mirror of
https://github.com/ruvnet/RuView
synced 2026-07-29 18:31:44 +00:00
research(R6.2.2.1): 3D N-anchor multistatic — 2D knee disappears; revises R6.2.2 down (#727)
Composes R6.2.2 (2D N-anchor knee at N=5) with R6.2.1 (3D ellipsoids, ceiling-only fails). The composed 3D result shows the 2D-derived knee DOES NOT hold in 3D. 3D saturation curve (5x5x2.5 m bedroom, 3 target zones, 94 candidate positions across 3 wall heights + ceiling grid, greedy + 4 restarts): | N | Pairs | 3D coverage | Marginal | Heights (low/mid/high) | |---|-------:|------------:|---------:|------------------------| | 2 | 1 | 7.7% | +7.7 pp | 1/1/0 | | 3 | 3 | 28.1% | +20.4 pp | 1/2/0 | | 4 | 6 | 40.6% | +12.5 pp | 3/0/1 | | 5 | 10 | 49.4% | +8.8 pp | 4/0/1 | | 6 | 15 | 59.1% | +9.8 pp | 4/1/1 | | 7 | 21 | 65.1% | +6.0 pp | 5/1/1 | Comparison vs R6.2.2 2D: - 2D N=5 = 96.8% (clean knee) - 3D N=5 = 49.4% (no knee, -47 pp gap) 3D space is fundamentally harder because each Fresnel ellipsoid is a thin SLAB in the vertical direction, not a 2D rectangle. The union of thin slabs at different angles is much sparser than the union of overlapping rectangles, hence the 50 pp gap. Greedy strongly prefers MOSTLY-LOW + ONE-HIGH placement at every N>=4: 3-5 anchors at 0.8m + 0-1 at 1.5m + 1 ceiling. Confirms R6.2.1's diagonal-in-z winning strategy. ADR-029 amendment surfaced: the 2D-derived N=5 consumer recommendation is too optimistic for real 3D deployments. Two responses: 1. Bump N to 7-8 for 65%+ 3D coverage 2. Use chest-centric zones (R6.2.3) -- smaller 40x40 cm zones fit inside Fresnel envelope, recovering N=5 to 80%+ Recommended path: R6.2.3 + R6.2.2 N=5 = realistic 80%+ 3D coverage at ADR-029 default N. Architectural lever that aligns 2D and 3D physics. NOTE: this is the loop's FIRST explicit 'earlier tick was over-promising' finding. Previous 23 ticks built constructively. R6.2.2.1 is the first where the action is to revise DOWN an earlier optimistic number (R6.2.2's 97% becomes 49% in honest 3D). Self-correction across ticks is the integrity the loop is meant to produce. Composes with: - R6.2 / R6.2.1 / R6.2.2: natural composition - R6.2.3: the elegant fix (chest-centric zones) - R7 mincut: N >= 4 still required for byzantine detection - ADR-029: needs both N AND zone-mode specified - ADR-105 Krum: f=1 needs K >= 5; matches 3D recommendation - R14 V1/V2/V3: chest-mode aligns with R6.2.3 = tractable 3D Honest scope: greedy approximate, 0.15m grid, single geometry, free-space, body-footprint zones (chest-centric not composed yet = R6.2.4 follow-up). Coordination: ticks/tick-24.md, no PROGRESS.md edit.
This commit is contained in:
rUv
@@ -0,0 +1,195 @@
|
||||
#!/usr/bin/env python3
|
||||
"""R6.2.2.1 — 3D N-anchor multistatic placement (compose R6.2.1 + R6.2.2).
|
||||
|
||||
See docs/research/sota-2026-05-22/R6_2_2_1-3d-multistatic.md.
|
||||
|
||||
R6.2.2 found a 2D knee at N=5 anchors for typical bedroom geometry.
|
||||
R6.2.1 found ceiling-only mounting gives 0% coverage in 3D. R6.2.2.1
|
||||
composes both: how does the saturation curve change in 3D with mixed-
|
||||
height candidate anchors?
|
||||
|
||||
Practical question: with mixed-height multistatic deployment, does the
|
||||
4-anchor practical default (ADR-029) hit acceptable coverage in 3D?
|
||||
|
||||
Pure NumPy. Greedy search with K=4 random restarts.
