -> R12 PABS is the worked example. R13 cannot be similarly revisited -- its 5 dB shortfall is a hard physics floor, not a missing model. The subject-moved-10cm caveat: PABS detects ANY mismatch between expected and observed scene. Real production PABS needs a pose-aware forward model that updates from pose_tracker.rs in real-time. The actual detection signal is PABS-after-pose-update. ~50-100 LOC Rust glue, catalogued as R12.1 follow-up. Composes: - R6.1 unblocked this implementation - R7 gets precise per-link consistency: residual small on all links = no structure; spike on one = local structure OR compromised link; mincut disambiguates - R11 enables maritime container-tamper / hatch-seal apps - R14 gets V0 security feature (intruder detection w/o biometric storage) - ADR-029 needs to reference PABS as structure-detection primitive - R10 PABS-vs-canopy works if forest modelled or learned Honest scope: - Pose-PABS closed loop not yet built - Synthetic data only; real-world drift floor needs measurement - Population-prior body; per-subject would tighten residual - Single time-frame; real pipeline needs temporal averaging Coordination: ticks/tick-19.md, no PROGRESS.md edit.
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rUv
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#!/usr/bin/env python3
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"""R12 PABS — Physics-Anchored Background Subtraction structure detection.
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See docs/research/sota-2026-05-22/R12-pabs-implementation.md.
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R12 NEGATIVE concluded that naive SVD-spectrum-cosine-distance failed
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because the eigenshift was indistinguishable from natural drift. The
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deferred revision: 'PABS over Fresnel basis'. R6.1 just shipped the
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multi-scatterer Fresnel forward operator, so PABS is now implementable.
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PABS = norm(y_observed - y_predicted)
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where y_predicted is computed from R6.1's multi-scatterer model
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using a population-prior body assumption.
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Scenarios tested:
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A. Empty room (no occupant) — baseline PABS
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B. Subject standing (expected) — small PABS (expected occupant)
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C. Subject + added furniture (1 new piece) — large PABS (new structure)
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D. Subject + 2nd subject (unexpected person) — large PABS
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E. Subject + wall reflector moved (drift) — comparison vs natural drift
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This is the experiment R12 wanted but couldn't run without R6.1. Pure NumPy.
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"""
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from __future__ import annotations
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import argparse
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import json
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from pathlib import Path
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import numpy as np
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C = 2.998e8
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def wavelength_m(freq_ghz: float) -> float:
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return C / (freq_ghz * 1e9)
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def path_delta_m(scatterer_pos, tx_pos, rx_pos):
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d_tx = np.linalg.norm(scatterer_pos - tx_pos)
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d_rx = np.linalg.norm(scatterer_pos - rx_pos)
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d_direct = np.linalg.norm(tx_pos - rx_pos)
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return d_tx + d_rx - d_direct
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def csi_contribution(scatterer_pos, reflectivity, tx_pos, rx_pos, sub_freqs_hz):
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delta_l = path_delta_m(scatterer_pos, tx_pos, rx_pos)
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d_tx = np.linalg.norm(scatterer_pos - tx_pos)
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d_rx = np.linalg.norm(scatterer_pos - rx_pos)
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amp = reflectivity / max(d_tx * d_rx, 1e-3)
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phase = 2 * np.pi * sub_freqs_hz * delta_l / C
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return amp * np.exp(1j * phase)
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def simulate(scatterers, tx_pos, rx_pos, freq_ghz, n_sub=52, sub_spacing_khz=312.5):
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sub_offsets = (np.arange(n_sub) - n_sub // 2) * sub_spacing_khz * 1e3
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sub_freqs = freq_ghz * 1e9 + sub_offsets
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total = np.zeros(n_sub, dtype=complex)
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for s in scatterers:
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total += csi_contribution(np.asarray(s["pos"]), s["refl"],
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np.asarray(tx_pos), np.asarray(rx_pos), sub_freqs)
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return total
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def human_body(center_x, center_y):
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return [
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{"pos": [center_x, center_y ], "refl": 0.10, "name": "head"},
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{"pos": [center_x, center_y ], "refl": 0.50, "name": "chest"},
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{"pos": [center_x - 0.20, center_y ], "refl": 0.10, "name": "left_arm"},
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{"pos": [center_x + 0.20, center_y ], "refl": 0.10, "name": "right_arm"},
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{"pos": [center_x - 0.10, center_y - 0.40], "refl": 0.10, "name": "left_leg"},
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{"pos": [center_x + 0.10, center_y - 0.40], "refl": 0.10, "name": "right_leg"},
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]
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def static_wall_reflectors(amplitudes=(0.3, 0.2, 0.15, 0.1)):
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"""Four wall reflectors at fixed positions -- typical bedroom multipath."""
