Aether

<title>Aether — Feasibility & Reality Check</title>

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<div class="wrap">

<header>

<div class="col">

<p class="eyebrow">Aether · UWB + IMU positioning mesh · reality check</p>

<h1>Can 4 phones survey themselves indoors?</h1>

<p class="thesis">An honest, physics-first read on the ask. Short version: the field trouble is not a code

defect — it is the predictable signature of an <b>over-stacked target</b>, and the decisive lever is

<b>provisioning, not more software</b>.</p>

<div class="meta">

<span><b>Scope</b> feasibility &amp; mission</span>

<span><b>Basis</b> code · roadmap · 2 field captures · UWB-RTLS literature</span>

<span><b>Verdict</b> re-scope + provision</span>

</div>

</div>

<figure class="figure">

<p class="cap">The thesis, as one number</p>

<div class="chartscroll">

<svg class="chart" viewBox="0 0 640 250" role="img" aria-label="Spare inter-anchor constraints versus anchor count: zero at four anchors, one at five, then three, six and ten at eight.">

<line x1="60" y1="200" x2="620" y2="200" style="stroke:var(--border);stroke-width:1.5"/>

<text class="axis" x="618" y="224" text-anchor="end">anchors →</text>

<text class="axis" x="18" y="112" text-anchor="middle" transform="rotate(-90 18 112)">spare constraints</text>

<!-- n=4 : v=0 (the wall) -->

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<text class="bar-v" x="128" y="188" text-anchor="middle" style="fill:var(--hard)">0</text>

<text class="bar-n" x="128" y="220" text-anchor="middle" style="fill:var(--hard)">4</text>

<text class="axis" x="128" y="240" text-anchor="middle" style="fill:var(--hard)">undetectable</text>

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<text class="axis" x="232" y="240" text-anchor="middle" style="fill:var(--accent)">detectable</text>

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<text class="bar-v" x="544" y="41" text-anchor="middle">10</text>

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</div>

<p class="sub">Spare inter-anchor constraints = <span class="k">C(n,2) − (3n−6)</span>. At <b>4 anchors it is

exactly 0</b> — a biased or body-blocked link is mathematically undetectable. Every reliability property

the project wants begins at <b>5</b>.</p>

</figure>

</header>

<div class="verdict col">

<p class="eyebrow">Bottom line, up front</p>

<p>A cooperative, self-solving indoor UWB+IMU mesh is <strong>sound and buildable</strong>. The <em>reliable</em>

version is a <strong>static mesh of ≥5–6 geometrically- and vertically-diverse anchors</strong>, with NLOS

mitigation, solved-and-locked over time, a ranging schedule for clients, interior coverage, and

<strong>decimetre</strong> expectations. What the physics does <em>not</em> support is the maximalist reading of

today's ask — <strong>survey-free · sub-centimetre · phone-only · 4-anchor · widely-spaced · indoor · exterior

clients · live human traffic — all at once.</strong></p>

</div>

<section class="col">

<h2><span class="num">01</span> The system as it stands</h2>

<p class="lede">What we are actually judging, from the code, the roadmap, capture4, and the layout video.</p>

<p><strong>4 anchors</strong>, one the root — physically 3 on tripods at ~1.2–1.45 m plus one low in a red cup at

~0.89 m, in a <strong>~2.3 m × 3.7 m</strong> footprint inside a small furnished living room.

<strong>Phone-class UWB</strong> (Galaxy-class anchors; Pixel observer), not dedicated RTLS hardware.

<strong>Survey-free</strong>: the frame is solved purely from inter-anchor ranges — for 4 anchors that is

<span class="k">6 ranges = 6 DOF</span>, an <strong>exactly-rigid graph with zero redundancy</strong>. In the

field, A3's cross-room links read <strong>+0.57 / +0.75 m long</strong> (a stable NLOS bias where the links

physically cross furniture), devices disagreed on the shape, the mesh didn't reliably lock, and one link went

dark. Production intent adds <strong>wider spacing</strong> and <strong>several clients wandering interior and

exterior</strong> through <strong>human line-of-sight blockage</strong>.</p>

</section>

<section class="col">

<h2><span class="num">02</span> The physics that decides it</h2>

<p class="lede">Four UWB-positioning invariants — not Aether-specific, each externally sourced — govern every

answer below.</p>

<ul class="facts">

<li><span class="idx">i</span><p><strong>UWB is LoS-accurate, NLOS-biased.</strong> ~10 cm in clear line of

sight; a <strong>human body pushes it to ~0.5 m</strong>, positive-biased. Capture4's +0.57/+0.75 m is a

textbook NLOS bias, not a bug — and NLOS is the dominant indoor error source.</p></li>

<li><span class="idx">ii</span><p><strong>Range budget is finite; phones sit at the bottom of it.</strong>

