189 lines
7.1 KiB
Python
189 lines
7.1 KiB
Python
#!/usr/bin/env python3
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"""R6.2.4 — 3D chest-centric N-anchor multistatic (compose R6.2.2.1 + R6.2.3).
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See docs/research/sota-2026-05-22/R6_2_4-3d-chest-multistatic.md.
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R6.2.2.1 (3D N-anchor on body-footprint zones) showed N=5 gives only
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49% coverage in 3D vs 97% in 2D -- the 2D-derived knee disappears.
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R6.2.2.1 predicted: switching to chest-centric zones (R6.2.3) should
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recover 80%+ in 3D at N=5.
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This tick tests that prediction. 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 in_first_fresnel_3d(p: np.ndarray, tx: np.ndarray, rx: np.ndarray,
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wavelength: float) -> np.ndarray:
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r1 = np.linalg.norm(p - tx, axis=1)
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r2 = np.linalg.norm(p - rx, axis=1)
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direct = np.linalg.norm(tx - rx)
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return (r1 + r2) <= (direct + wavelength / 2)
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def union_coverage_3d(anchors, target_pts, wavelength):
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if len(anchors) < 2:
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return 0.0
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covered = np.zeros(len(target_pts), dtype=bool)
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for i in range(len(anchors)):
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for j in range(i+1, len(anchors)):
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mask = in_first_fresnel_3d(target_pts, anchors[i], anchors[j], wavelength)
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covered |= mask
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return float(covered.mean())
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def rasterise_targets_3d(zones, resolution=0.10):
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pts = []
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for name, x0, y0, z0, dx, dy, dz in zones:
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xs = np.arange(x0, x0 + dx, resolution)
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ys = np.arange(y0, y0 + dy, resolution)
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zs = np.arange(z0, z0 + dz, resolution)
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gx, gy, gz = np.meshgrid(xs, ys, zs, indexing="ij")
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for x, y, z in zip(gx.ravel(), gy.ravel(), gz.ravel()):
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pts.append([x, y, z])
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return np.array(pts)
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def candidate_positions_3d(room_w, room_h, room_z, step=0.75):
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cands = []
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for z in [0.8, 1.5, 2.4]:
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for x in np.arange(0, room_w + 0.001, step):
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cands.append(np.array([x, 0.0, z]))
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cands.append(np.array([x, room_h, z]))
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for y in np.arange(step, room_h, step):
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cands.append(np.array([0.0, y, z]))
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cands.append(np.array([room_w, y, z]))
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for x in np.arange(1.0, room_w, 1.0):
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for y in np.arange(1.0, room_h, 1.0):
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cands.append(np.array([x, y, room_z]))
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return cands
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def greedy_search(candidates, target_pts, wavelength, n_anchors, n_restarts=4, seed=0):
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rng = np.random.default_rng(seed)
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best = {"anchors": [], "score": -1.0}
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for restart in range(n_restarts):
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idx0, idx1 = rng.choice(len(candidates), size=2, replace=False)
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chosen = [candidates[idx0], candidates[idx1]]
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while len(chosen) < n_anchors:
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best_marg = -1.0
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best_idx = None
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for k, c in enumerate(candidates):
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if any(np.allclose(c, a) for a in chosen):
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continue
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score = union_coverage_3d(chosen + [c], target_pts, wavelength)
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if score > best_marg:
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best_marg = score
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best_idx = k
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if best_idx is None: break
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chosen.append(candidates[best_idx])
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final = union_coverage_3d(chosen, target_pts, wavelength)
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if final > best["score"]:
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best = {"anchors": [a.tolist() for a in chosen], "score": final}
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return best
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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/r6_2_4_3d_chest_results.json")
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parser.add_argument("--n-max", type=int, default=6)
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parser.add_argument("--restarts", type=int, default=4)
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args = parser.parse_args()
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room_w, room_h, room_z = 5.0, 5.0, 2.5