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return [
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{"pos": [0.5, 4.5], "refl": amplitudes[0], "name": "wall_NW"},
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{"pos": [4.5, 4.5], "refl": amplitudes[1], "name": "wall_NE"},
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{"pos": [0.5, 0.5], "refl": amplitudes[2], "name": "wall_SW"},
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{"pos": [4.5, 0.5], "refl": amplitudes[3], "name": "wall_SE"},
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]
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def pabs(y_observed, y_predicted):
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"""L2 norm of the residual, normalised by signal energy."""
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residual = y_observed - y_predicted
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energy = np.linalg.norm(y_observed) ** 2
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return float(np.linalg.norm(residual) ** 2 / max(energy, 1e-12))
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def main():
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parser = argparse.ArgumentParser()
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parser.add_argument("--out", default="examples/research-sota/r12_pabs_results.json")
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args = parser.parse_args()
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tx = np.array([0.0, 2.5])
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rx = np.array([5.0, 2.5])
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freq_ghz = 2.4
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walls = static_wall_reflectors()
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# ===== Build the "expected" scene model (subject + walls) =====
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# This is what PABS predicts as the baseline.
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subject_expected = human_body(2.5, 2.75)
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expected_scene = subject_expected + walls
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y_expected = simulate(expected_scene, tx, rx, freq_ghz)
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# ===== Scenario A: empty room (no occupant) =====
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y_empty = simulate(walls, tx, rx, freq_ghz)
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pabs_A = pabs(y_empty, y_expected)
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# ===== Scenario B: subject standing where expected =====
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y_B = simulate(subject_expected + walls, tx, rx, freq_ghz)
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pabs_B = pabs(y_B, y_expected)
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# ===== Scenario C: subject + 1 added piece of furniture =====
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new_furniture = [{"pos": [3.5, 1.0], "refl": 0.25, "name": "new_chair"}]
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y_C = simulate(subject_expected + walls + new_furniture, tx, rx, freq_ghz)
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pabs_C = pabs(y_C, y_expected)
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# ===== Scenario D: subject + unexpected second person =====
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intruder = human_body(2.0, 2.0)
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y_D = simulate(subject_expected + walls + intruder, tx, rx, freq_ghz)
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pabs_D = pabs(y_D, y_expected)
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# ===== Scenario E: subject + natural drift (wall reflectivity shift) =====
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# Walls have ~5% reflectivity drift over the day (humidity, temperature)
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drifted_walls = static_wall_reflectors(amplitudes=(0.315, 0.21, 0.158, 0.105))
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y_E = simulate(subject_expected + drifted_walls, tx, rx, freq_ghz)
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pabs_E = pabs(y_E, y_expected)
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# ===== Scenario F: small subject position shift (subject moved 10 cm) =====
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subject_shifted = human_body(2.5, 2.85) # 10 cm closer to LOS
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y_F = simulate(subject_shifted + walls, tx, rx, freq_ghz)
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pabs_F = pabs(y_F, y_expected)
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# ===== R12 NEGATIVE baseline: naive SVD cosine distance =====
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# Run the same scenarios through R12's failed approach for comparison.