Dedicated modules reach 50–100 m; phone-class HRP UWB is “several tens of metres, ~Bluetooth range,” and far

less through walls or bodies. Android AoA is coarse or absent.</p></li>

<li><span class="idx">iii</span><p><strong>Position error = ranging error × GDOP.</strong> Multilateration is

well-conditioned <strong>inside the convex hull</strong> of the anchors and blows up <strong>outside it</strong>;

it needs angular diversity and enclosed volume. A near-coplanar set is weak vertically and carries a mirror

ambiguity.</p></li>

<li><span class="idx">iv</span><p><strong>Redundancy buys reliability.</strong> The inter-anchor graph has spare

constraints only at <strong>N ≥ 5</strong>; at 4, a biased or blocked edge is undetectable. RTLS guidance:

4 is the floor, <strong>5–6 preferred</strong>, 8+ diminishing.</p></li>

</ul>

<p style="margin-top:14px">A fifth fact governs scale, not accuracy: <strong>two-way ranging scales poorly with

many tags</strong> unless coordinated by a <strong>TDMA schedule</strong> (or moved to TDoA).</p>

</section>

<section class="col">

<h2><span class="num">03</span> Straight answers</h2>

<p class="lede">The questions as asked, answered without hedging.</p>

<div class="qa">

<div class="item"><p class="q">Can a 4-anchor phone mesh solve reliably <em>and</em> withstand clients + humans crossing LoS?</p>

<p class="a"><span class="tag no">No — not reliably</span>It can be solved in a clean moment and <em>held</em> (worth doing), but with zero redundancy any single blocked/biased link has nothing to out-vote it, and indoors a body may be sitting on one at any instant. There is no built-in error detection by construction.</p></div>

<div class="item"><p class="q">Can software solve it — developed, COTS, or a mix?</p>

<p class="a"><span class="tag part">Mitigate, not overcome</span>On a zero-redundancy graph, <em>no</em> estimator — robust least-squares, RANSAC, a neural NLOS classifier, factor graphs, anything COTS — can detect a lone biased edge; the residual is identically zero. That is an information limit. Software wins only <em>with</em> the right geometry, or by using time (average a static mesh) or extra sensors (IMU/observer).</p></div>

<div class="item"><p class="q">Is success guaranteed by adding hardware (more anchors)?</p>

<p class="a"><span class="tag ok">Highest-leverage lever</span>Near-sufficient — with caveats. 4→5 flips redundancy 0→1 (a biased edge becomes detectable); 6–8 gives graceful degradation and LoS diversity against blockage. But added anchors must bring <strong>geometric + height diversity</strong>, and many radios need a schedule. Boxes placed badly don't help.</p></div>

<div class="item"><p class="q">Is it the shape of the constellation?</p>

<p class="a"><span class="tag part">Secondarily</span>The set is near-coplanar (weak vertical + mirror ambiguity) and its small hull dooms exterior clients to runaway GDOP. But shape is downstream of the deeper issues — redundancy = 0 and uncorrected NLOS. Fix those and the shape problem largely dissolves.</p></div>

<div class="item"><p class="q">Could they be spaced <em>further</em> apart and still range/solve?</p>

<p class="a"><span class="tag no">Inverted indoors</span>Farther links mean lower SNR <em>and</em> more obstructions per link — indoors with phones, wider spacing makes reliability worse, not better. Wide spacing is an open-LoS / better-antenna property. Denser, well-placed anchors win.</p></div>

<div class="item"><p class="q">Is the indoor setting the cause?</p>

<p class="a"><span class="tag yes">Primarily, yes</span>Multipath, NLOS, and human-body blockage are the dominant error sources; the same 4 phones outdoors in clear LoS would solve far more reliably. “Indoor” is the difficulty multiplier; “4 anchors” and “no survey” remove the margin that would absorb it.</p></div>

</div>

</section>

<section>

<div class="col"><h2><span class="num">04</span> Fundamental limits — hard vs soft</h2>

<p class="lede"><span class="chip hard">HARD</span> a physics/geometry/information wall no code crosses on this

hardware. <span class="chip soft">SOFT</span> addressable in software or protocol. The two problems the project

spent most on — agreement and accuracy — both sit on top of L1, which is hard.</p></div>

<div class="tablescroll">

<table>

<thead><tr><th>#</th><th>Limitation</th><th>Kind</th><th>Caps</th><th>Lever</th></tr></thead>

<tbody>

<tr><td class="id">L1</td><td><strong>4 anchors = 0 redundancy</strong> — a biased/blocked edge is undetectable</td><td><span class="chip hard">HARD</span></td><td>reliability of the anchor solve</td><td>≥5–6 anchors</td></tr>

<tr><td class="id">L2</td><td><strong>Near-coplanar</strong> — weak vertical, mirror ambiguity</td><td><span class="chip hard">HARD</span></td><td>vertical accuracy, lock stability</td><td>≥3 distinct heights</td></tr>

<tr><td class="id">L3</td><td><strong>Exterior clients</strong> outside the anchor hull</td><td><span class="chip hard">HARD</span></td><td>exterior accuracy</td><td>anchors <em>around</em> coverage</td></tr>