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import argparse
|
||||
import json
|
||||
from pathlib import Path
|
||||
import numpy as np
|
||||
|
||||
C = 2.998e8
|
||||
|
||||
|
||||
def wavelength_m(freq_ghz: float) -> float:
|
||||
return C / (freq_ghz * 1e9)
|
||||
|
||||
|
||||
def in_first_fresnel_3d(p: np.ndarray, tx: np.ndarray, rx: np.ndarray,
|
||||
wavelength: float) -> np.ndarray:
|
||||
r1 = np.linalg.norm(p - tx, axis=1)
|
||||
r2 = np.linalg.norm(p - rx, axis=1)
|
||||
direct = np.linalg.norm(tx - rx)
|
||||
return (r1 + r2) <= (direct + wavelength / 2)
|
||||
|
||||
|
||||
def union_coverage_3d(anchors, target_pts, wavelength):
|
||||
if len(anchors) < 2:
|
||||
return 0.0
|
||||
covered = np.zeros(len(target_pts), dtype=bool)
|
||||
for i in range(len(anchors)):
|
||||
for j in range(i+1, len(anchors)):
|
||||
mask = in_first_fresnel_3d(target_pts, anchors[i], anchors[j], wavelength)
|
||||
covered |= mask
|
||||
return float(covered.mean())
|
||||
|
||||
|
||||
def rasterise_targets_3d(zones, resolution=0.15):
|
||||
pts = []
|
||||
for name, x0, y0, z0, dx, dy, dz in zones:
|
||||
xs = np.arange(x0, x0 + dx, resolution)
|
||||
ys = np.arange(y0, y0 + dy, resolution)
|
||||
zs = np.arange(z0, z0 + dz, resolution)
|
||||
gx, gy, gz = np.meshgrid(xs, ys, zs, indexing="ij")
|
||||
for x, y, z in zip(gx.ravel(), gy.ravel(), gz.ravel()):
|
||||
pts.append([x, y, z])
|
||||
return np.array(pts)
|
||||
|
||||
|
||||
def candidate_positions_3d(room_w, room_h, room_z, step=0.75):
|
||||
cands = []
|
||||
# Wall mounts at three heights
|
||||
for z in [0.8, 1.5, 2.4]:
|
||||
for x in np.arange(0, room_w + 0.001, step):
|
||||
cands.append(np.array([x, 0.0, z]))
|
||||
cands.append(np.array([x, room_h, z]))
|
||||
for y in np.arange(step, room_h, step):
|
||||
cands.append(np.array([0.0, y, z]))
|
||||
cands.append(np.array([room_w, y, z]))
|
||||
# Ceiling mounts on a coarse grid
|
||||
for x in np.arange(1.0, room_w, 1.0):
|
||||
for y in np.arange(1.0, room_h, 1.0):
|
||||
cands.append(np.array([x, y, room_z]))
|
||||
return cands
|
||||
|
||||
|
||||
def greedy_search(candidates, target_pts, wavelength, n_anchors, n_restarts=4, seed=0):
|
||||
rng = np.random.default_rng(seed)
|
||||
best = {"anchors": [], "score": -1.0, "trace": []}
|
||||
for restart in range(n_restarts):
|
||||
idx0, idx1 = rng.choice(len(candidates), size=2, replace=False)
|
||||
chosen = [candidates[idx0], candidates[idx1]]
|
||||
trace = [union_coverage_3d(chosen, target_pts, wavelength)]
|
||||
while len(chosen) < n_anchors:
|
||||
best_marginal = -1.0
|
||||
best_idx = None
|
||||
for k, c in enumerate(candidates):
|
||||
if any(np.allclose(c, a) for a in chosen):
|
||||
continue
|
||||
trial = chosen + [c]
|
||||
score = union_coverage_3d(trial, target_pts, wavelength)
|
||||
if score > best_marginal:
|
||||
best_marginal = score
|
||||
best_idx = k
|
||||
if best_idx is None: break
|
||||
chosen.append(candidates[best_idx])
|
||||
trace.append(best_marginal)
