Estimated Accuracy

When MeshMonitor draws a node at an estimated position, it also draws a dashed accuracy circle around it. This page explains exactly how that circle — the node's uncertaintyKm — is computed, so you can read it with confidence and know when to trust an estimate.

In one sentence

The estimate is an SNR- and time-weighted centroid of every anchor that heard the node; the circle radius is the weighted spread of those anchors, shrunk by how many effective observations you really have. One anchor → a big "somewhere within radio range" circle; many converging anchors → a small, confident circle.

For what position estimation is, how to turn it on, and the settings that control it, see Position Estimation. This page is the deep-dive on the accuracy math.

The pipeline at a glance

 traceroutes ┐                 ┌─ weight each observation ─┐
             │   observations  │   w = time-decay × SNR     │   weighted
 neighbor ───┼──▶ (anchor pos, ├──────────────────────────▶├─▶ centroid  ─▶ (lat, lon)
   info     ┘     SNR, time)   │                            │      │
                               └────────────────────────────┘      ▼
                                                            uncertainty radius
                                                          (spread ÷ √effective-N,
                                                           blended w/ radio range)

Every estimate is a pure function of a node's observations. An observation is "an anchor (a node whose position we already know) heard this node, at this SNR, at this time." Two data sources produce them:

Source	Observation it creates	SNR used
Traceroute	each A → X → B hop anchors the middle node X toward its positioned path-neighbors	per-hop SNR (raw ÷ 4 → dB)
NeighborInfo	a direct-RF pair anchors the unpositioned side to the positioned side	link SNR (already dB)

Step 1 — Weight each observation

Every observation gets a single scalar weight, the product of two independent factors:

weight = time_decay × snr_weight

SNR weight — stronger signal pulls harder

SNR is converted to linear signal power:

snr_weight = 10 ^ (SNR_dB / 10)

This is the physically correct mapping: a higher (less-negative) SNR means the anchor is more likely to be near the node, so it should pull the estimate toward itself harder. Weak signals barely move the estimate.

 SNR (dB)   snr_weight = 10^(SNR/10)     relative pull
 ───────    ───────────────────────     ─────────────────────────
  +15            31.6                    ████████████████████████  very strong
  +10            10.0                    ████████████              strong
   +5             3.16                   ████                      good
    0             1.0                    █                         reference
   −6             0.251                  ▏                         weak
  −12             0.063                  ·                         very weak (poor link)
  −20             0.01                   ·                         near noise floor

A −12 dB anchor barely counts

At −12 dB an anchor carries ~0.06 of the weight of a 0 dB anchor and ~1/160th of a +10 dB anchor. That asymmetry is the heart of the accuracy math below — and the reason a single weak anchor must never produce a confident estimate.

Time-decay weight — newer observations count more

Observations lose half their weight every 24 hours:

time_decay = 0.5 ^ (age_hours / 24)     (exponential, half-life = 24h)

 age        time_decay
 ────       ──────────
 now        1.00
 12 h       0.71
 24 h       0.50
 48 h       0.25
 72 h       0.125
 7 days     0.008

So a fresh −6 dB report can outweigh a three-day-old +0 dB report. The lookback window sets how far back observations are even considered.

Step 2 — Weighted centroid (the position)

The estimated location is the weight-weighted average of all anchor positions:

        Σ (wᵢ · latᵢ)              Σ (wᵢ · lonᵢ)
 lat =  ─────────────       lon =  ─────────────
            Σ wᵢ                       Σ wᵢ

For the simplest case — a single traceroute segment with two anchors — this reduces exactly to the classic SNR-weighted midpoint. With many anchors heard from many directions, the centroid converges on the node's true location:

   Anchor B (SNR +8, w≈6)
        ●
         \                      ★ = weighted centroid (the estimate)
          \                     ●  pulls toward the strong/near anchors,
     ★     \                       barely toward the weak/far ones
   ●────────●  Anchor A (SNR 0, w=1)
   │
   ● Anchor C (SNR −10, w≈0.1)   ← far + weak ⇒ almost no pull

Step 3 — The accuracy radius (uncertaintyKm)

This is the circle you see. It is built from three ingredients.

3a. Weighted RMS spread

How far the anchors sit from the centroid, weighted:

            ┌─────────────────────────┐
 rms_km  =  │  Σ (wᵢ · distᵢ²)  /  Σ wᵢ
            └─────────────────────────┘   (square root of the weighted mean
                                            squared distance to the centroid)

3b. Effective sample size (Kish)

Counting anchors naively is misleading when one anchor dominates the weights, so we use the Kish effective sample size:

          (Σ wᵢ)²
 n_eff =  ────────
           Σ wᵢ²

n_eff answers "how many balanced observations is this really worth?"

• Two equally-weighted anchors → n_eff = 2.
• One anchor at weight 10 plus one at weight 0.06 → n_eff ≈ 1.01 — i.e. effectively a single observation, even though two anchors exist.