<tr><td class="id">L4</td><td><strong>Indoor NLOS / human blockage</strong> — time-varying bias &amp; dropouts</td><td><span class="chip mix">SOFT·ish</span></td><td>instantaneous accuracy</td><td>NLOS reject · average+lock · redundancy</td></tr>

<tr><td class="id">L5</td><td><strong>Phone-class radios</strong> — short range, coarse AoA, thin CIR, session caps</td><td><span class="chip mix">HARD·ish</span></td><td>range, AoA, client capacity</td><td>dedicated anchors; phones as clients</td></tr>

<tr><td class="id">L6</td><td><strong>Many clients over TWR</strong> — channel capacity</td><td><span class="chip soft">SOFT</span></td><td>simultaneous clients / rate</td><td>TDMA schedule or TDoA</td></tr>

<tr><td class="id">L7</td><td><strong>Survey-free</strong> — no external scale reference</td><td><span class="chip mix">CHOICE</span></td><td>immunity to a wrong-scale edge</td><td>one known baseline, or redundancy</td></tr>

</tbody>

</table>

</div>

</section>

<section class="col">

<h2><span class="num">05</span> What actually moves the needle</h2>

<p class="lede">Ranked by leverage. The numbering is the priority order — do them roughly in sequence.</p>

<ol class="path">

<li><p><span class="lever">Provision ≥5–6 anchors with geometric + height diversity.</span> The biggest lever. Five flips redundancy to 1; six gives graceful degradation and LoS diversity. Place them convex around the coverage area at ≥3 heights — and this <em>activates the #63/#69 software that is inert on 4</em>.</p></li>

<li><p><span class="lever">Turn NLOS mitigation from stub to real (#62 → classifier).</span> Capture first-path/RSSI (started) and reject or down-weight blocked links — the standard technique. Accept that phone radios cap how good it gets.</p></li>

<li><p><span class="lever">Solve-once-and-lock the static mesh; average over time.</span> Anchors don't move: solve in a clean window, lock, re-solve only on a persistent change. Turns transient human blockage from a solve-killer into a non-event.</p></li>

<li><p><span class="lever">Add a ranging schedule (TDMA) — or move clients to TDoA.</span> Uncoordinated TWR hits a capacity wall for several clients (and is a prime suspect for the dark link). This is how COTS RTLS reaches many tags.</p></li>

<li><p><span class="lever">Keep the over-determination software (#63/#69).</span> No change — it earns its keep once step 1 lands.</p></li>

<li><p><span class="lever">Set exterior-client expectations honestly.</span> Outside the hull, multilateration can't be accurate. Ring the exterior with its own anchors, or declare it “presence, not precision.”</p></li>

<li><p><span class="lever">Consider a hardware-tier split.</span> Dedicated UWB anchors for fixed infrastructure (real antennas, CIR, range); phones as clients only — what every serious indoor RTLS does.</p></li>

</ol>

</section>

<section class="col">

<h2><span class="num">06</span> Re-scope the acceptance criteria into tiers</h2>

<p class="lede">Today's criteria conflate asks that conflict: wide spacing vs indoor NLOS; exterior clients vs a

clustered hull; survey-free sub-cm vs a biased edge; phone-only vs range + NLOS rejection. Split the definition

of done.</p>

<div class="tiers">

<div class="tier a"><span class="badge">Tier A · now</span><h3>Locked interior mesh</h3><p>Static 4–6-anchor mesh, interior clients, solved-and-locked, <strong>decimetre</strong>, NLOS-mitigated, low client count. Essentially the convergence gate with a realistic tolerance and a 5th anchor. A real, demonstrable product.</p></div>

<div class="tier b"><span class="badge">Tier B · provision</span><h3>Multi-client + resilient</h3><p>Several clients, blockage-resilient, via 6–8 anchors + a ranging schedule. Needs the provisioning and scheduling levers (steps 1 &amp; 4).</p></div>

<div class="tier c"><span class="badge">Tier C · renegotiate</span><h3>The maximalist ask</h3><p>Survey-free sub-cm <em>and</em> exterior clients <em>and</em> phone-only <em>and</em> wide spacing. Pick one or two to relax — all four together isn't supported by the physics on this hardware.</p></div>

</div>

</section>

<section class="col">

<h2><span class="num">07</span> Revised constraints — courses of action, updated</h2>

<p class="lede">A later framing fixes four constraints and relaxes the rest. Freeing <strong>anchor count</strong>

and <strong>survey</strong> dissolves the hard limits above (L1/L2/L3/L7) and <em>activates</em> the #63/#69

over-determination code that was inert on 4 anchors — the geometry problem becomes a provisioning problem, and

provisioning is now allowed.</p>

<div class="constraints">

<div class="cgroup"><span class="clabel bind">Binding</span>

<span class="pill">human traffic</span><span class="pill">rapid clients</span>

<span class="pill">low-latency cm</span><span class="pill">commercial devices only</span></div>

<div class="cgroup"><span class="clabel relax">Relaxed</span>

<span class="pill off">anchor count</span><span class="pill off">survey</span>

<span class="pill off">spacing</span><span class="pill off">exterior</span></div>