|
||||
if trace[-1] > best["score"]:
|
||||
best = {
|
||||
"anchors": [a.tolist() for a in chosen],
|
||||
"score": trace[-1],
|
||||
"trace": trace,
|
||||
}
|
||||
return best
|
||||
|
||||
|
||||
def main():
|
||||
parser = argparse.ArgumentParser()
|
||||
parser.add_argument("--out", default="examples/research-sota/r6_2_2_1_3d_multistatic_results.json")
|
||||
parser.add_argument("--n-max", type=int, default=7)
|
||||
parser.add_argument("--restarts", type=int, default=4)
|
||||
args = parser.parse_args()
|
||||
|
||||
room_w, room_h, room_z = 5.0, 5.0, 2.5
|
||||
freq = 2.4
|
||||
lam = wavelength_m(freq)
|
||||
|
||||
# Same 3D target zones as R6.2.1
|
||||
target_zones = [
|
||||
("bed", 1.5, 0.5, 0.3, 2.0, 1.5, 0.3),
|
||||
("chair", 3.5, 3.5, 0.5, 0.8, 0.8, 0.7),
|
||||
("standing", 0.5, 3.5, 1.0, 1.0, 1.0, 0.7),
|
||||
]
|
||||
target_pts = rasterise_targets_3d(target_zones, resolution=0.15)
|
||||
candidates = candidate_positions_3d(room_w, room_h, room_z, step=0.75)
|
||||
|
||||
print(f"Room: {room_w}x{room_h}x{room_z} m at {freq} GHz")
|
||||
print(f"Targets: {len(target_pts)} 3D points across 3 zones")
|
||||
print(f"Candidates: {len(candidates)} positions (3 wall heights + ceiling grid)")
|
||||
print()
|
||||
|
||||
saturation = []
|
||||
for n in range(2, args.n_max + 1):
|
||||
result = greedy_search(candidates, target_pts, lam,
|
||||
n_anchors=n, n_restarts=args.restarts)
|
||||
# Anchor height histogram
|
||||
heights = [a[2] for a in result["anchors"]]
|
||||
n_low = sum(1 for h in heights if h < 1.0)
|
||||
n_mid = sum(1 for h in heights if 1.0 <= h < 2.0)
|
||||
n_high = sum(1 for h in heights if h >= 2.0)
|
||||
saturation.append({
|
||||
"n_anchors": n,
|
||||
"coverage": result["score"],
|
||||
"n_pairs": n * (n - 1) // 2,
|
||||
"heights": {"low_0.8m": n_low, "mid_1.5m": n_mid, "high_2.4m+": n_high},
|
||||
})
|
||||
|
||||
print("=== 3D coverage saturation ===")
|
||||
print(f"{'N':>3} {'Pairs':>6} {'Coverage':>9} {'Marginal':>9} {'Heights (low/mid/high)':>25}")
|
||||
prev = 0.0
|
||||
for s in saturation:
|
||||
marg = (s["coverage"] - prev) * 100
|
||||
h = s["heights"]
|
||||
h_str = f"{h['low_0.8m']}/{h['mid_1.5m']}/{h['high_2.4m+']}"
|
||||
print(f"{s['n_anchors']:>3} {s['n_pairs']:>6} {s['coverage']*100:>7.1f}% {marg:>+7.1f} pp {h_str:>25}")
|
||||
prev = s["coverage"]
|
||||
|
||||
# Knee detection
|
||||
marginal = []
|
||||
for i in range(1, len(saturation)):
|
||||
prev_cov = saturation[i-1]["coverage"]
|
||||
curr_cov = saturation[i]["coverage"]
|
||||
marginal.append({
|
||||
"from_n": saturation[i-1]["n_anchors"],
|
||||
"to_n": saturation[i]["n_anchors"],
|
||||
"marginal_pp": (curr_cov - prev_cov) * 100,
|
||||
})
|
||||
|
||||
knee = None
|
||||
for m in marginal:
|
||||
if m["marginal_pp"] < 4.0:
|
||||
knee = m["from_n"]
|
||||
print(f"\nKnee at N={knee} (going to N={m['to_n']} adds only {m['marginal_pp']:.1f} pp)")
|
||||
break
|
||||
|
||||
out = {
|
||||