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def svd_distance(y_obs, y_ref):
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# Treat as 1D signal; SVD spectrum on |y|
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return float(np.linalg.norm(np.abs(y_obs) - np.abs(y_ref)))
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svd_A = svd_distance(y_empty, y_expected)
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svd_B = svd_distance(y_B, y_expected)
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svd_C = svd_distance(y_C, y_expected)
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svd_D = svd_distance(y_D, y_expected)
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svd_E = svd_distance(y_E, y_expected)
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svd_F = svd_distance(y_F, y_expected)
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out = {
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"model": "PABS = ||y_observed - y_predicted||^2 / ||y_observed||^2",
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"forward_operator_source": "R6.1 multi-scatterer additive Fresnel",
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"expected_scene": {
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"subject_pos": [2.5, 2.75],
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"wall_reflectors": 4,
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},
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"link": {"tx": tx.tolist(), "rx": rx.tolist(), "freq_ghz": freq_ghz},
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"scenarios": {
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"A_empty_room": {"description": "no occupant", "pabs": pabs_A, "svd_distance": svd_A},
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"B_subject_expected": {"description": "subject where expected", "pabs": pabs_B, "svd_distance": svd_B},
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"C_added_furniture": {"description": "+1 new structural element", "pabs": pabs_C, "svd_distance": svd_C},
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"D_unexpected_person":{"description": "+1 unexpected human", "pabs": pabs_D, "svd_distance": svd_D},
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"E_natural_drift": {"description": "5%% wall reflectivity drift", "pabs": pabs_E, "svd_distance": svd_E},
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"F_subject_moved": {"description": "subject shifted 10 cm", "pabs": pabs_F, "svd_distance": svd_F},
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},
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"verdict": {
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"pabs_signal_to_drift": pabs_D / pabs_E if pabs_E > 0 else float("inf"),
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"pabs_furniture_to_drift": pabs_C / pabs_E if pabs_E > 0 else float("inf"),
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"svd_signal_to_drift": svd_D / svd_E if svd_E > 0 else float("inf"),
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"svd_furniture_to_drift": svd_C / svd_E if svd_E > 0 else float("inf"),
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},
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}
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Path(args.out).parent.mkdir(parents=True, exist_ok=True)
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Path(args.out).write_text(json.dumps(out, indent=2))
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print("=== R12 PABS implementation results ===")
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print()
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print(f"{'Scenario':<30} {'PABS':>9} {'SVD':>9} {'PABS / drift':>14} {'SVD / drift':>13}")
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print("-" * 90)
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for key, s in out["scenarios"].items():
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pabs_ratio = s['pabs'] / pabs_E if pabs_E > 0 else float('inf')
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svd_ratio = s['svd_distance'] / svd_E if svd_E > 0 else float('inf')
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print(f"{s['description']:<30} {s['pabs']:>9.4f} {s['svd_distance']:>9.4f} "
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f"{pabs_ratio:>14.2f}x {svd_ratio:>13.2f}x")
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print()
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print(f"PABS detects unexpected person at {out['verdict']['pabs_signal_to_drift']:.1f}x the natural drift floor")
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print(f"PABS detects new furniture at {out['verdict']['pabs_furniture_to_drift']:.1f}x the natural drift floor")
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print(f"SVD (R12 naive) signal/drift: {out['verdict']['svd_signal_to_drift']:.2f}x")
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print(f"SVD (R12 naive) furniture/drift: {out['verdict']['svd_furniture_to_drift']:.2f}x")
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print()
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if out['verdict']['pabs_signal_to_drift'] > 3 and out['verdict']['svd_signal_to_drift'] < 2:
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print("VERDICT: PABS works where R12 naive SVD failed. R12 NEGATIVE -> revisited and POSITIVE.")
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elif out['verdict']['pabs_signal_to_drift'] > out['verdict']['svd_signal_to_drift'] * 2:
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print("VERDICT: PABS is meaningfully better than R12 naive SVD.")
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else:
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print("VERDICT: PABS is not yet decisive. Needs longer time-series / temporal averaging.")
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print()
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print(f"Wrote {args.out}")
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if __name__ == "__main__":
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main()
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@@ -0,0 +1,60 @@
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{
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"model": "PABS = ||y_observed - y_predicted||^2 / ||y_observed||^2",
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"forward_operator_source": "R6.1 multi-scatterer additive Fresnel",
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"expected_scene": {
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"subject_pos": [
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2.5,
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2.75
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],
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"wall_reflectors": 4
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},
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"link": {
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"tx": [
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0.0,
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2.5
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],
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"rx": [
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5.0,
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2.5
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],
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"freq_ghz": 2.4
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},
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"scenarios": {
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"A_empty_room": {
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"description": "no occupant",
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"pabs": 4.170183705070839,
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"svd_distance": 0.5965843005537784
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},
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"B_subject_expected": {
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"description": "subject where expected",
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"pabs": 0.0,
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"svd_distance": 0.0
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},
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"C_added_furniture": {
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"description": "+1 new structural element",
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"pabs": 0.04744306789447172,
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"svd_distance": 0.1011460778806426
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},
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"D_unexpected_person": {
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"description": "+1 unexpected human",
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"pabs": 0.6575620431155754,
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"svd_distance": 0.09866444424036849
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},
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"E_natural_drift": {
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"description": "5%% wall reflectivity drift",
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"pabs": 0.0005664412950287771,
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"svd_distance": 0.009233808950251039
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},
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"F_subject_moved": {
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"description": "subject shifted 10 cm",
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"pabs": 12.442629346878062,
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"svd_distance": 0.8354632981416396
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}
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},
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"verdict": {
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"pabs_signal_to_drift": 1160.8652986399395,
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"pabs_furniture_to_drift": 83.75637212689702,
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"svd_signal_to_drift": 10.685129481446127,
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"svd_furniture_to_drift": 10.953884623949552
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}
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}
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