</div>

<div class="verdict" style="border-left-color:var(--hard); margin-top:22px">

<p class="eyebrow" style="color:var(--hard)">The new binding tension</p>

<p><strong>Centimetre + rapid motion + consumer-only</strong> collide. Consumer per-range ≈ 8–12 cm; a dense

surveyed field lands position at <strong>≈5–10 cm</strong> — single-digit cm, <em>not</em> sub-cm. A moving tag

can't average ranges down; <strong>true ≤1 cm needs carrier-phase, which phone APIs don't expose</strong>; and

consumer clocks can't sync to the sub-ns TDoA needs (1 ns ≈ 30 cm), so ranging stays two-way. Human traffic is

now beaten by <strong>anchor density</strong> + NLOS rejection + IMU coasting.</p>

</div>

<div class="tiers" style="margin-top:22px">

<div class="tier a"><span class="badge">CoA A · recommended</span><h3>Dense surveyed lattice + TWR + IMU</h3>

<p>8–16 surveyed, height-diverse consumer anchors (≥6–8 in LoS everywhere) · robust redundant multilateration (#63/#69, now active) · NLOS rejection (#62) · ES-EKF IMU fusion (predict 100–200 Hz → low latency + smooth fast motion) · TDMA scheduling. <strong>≈5–10 cm, low-latency, traffic-robust</strong> — built on the existing stack.</p></div>

<div class="tier b"><span class="badge">CoA B · bonus</span><h3>Client AoA / PDoA refinement</h3>

<p>Where a client exposes direction (iPhone U1/U2; some Samsung), fuse the angle for a tighter fix. Real but coarse and device-specific — a refinement on A, not a foundation.</p></div>

<div class="tier c"><span class="badge">CoA C · the fork</span><h3>Relax one constraint for true ≤1 cm</h3>

<p>Sub-cm on fast movers isn't reachable consumer-only. Relax exactly one: <strong>(i)</strong> a dedicated commercial UWB anchor tier (CIR + carrier-phase + sync → TDoA RTLS; phones stay clients), or <strong>(ii)</strong> cm → few-cm and take A's ≈5–10 cm. A product decision.</p></div>

</div>

<p style="margin-top:18px"><strong>Recommendation.</strong> Build <strong>CoA A</strong> now (consumer-only optimum,

mostly wiring the existing engine), <strong>instrument the achieved σ</strong>, and let that number drive the CoA C

decision — the walk-capture in progress measures exactly it. Net-new engine work: a <span class="k">TDMA ranging

scheduler</span>, <span class="k">dense-anchor auto-survey / calibration</span>, an <span class="k">IMU-forward

low-latency output</span>, and <span class="k">live NLOS rejection</span> (mandatory at cm budget).</p>

</section>

<section class="col">

<h2><span class="num">08</span> Relaxing sub-cm — the triggers survive</h2>

<p class="lede">Sub-cm is relaxed to CoA-A's ≈5–10 cm on one condition: the geometric-predicate triggers stay

accurate and low-latency. They do — because of one reframe.</p>

<div class="verdict" style="margin-top:6px">

<p class="eyebrow">The reframe</p>

<p><strong>Predicate reliability ≠ position accuracy.</strong> Evaluate a predicate against the position <em>and

its covariance</em> (the EKF already emits per-axis σ), and coarser position costs <strong>granularity — the

smallest resolvable zone / object / gap, not reliability.</strong> Margins are spatial, so <strong>latency is

untouched</strong> — crossings can even fire predictively off the fused velocity. The only real cost: at σ ≈

5–10 cm, features closer than ~0.5 m can't be cleanly separated.</p>

</div>

<ul class="facts" style="margin-top:18px">

<li><span class="idx">▢</span><p><strong>Enter / leave a zone.</strong> Two-threshold <strong>hysteresis</strong> (enter when confidently inside by ~2–3σ; leave when confidently outside) + a <strong>covariance gate</strong>. No boundary chatter; correct within a defined band.</p></li>

<li><span class="idx">→</span><p><strong>Point at an object.</strong> Angular, and <strong>dominated by orientation error, not position</strong> (10 cm at 3 m ≈ 1.9°) — so relaxing position sub-cm barely touches it; the real lever is the heading reference (#64). A <strong>σ-driven pointing cone</strong>, evaluated in the shared frame so common-mode error cancels.</p></li>

<li><span class="idx">⌇</span><p><strong>Cross a lane / plane.</strong> <strong>Velocity-gated</strong> crossing (a genuine directional transit from the IMU-fused velocity) + directional hysteresis. Separates a real crossing from jitter in one–two fixes — reliable <em>and</em> low-latency, even predictive.</p></li>

</ul>

<div class="verdict" style="border-left-color:var(--soft); margin-top:18px">

<p class="eyebrow" style="color:var(--soft)">Forward-compatible by design</p>

<p>Make every margin <strong>σ-driven</strong> and reintroducing sub-cm is <strong>automatic</strong>: feed

lower-variance measurements (better radios, a dedicated-anchor tier, or carrier-phase) → the covariance drops →

every predicate margin <strong>shrinks on its own</strong> and the triggers sharpen, with no predicate change.