3c. Confidence blend

A raw "spread ÷ √n_eff" statistic looks dangerously confident when n_eff is barely above 1 (the dominated case above). So the final radius blends a conservative radio-range default toward the statistical estimate, using a confidence factor derived from n_eff:

 statistical_km = rms_km / √n_eff          (clamped to ≥ 0.05 km)
 confidence     = clamp(n_eff − 1, 0, 1)   (0 at n_eff=1 … 1 at n_eff≥2)

 uncertainty_km = 5 km × (1 − confidence)  +  statistical_km × confidence

 n_eff   confidence   what the circle reflects
 ─────   ──────────   ────────────────────────────────────────────
  1.0       0.00      pure 5 km radio-range default (single / dominated)
  1.25      0.25      mostly default, a little statistics
  1.5       0.50      half-and-half
  1.75      0.75      mostly statistics
 ≥2.0       1.00      pure statistical radius (balanced multi-anchor)

• A lone anchor can only say "within radio range," so it gets the full ~5 km default.
• A balanced multi-anchor solve (n_eff ≥ 2) trusts the geometry fully and can report a sub-kilometre radius.
• Anything in between is blended, so a near-single solve can never sneak out a falsely tight circle.

Why the blend exists (issue #3616)

Before this refinement, the radius was just rms_km / √n_eff. With one strong anchor and one weak/far anchor, the centroid collapses onto the strong anchor, the weak anchor contributes almost nothing to rms_km, and n_eff lands at ~1.01 — just above the single-anchor cut-off. The result was a tiny, falsely confident circle for what was effectively one observation (a node heard once at −12 dB appearing pinned, with confidence, inside the one house that heard it). Blending on n_eff closes that gap without changing the correct weight model or any genuinely balanced estimate.

Worked examples

All three assume fresh observations (time_decay ≈ 1) so we can focus on SNR and geometry.

Example A — single anchor (one house heard it once)

 Observations: 1   ·   anchor at the listener, SNR −12 dB
 wSum = 0.063      w²Sum = 0.063²        n_eff = 0.063² / 0.063² = 1.00
 centroid = the anchor itself  ⇒  rms_km = 0
 confidence = clamp(1 − 1) = 0
 uncertainty = 5 km × 1  +  0.05 km × 0  =  5 km

➡ Estimate sits at the anchor, circle = 5 km. Correctly screams "I only know it's within radio range of this one node."

Example B — one strong + one weak/far anchor (the #3616 case)

 Anchor 1: SNR +10 (w = 10)   at the reporter's house
 Anchor 2: SNR −12 (w = 0.063) ~4 km away

 wSum = 10.063   w²Sum = 100.004   n_eff = 10.063² / 100.004 ≈ 1.013
 centroid ≈ 0.025 km from anchor 1 (the weak anchor barely tugs it)
 rms_km ≈ 0.32 km        statistical_km ≈ 0.31 km
 confidence = clamp(1.013 − 1) = 0.013

 uncertainty = 5 km × 0.987  +  0.31 km × 0.013  ≈  4.94 km

➡ Estimate near the strong anchor, but circle ≈ 4.94 km — honestly unreliable. (Before the blend fix this reported ≈ 0.31 km — confident and wrong.)

Example C — balanced four-anchor solve

 Four anchors, comparable SNR (w ≈ 1 each), ~1 km from the node on four sides
 wSum = 4   w²Sum = 4   n_eff = 16 / 4 = 4   →  confidence = 1
 rms_km ≈ 1 km          statistical_km = 1 / √4 = 0.5 km
 uncertainty = 5 km × 0  +  0.5 km × 1  =  0.5 km

➡ Tight 0.5 km circle — the geometry is trusted because four independent directions genuinely constrain the node.

Reading the circle on the map

Circle	Meaning	Typical cause
Large (~5 km)	low confidence — "within radio range of one node"	single anchor, or one dominant anchor
Medium (1–3 km)	partial triangulation	a few anchors, uneven SNR
Small (< 1 km)	well-triangulated, trustworthy	several balanced anchors from different directions

Show or hide circles with the Show Accuracy toggle in the Map Features panel; the marker itself follows Show Estimated Positions. A circle is only ever drawn together with its marker.

Hiding the loose ones automatically

Because the biggest circles are the honest ~5 km single-anchor estimates, you can keep the map clean with Global Settings → Position Estimation → Maximum acceptable accuracy: any estimate whose uncertaintyKm exceeds your cutoff is discarded instead of stored. A value of 2–3 km keeps well-triangulated nodes and drops the "somewhere out there" guesses. 0 means no limit. See Choosing a maximum accuracy.

Properties worth knowing

• Deterministic. Same observations in the lookback window → same estimate and same circle, every run. There is no randomness.
• Meshtastic-only, global. Observations are pooled across all Meshtastic sources (including the embedded MQTT broker and bridges) into one estimate per physical node. MeshCore sources are excluded.
• Self-correcting. As soon as a node reports a real GPS position it leaves the estimate set and instead becomes an anchor for everyone else.
• Floored, not zeroed. The radius can never drop below 0.05 km, so a multi-anchor estimate never claims absurd precision.

Reference — the formulas

 weight          wᵢ      = 0.5^(age_h / 24) · 10^(SNR_dB / 10)
 position        lat,lon = Σ(wᵢ·posᵢ) / Σwᵢ            (weighted centroid)
 spread          rms     = √( Σ(wᵢ·distᵢ²) / Σwᵢ )
 effective N     n_eff   = (Σwᵢ)² / Σwᵢ²               (Kish)
 statistical     stat    = max(0.05, rms / √n_eff)
 confidence      c       = clamp(n_eff − 1, 0, 1)
 accuracy circle unc_km  = max(0.05, 5·(1−c) + stat·c)

Implementation: observationWeight() and solveNodePosition() in src/server/services/positionEstimationService.ts.

Related

• Position Estimation — enabling it, settings, the map toggles
• Interactive Maps
• Map Analysis
• Link Quality & Smart Hops