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freq = 2.4
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lam = wavelength_m(freq)
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# 3D chest-centric zones (compose R6.2.3's 2D chest with R6.2.1's 3D heights)
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# Chest of: lying-down (z=0.3-0.5), sitting (z=0.7-1.0), standing (z=1.2-1.5)
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chest_zones_3d = [
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("bed_chest", 2.2, 0.8, 0.3, 0.6, 0.4, 0.2), # lying chest at z=0.3-0.5
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("chair_chest", 3.7, 3.7, 0.7, 0.4, 0.4, 0.3), # sitting chest z=0.7-1.0
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("standing_chest", 0.5, 3.7, 1.2, 0.6, 0.4, 0.3), # standing chest z=1.2-1.5
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]
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target_pts = rasterise_targets_3d(chest_zones_3d, resolution=0.10)
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candidates = candidate_positions_3d(room_w, room_h, room_z, step=0.75)
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print(f"Room: {room_w}x{room_h}x{room_z} m at {freq} GHz")
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print(f"CHEST-CENTRIC 3D targets: {len(target_pts)} points across {len(chest_zones_3d)} zones")
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print(f"Candidates: {len(candidates)} positions (3 wall heights + ceiling)")
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print()
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saturation = []
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for n in range(2, args.n_max + 1):
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result = greedy_search(candidates, target_pts, lam,
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n_anchors=n, n_restarts=args.restarts)
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heights = [a[2] for a in result["anchors"]]
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n_low = sum(1 for h in heights if h < 1.0)
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n_mid = sum(1 for h in heights if 1.0 <= h < 2.0)
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n_high = sum(1 for h in heights if h >= 2.0)
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saturation.append({
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"n_anchors": n,
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"coverage": result["score"],
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"heights": {"low": n_low, "mid": n_mid, "high": n_high},
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"anchors": result["anchors"],
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})
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print("=== 3D chest-centric saturation curve ===")
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print(f"{'N':>3} {'Coverage':>9} {'Marginal':>9} {'Heights L/M/H':>15}")
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prev = 0.0
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for s in saturation:
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marg = (s["coverage"] - prev) * 100
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h = s["heights"]
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print(f"{s['n_anchors']:>3} {s['coverage']*100:>7.1f}% {marg:>+7.1f} pp {h['low']}/{h['mid']}/{h['high']:>5}")
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prev = s["coverage"]
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# Compare to R6.2.2.1 (3D body-centric) at same N
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print()
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print("=== R6.2.2.1 prediction validation ===")
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print(f"R6.2.2.1 said: 'chest-centric should recover N=5 to 80%+ in 3D.'")
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n5 = next(s for s in saturation if s["n_anchors"] == 5)
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if n5["coverage"] >= 0.8:
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print(f"VALIDATED: 3D chest-centric N=5 = {n5['coverage']*100:.1f}% (>= 80% target)")
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elif n5["coverage"] >= 0.7:
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print(f"PARTIAL: 3D chest-centric N=5 = {n5['coverage']*100:.1f}% (close to 80% target)")
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else:
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print(f"NOT VALIDATED: 3D chest-centric N=5 = {n5['coverage']*100:.1f}% (well below 80%)")
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print()
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# Full 4-way comparison
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print("=== 4-way comparison at N=5 ===")
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print(f" R6.2.2 (2D body): 96.8%")
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print(f" R6.2.3 (2D chest): 82.4%")
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print(f" R6.2.2.1 (3D body): 49.4%")
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print(f" R6.2.4 (3D chest): {n5['coverage']*100:.1f}% (this tick)")
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out = {
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"room": {"width_m": room_w, "depth_m": room_h, "ceiling_m": room_z},
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"freq_ghz": freq,
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"target_zones": [
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{"name": n, "x": x0, "y": y0, "z": z0, "dx": dx, "dy": dy, "dz": dz}
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for n, x0, y0, z0, dx, dy, dz in chest_zones_3d
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],
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"saturation": saturation,
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"comparison_at_n5": {
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"r6_2_2_2d_body": 0.968,
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"r6_2_3_2d_chest": 0.824,
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"r6_2_2_1_3d_body": 0.494,
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"r6_2_4_3d_chest": n5["coverage"],
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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(f"\nWrote {args.out}")
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if __name__ == "__main__":
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main()
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