So better tech is a <strong>recalibration</strong> (anchor positions + delays) at most; a new modality

(carrier-phase / TDoA) enters as <strong>one added EKF factor</strong>; the predicate logic never moves.

<strong>Design mandate: never hardcode a spatial tolerance — derive it from the live covariance.</strong> The

accuracy tier becomes a dial, not a rebuild.</p>

</div>

</section>

<section class="col">

<h2><span class="num">09</span> Below the floor — huddle-scale predicates (&lt;1 m)</h2>

<p class="lede">Real predicates put entities &lt;1 m apart (a huddle is ~0.3–0.5 m) — below §08's ~0.5 m

granularity floor, so it needs better than 5–10 cm. Does more hardware get there?</p>

<div class="verdict" style="border-left-color:var(--hard); margin-top:6px">

<p class="eyebrow" style="color:var(--hard)">More anchors ≠ sub-cm</p>

<p>Range error is <strong>random</strong> (averages ~1/√(N·M)) ⊕ <strong>systematic</strong> (antenna delay,

multipath, NLOS bias, timestamp quantization — persistent, not zero-mean). ToF resolution is set by

<strong>bandwidth</strong> (UWB 0.5–1 GHz → ~15–30 cm raw, few-cm refined), not anchor count. So anchors

asymptote at the <strong>systematic floor (~2–5 cm)</strong> and never reach sub-cm — and in a huddle the

<strong>bodies NLOS the anchor links</strong>, degrading it further. Crossing the floor needs a different

<em>measurement modality</em>, not more boxes.</p>

</div>

<p style="margin-top:18px"><strong>The unlock — relative, not absolute.</strong> The huddle is a

<em>tell-them-apart</em> question, and relative accuracy is cheaper: <strong>direct peer-to-peer ranging</strong>

measures a separation with no anchors, and <strong>common-mode anchor error cancels</strong> between co-located

devices. Match need to rung:</p>

<div class="tablescroll" style="margin-top:12px">

<table>

<thead><tr><th>Resolve</th><th>Needs error</th><th>Reachable by</th></tr></thead>

<tbody>

<tr><td>~1.0 m</td><td>~0.50 m</td><td>CoA A (5–10 cm) — already fine</td></tr>

<tr><td>~0.5 m loose huddle</td><td>~0.25 m</td><td>CoA A + dense anchors</td></tr>

<tr><td>~0.3 m huddle</td><td>~0.15 m</td><td><strong>CoA D</strong> — P2P relative ~5–10 cm</td></tr>

<tr><td>~0.1 m</td><td>~0.05 m</td><td><strong>CoA E / G</strong> — carrier-phase / optical</td></tr>

<tr><td>~0.02 m sub-cm</td><td>~0.01 m</td><td><strong>CoA E / F</strong> — carrier-phase, RTLS</td></tr>

</tbody>

</table>

</div>

<ul class="coa" style="margin-top:18px">

<li><span class="cb soft">CoA D</span><p><strong>Peer-to-peer relative ranging + joint solver.</strong>

<em>Achieves</em> relative ~5–10 cm (resolves 0.3–0.5 m huddles; identities never confused). <em>Needs</em>

client↔client ranging + a P2P scheduler + a joint factor-graph solver. <em>Trade-off</em> air-time/capacity;

still ToF-limited (not sub-cm); solver cost grows with cluster size. <strong>Consumer-safe.</strong></p></li>

<li><span class="cb accent">CoA E</span><p><strong>Carrier-phase / PDoA ranging.</strong> <em>Achieves</em>

mm–cm → true sub-cm; the only path below ~2 cm. <em>Needs</em> phase/CIR-exposing radios (dedicated modules,

not phones) + integer-ambiguity resolution + CIR multipath exclusion. <em>Trade-off</em> new hardware tier;

multipath-fragile (huddle bodies can break phase lock → falls back to cm); highest complexity.</p></li>

<li><span class="cb caution">CoA F</span><p><strong>Synced dedicated-anchor TDoA + phase (industrial RTLS).</strong>

<em>Achieves</em> sub-cm–mm. <em>Needs</em> wired/RF-synced dedicated anchors + pro survey; dedicated tags for

sub-cm. <em>Trade-off</em> cost, cabling, fixed + not portable, not consumer — opposite of the vision.</p></li>

<li><span class="cb accent">CoA G</span><p><strong>Multi-modal fusion (UWB + optical / acoustic).</strong>

<em>Achieves</em> relative cm at short range (camera photogrammetry, or phone acoustic chirp) fused with UWB.