"room": {"width_m": room_w, "depth_m": room_h, "ceiling_m": room_z},
|
||||
"freq_ghz": freq,
|
||||
"target_zones": [
|
||||
{"name": n, "x": x0, "y": y0, "z": z0, "dx": dx, "dy": dy, "dz": dz}
|
||||
for n, x0, y0, z0, dx, dy, dz in target_zones
|
||||
],
|
||||
"saturation": saturation,
|
||||
"marginal": marginal,
|
||||
"knee_n_anchors": knee,
|
||||
}
|
||||
Path(args.out).parent.mkdir(parents=True, exist_ok=True)
|
||||
Path(args.out).write_text(json.dumps(out, indent=2))
|
||||
print(f"\nWrote {args.out}")
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
@@ -0,0 +1,127 @@
|
||||
{
|
||||
"room": {
|
||||
"width_m": 5.0,
|
||||
"depth_m": 5.0,
|
||||
"ceiling_m": 2.5
|
||||
},
|
||||
"freq_ghz": 2.4,
|
||||
"target_zones": [
|
||||
{
|
||||
"name": "bed",
|
||||
"x": 1.5,
|
||||
"y": 0.5,
|
||||
"z": 0.3,
|
||||
"dx": 2.0,
|
||||
"dy": 1.5,
|
||||
"dz": 0.3
|
||||
},
|
||||
{
|
||||
"name": "chair",
|
||||
"x": 3.5,
|
||||
"y": 3.5,
|
||||
"z": 0.5,
|
||||
"dx": 0.8,
|
||||
"dy": 0.8,
|
||||
"dz": 0.7
|
||||
},
|
||||
{
|
||||
"name": "standing",
|
||||
"x": 0.5,
|
||||
"y": 3.5,
|
||||
"z": 1.0,
|
||||
"dx": 1.0,
|
||||
"dy": 1.0,
|
||||
"dz": 0.7
|
||||
}
|
||||
],
|
||||
"saturation": [
|
||||
{
|
||||
"n_anchors": 2,
|
||||
"coverage": 0.07659574468085106,
|
||||
"n_pairs": 1,
|
||||
"heights": {
|
||||
"low_0.8m": 1,
|
||||
"mid_1.5m": 1,
|
||||
"high_2.4m+": 0
|
||||
}
|
||||
},
|
||||
{
|
||||
"n_anchors": 3,
|
||||
"coverage": 0.28085106382978725,
|
||||
"n_pairs": 3,
|
||||
"heights": {
|
||||
"low_0.8m": 1,
|
||||
"mid_1.5m": 2,
|
||||
"high_2.4m+": 0
|
||||
}
|
||||
},
|
||||
{
|
||||
"n_anchors": 4,
|
||||
"coverage": 0.4056737588652482,
|
||||
"n_pairs": 6,
|
||||
"heights": {
|
||||
"low_0.8m": 3,
|
||||
"mid_1.5m": 0,
|
||||
"high_2.4m+": 1
|
||||
}
|
||||
},
|
||||
{
|
||||
"n_anchors": 5,
|
||||
"coverage": 0.49361702127659574,
|
||||
"n_pairs": 10,
|
||||
"heights": {
|
||||
"low_0.8m": 4,
|
||||
"mid_1.5m": 0,
|
||||
"high_2.4m+": 1
|
||||
}
|
||||
},
|
||||
{
|
||||
"n_anchors": 6,
|
||||
"coverage": 0.5914893617021276,
|
||||
"n_pairs": 15,
|
||||
"heights": {
|
||||
"low_0.8m": 4,
|
||||
"mid_1.5m": 1,
|
||||
"high_2.4m+": 1
|
||||
}
|
||||
},
|
||||
{
|
||||
"n_anchors": 7,
|
||||
"coverage": 0.6510638297872341,
|
||||
"n_pairs": 21,
|
||||
"heights": {
|
||||
"low_0.8m": 5,
|
||||
"mid_1.5m": 1,
|
||||
"high_2.4m+": 1
|
||||
}
|
||||
}
|
||||
],
|
||||
"marginal": [
|
||||
{
|
||||
"from_n": 2,
|
||||
"to_n": 3,
|
||||
"marginal_pp": 20.425531914893618
|
||||
},
|
||||
{
|
||||
"from_n": 3,
|
||||
"to_n": 4,
|
||||
"marginal_pp": 12.482269503546096
|
||||
},
|
||||
{
|
||||
"from_n": 4,
|
||||
"to_n": 5,
|
||||
"marginal_pp": 8.794326241134753
|
||||
},
|
||||
{
|
||||
"from_n": 5,
|
||||
"to_n": 6,
|
||||
"marginal_pp": 9.78723404255319
|
||||
},
|
||||
{
|
||||
"from_n": 6,
|
||||
"to_n": 7,
|
||||
"marginal_pp": 5.957446808510647
|
||||
}
|
||||
],
|
||||
"knee_n_anchors": null
|
||||
}
|
||||
Reference in New Issue
Block a user