<em>Needs</em> a fusion layer + camera/mic. <em>Trade-off</em> light/quiet/LoS dependence, privacy, new

failure modes.</p></li>

<li><span class="cb soft">CoA H</span><p><strong>Predicate redesign to identity + relative.</strong>

<em>Achieves</em> the intent of many huddle predicates for free — UWB identity (never confuses people) +

direct P2P range/bearing + §08's uncertainty logic. <em>Trade-off</em> no &lt;10 cm discrimination; the rest

need E/F/G. <strong>Free.</strong></p></li>

</ul>

<div class="verdict" style="border-left-color:var(--soft); margin-top:18px">

<p class="eyebrow" style="color:var(--soft)">Layer them — accuracy becomes per-zone</p>

<p>Because the engine is σ-driven, these aren't rival tiers — each is a measurement factor you add. Default to

<strong>A + H + D</strong> (all consumer-safe; resolves the huddle, keeps identities); add <strong>E or G only in

the zones that truly need &lt;5 cm</strong>; reserve <strong>F</strong> for guaranteed-mm fixed installs. You

never need one global tier — a huddle zone runs P2P + optical while the rest runs anchor-only, and every

predicate consumes whatever covariance its region delivers.</p>

</div>

</section>

<section class="col">

<h2><span class="num">10</span> Interlacing meshes for sub-cm — consumer-only</h2>

<p class="lede">Constraint restored to consumer devices only. Can layering multiple meshes over a shared band

reach sub-cm? Yes — but not by stacking UWB.</p>

<div class="verdict" style="border-left-color:var(--hard); margin-top:6px">

<p class="eyebrow" style="color:var(--hard)">Stacking UWB doesn't cross the floor</p>

<p>More UWB — spatial, frequency-diverse, or differential (RTK-style) — all shares the same

ToF/bandwidth/multipath floor, so it clusters at <strong>low-cm (~2–3 cm), never sub-cm on a mover.</strong>

Consumer APIs give a distance per channel, not raw phase, so you can average channels but not <em>coherently

synthesize bandwidth</em>; and UWB multipath decorrelates within ~one wavelength (~4 cm), so a differential

reference can't cancel the rover's local multipath. Same physics floor, N times.</p>

</div>

<p style="margin-top:18px"><strong>The crossing needs a different-physics layer — and one is pure consumer:

acoustic.</strong> Sound is ~10⁶× slower than RF, so the sub-ns timing that's brutal for UWB is trivial for sound:

a 48 kHz mic samples every ~7 mm, cross-correlated to <strong>cm — sub-cm at short range.</strong> Speaker + mic

are on every phone; ultrasonic (18–24 kHz) keeps it inaudible. Its weaknesses (short range, noise, bodies) are

exactly UWB's strengths — which is why you <em>layer</em> them.</p>

<div class="stack">

<div class="layer uwb"><span class="lname">UWB</span><span class="lrole">absolute frame · identity · coverage · cm range + peer-to-peer</span></div>

<div class="layer aco"><span class="lname">ACOUSTIC</span><span class="lrole">short-range cm–sub-cm <strong>relative</strong> in the huddle (ultrasonic chirp ToF)</span></div>

<div class="layer imu"><span class="lname">IMU</span><span class="lrole">dynamics · low latency · coasting through dropouts</span></div>

<div class="layer opt"><span class="lname">OPTICAL</span><span class="lrole">optional — camera photogrammetry, mm relative (light / LoS / privacy)</span></div>

</div>

<ul class="coa">

<li><span class="cb accent">CoA I</span><p><strong>Heterogeneous layered mesh over the shared band.</strong>

<em>Achieves</em> sub-cm <strong>relative</strong> in the huddle (acoustic) + cm absolute (UWB) + low-latency

(IMU), <strong>consumer-only</strong>. <em>Needs</em> an acoustic-ranging subsystem, shared-band time-sync +

a cross-mesh schedule (extend the netcode), mesh-to-mesh association (via UWB IDs), and a joint multi-modal

factor-graph solver. <em>Trade-off</em> acoustic is short-range + noise/NLOS/temperature-sensitive → a

huddle-zone layer, not global; sub-cm <em>relative</em>, not absolute (true absolute sub-cm still needs the

non-consumer E/F).</p></li>

</ul>

<div class="verdict" style="border-left-color:var(--accent); margin-top:18px">

<p class="eyebrow">Why it fits Aether</p>

<p>The shared band <strong>already exists</strong> — BroadcastBand + the Raft fabric is the cross-mesh sync +

measurement-exchange channel the question posits. The ES-EKF becomes a <strong>σ-weighted joint factor

graph</strong> ingesting heterogeneous edges (UWB range, P2P, acoustic, IMU, optical). Accuracy is then

<strong>per-edge and per-zone</strong>: a huddle lights its acoustic layer for sub-cm relative; open areas run

UWB-only. You beat the UWB floor not by stacking UWB, but by <strong>interlacing a slower-wave mesh over the

same band.</strong></p>

</div>

</section>

<section class="col">

<h2><span class="num">11</span> Reliable mesh solving — the dependable precursor to aiming</h2>

<p class="lede">Accept cm (not sub-cm) accuracy for now and make the mesh solve <em>reliably</em> first — because

accurate client aiming can't sit on a frame that isn't dependable. Can 4 anchors do it, at what cost, and what do

more anchors measurably buy?</p>

<div class="verdict" style="border-left-color:var(--caution); margin-top:6px">

<p class="eyebrow" style="color:var(--caution)">4 anchors: reliable only if you trade away four freedoms</p>

<p>With <strong>zero spare constraints</strong> (masthead), a 4-mesh can't detect its own bad edge — so to be

dependable it must <strong>surrender survey-free operation</strong> (pin the frame to the survey),

<strong>arbitrary placement</strong> (non-coplanar, clean LoS on all 6 edges), <strong>continuous re-solve</strong>

(solve-once-and-<b>lock</b>), and <strong>self-healing</strong> (manual re-commission if bumped). It reliably

solves a <em>static, surveyed, locked, lightly-trafficked</em> mesh — not a <em>survey-free, mobile, trafficked,

self-healing</em> one.</p>

</div>

<figure class="figure" style="margin-top:26px">

<p class="cap">What more anchors buy · (1) survives human traffic</p>

<div class="chartscroll">

<svg class="chart" viewBox="0 0 640 250" role="img" aria-label="Probability of at least four clean anchor line-of-sight paths versus anchor count, at 30 percent per-anchor blockage: 24 percent at four anchors, 53 at five, 74 at six, 87 at seven, 94 at eight.">

<line x1="60" y1="200" x2="620" y2="200" style="stroke:var(--border);stroke-width:1.5"/>

<line x1="60" y1="122" x2="620" y2="122" style="stroke:var(--ink-muted);stroke-width:1;stroke-dasharray:3 5;opacity:.5"/>

<text class="axis" x="64" y="118" text-anchor="start" style="opacity:.7">50% — coin-flip</text>

<text class="axis" x="618" y="224" text-anchor="end">anchors →</text>

<text class="axis" x="18" y="112" text-anchor="middle" transform="rotate(-90 18 112)">P(≥4 clean LoS)</text>

<!-- n=4 : 24% -->

<rect x="92" y="163" width="72" height="37" rx="2" style="fill:var(--hard)"/>

<text class="bar-v" x="128" y="154" text-anchor="middle" style="fill:var(--hard)">24%</text>

<text class="bar-n" x="128" y="220" text-anchor="middle" style="fill:var(--hard)">4</text>

<text class="axis" x="128" y="240" text-anchor="middle" style="fill:var(--hard)">drops ¾</text>

<!-- n=5 : 53% -->

<rect x="196" y="118" width="72" height="82" rx="2" style="fill:var(--caution)"/>

<text class="bar-v" x="232" y="109" text-anchor="middle" style="fill:var(--caution)">53%</text>

<text class="bar-n" x="232" y="220" text-anchor="middle" style="fill:var(--caution)">5</text>

<!-- n=6 : 74% (target) -->

<rect x="300" y="85" width="72" height="115" rx="2" style="fill:var(--soft)"/>

<text class="bar-v" x="336" y="76" text-anchor="middle" style="fill:var(--soft)">74%</text>

<text class="bar-n" x="336" y="220" text-anchor="middle" style="fill:var(--soft)">6</text>

<text class="axis" x="336" y="240" text-anchor="middle" style="fill:var(--soft)">◄ recommended</text>

<!-- n=7 : 87% -->

<rect x="404" y="65" width="72" height="135" rx="2" style="fill:var(--soft)"/>

<text class="bar-v" x="440" y="56" text-anchor="middle" style="fill:var(--soft)">87%</text>

<text class="bar-n" x="440" y="220" text-anchor="middle" style="fill:var(--soft)">7</text>

<!-- n=8 : 94% -->

<rect x="508" y="54" width="72" height="146" rx="2" style="fill:var(--soft)"/>

<text class="bar-v" x="544" y="45" text-anchor="middle" style="fill:var(--soft)">94%</text>

<text class="bar-n" x="544" y="220" text-anchor="middle" style="fill:var(--soft)">8</text>

</svg>

</div>

<p class="sub">Each anchor independently body-blockable at <span class="k">p=0.7</span>; a good 3-D fix needs

<b>≥4 clean anchors</b>. Going <b>4 → 6</b> takes a mesh from <b>dying when a person walks through it (24%)</b> to

<b>solving 3 of 4 moments (74%)</b>. This is the resilience metric that matters under real traffic.</p>

</figure>

<figure class="figure" style="margin-top:20px">

<p class="cap">What more anchors buy · (2) accuracy — but only down to the floor</p>

<div class="chartscroll">

<svg class="chart" viewBox="0 0 640 250" role="img" aria-label="Position error versus anchor count falls from about twelve centimetres at four anchors toward a systematic floor near four centimetres, asymptoting and never reaching sub-centimetre.">

<line x1="70" y1="200" x2="620" y2="200" style="stroke:var(--border);stroke-width:1.5"/>

<text class="axis" x="618" y="224" text-anchor="end">anchors →</text>

<text class="axis" x="20" y="120" text-anchor="middle" transform="rotate(-90 20 120)">position σ (cm)</text>

<!-- systematic floor -->

<line x1="70" y1="154" x2="620" y2="154" style="stroke:var(--hard);stroke-width:1.5;stroke-dasharray:6 5"/>

<text class="axis" x="614" y="149" text-anchor="end" style="fill:var(--hard)">systematic floor ~4 cm — anchors can't cross</text>

<!-- diminishing-returns curve -->

<polyline points="110,63 230,109 350,123 470,131 590,136" fill="none" style="stroke:var(--accent);stroke-width:2.5"/>

<g style="fill:var(--accent)">

<circle cx="110" cy="63" r="5"/><circle cx="230" cy="109" r="5"/><circle cx="350" cy="123" r="5"/>

<circle cx="470" cy="131" r="5"/><circle cx="590" cy="136" r="5"/>

</g>

<text class="bar-v" x="110" y="52" text-anchor="middle" style="fill:var(--hard)">~12</text>

<text class="bar-v" x="230" y="99" text-anchor="middle">~8</text>

<text class="bar-v" x="350" y="113" text-anchor="middle">6.7</text>

<text class="bar-v" x="470" y="121" text-anchor="middle">6.0</text>

<text class="bar-v" x="590" y="126" text-anchor="middle">5.6</text>

<text class="bar-n" x="110" y="220" text-anchor="middle">4</text>

<text class="bar-n" x="230" y="220" text-anchor="middle">5</text>

<text class="bar-n" x="350" y="220" text-anchor="middle">6</text>

<text class="bar-n" x="470" y="220" text-anchor="middle">7</text>

<text class="bar-n" x="590" y="220" text-anchor="middle">8</text>

</svg>

</div>

<p class="sub">Illustrative <span class="k">σ ≈ floor + A/(N−3)</span>. More anchors shrink the geometric/GDOP error

and <b>asymptote at the ToF systematic floor</b> — real gains, but <b>never sub-cm</b>. The takeaway divides

cleanly: <b>add anchors for reliability &amp; traffic-resilience (charts above), not to change the accuracy

class</b> (that needs §09–§10's different-physics layers).</p>

</figure>

<p style="margin-top:22px"><strong>Courses of action for a dependable solve — the R-series</strong>, ordered from

zero-hardware-today to the robust target:</p>

<ul class="coa">

<li><span class="cb accent">R1</span><p><strong>Surveyed &amp; frame-locked 4-anchor.</strong> <em>now · 0 hw</em>

Pin to the recorded survey, solve once, <strong>lock</strong>. <em>Sacrifice</em> survey-dependent · manual

re-commission · 24% traffic coverage. Dependable for a <b>static, light-traffic</b> solve today.</p></li>

<li><span class="cb accent">R2</span><p><strong>Observer-walk self-survey + lock.</strong> <em>near-term</em>

The #69b-i walk over-determines the frame → <strong>self-solve then lock</strong>, dropping the tape-measure.

<em>Sacrifice</em> a commissioning walk · still static-lock · still 24% traffic. Fixes <em>how you get</em> the

frame, not 4-anchor fragility.</p></li>

<li><span class="cb soft">R3</span><p><strong>Provision to 6 anchors.</strong> <em>target</em> 3 spare constraints

→ detect &amp; drop a bad edge, <b>74% coverage</b>, survey-free (self-checks), continuous re-solve,

self-diagnosis, mobility-tolerant. <em>Sacrifice</em> two more devices — the only real cost. Software is already

over-determined-ready (#69).</p></li>

<li><span class="cb caution">R4</span><p><strong>Static solve-and-LOCK + NLOS/σ gate.</strong> <em>cross-cutting</em>

Freeze the frame while clean; gate client range updates by an NLOS/σ test so a body-blocked spike can't corrupt

a position. <b>Mandatory at N=4</b>, belt-and-suspenders at N≥6. Makes <em>any</em> N dependable.</p></li>

</ul>

<div class="verdict" style="border-left-color:var(--accent); margin-top:18px">

<p class="eyebrow">Recommendation — lock now, provision to six for traffic</p>

<p><strong>NOW (0 hardware): R1 + R4</strong> — pin to survey, solve-once-and-lock, add the NLOS/σ gate → today's

mesh is dependable for a static, light-traffic solve, enough to start validating aiming against a frame that won't

move under you. <strong>NEAR-TERM: R2</strong> drops the tape-measure (validated by the walk capture).

<strong>TARGET: R3 — provision to 6 anchors</strong>, the honest precursor to reliable aiming under real traffic:

4 can be <em>made</em> reliable only by giving up mobility, blockage-tolerance and self-healing —

<b>6 buys all three back for the price of two devices.</b> Keep R4's lock-and-gate as the invariant.</p>

</div>

</section>

<div class="bottomline">

<p class="eyebrow">The mission, honestly</p>

<p>The premise is right and the software built so far is largely correct and necessary — it is simply operating

under a geometry that gives it nothing to work with. Spend the next effort on <b>anchors, placement, NLOS

signal, and a scheduler</b>, tier the acceptance criteria, and the achievable version is close at hand. The

walk-capture in progress will quantify exactly how much of the 4-anchor gap the observer lever can close — which

tells us whether a 5th anchor is <b>optional or mandatory</b> for the target tier.</p>

</div>