Lap detection

Dirt ovals are short, GPS is noisy at 10–18 Hz, and the car also drives pit roads and the infield. Lap detection therefore uses a gate with several guards and a full-loop progress check, never a single "distance to a point" rule.

Steps

1. Working set — valid GPS samples in local metres, split into runs at gaps > 1 s. Heading is taken from a 5-sample moving average of positions and is undefined below 2 m/s.
2. Racing surface — samples faster than 8 m/s (≈ 18 mph) define the loop; a preliminary centerline gives its length $L_0$ and direction (sign of the net heading change: counter-clockwise = left turns).
3. Start/finish gate — placed automatically at the centre of the longest straight (lowest curvature over the longest arc), perpendicular to the centerline, half-width $w = \max(15\,\mathrm{m},\; 3 \times \text{median lateral spread})$. Lap times of complete laps do not depend on where the gate sits.
4. Crossings — consecutive samples whose segment intersects the gate, with speed ≥ 3 m/s, heading within 45° of the gate direction, and at least 6 s after the previous accepted crossing. The crossing time is interpolated: $t_c = t_{i-1} + (t_i - t_{i-1})\,\lambda$, where $\lambda$ is the intersection parameter along the sample segment. Every rejected crossing keeps its reason. Crossing confidence: $\mathrm{clip}(1 - |n|/w)\cdot\mathrm{clip}(\cos\theta)$ from the lateral offset $n$ at the gate and the heading error $\theta$.
5. Lap assembly — intervals between consecutive crossings in one run. Before the first crossing: partial (start); after the last: partial (end).
6. Progress check — each candidate lap is projected onto the centerline (see Track progress). A genuine lap covers ≥ 95 % of $L_0$, never steps backward more than 10 m, has an integrated distance within ±10 % of $L_0$, and does not lose projection for more than 5 consecutive samples or 5 % of its samples.

Classification

Evaluated in this order; the first matching rule wins and the reason is stored on the lap.

result	rule	notes
pit	more than 2 s below 2 m/s	stopped on track / pit road / red flag
invalid: did not complete the loop / went backwards on track / distance does not match the track length / GPS projection lost	progress check failed	see step 6
invalid: GPS quality too low	valid fraction < 0.9 or a gap > 1 s
invalid: implausibly fast for the track length	lap time < 0.95 × $L_0 / v_{max}$	physical bound
caution	lap time > 1.35 × fastest candidate, or mean speed < 0.7 × best mean speed
racing	everything else

Observed on real data: racing laps 18.8–22.9 s, caution laps 39–52 s, first partial 47–52 s, so the 1.35 factor separates cleanly. The fastest candidate is used (not a percentile) because sessions with a single green lap exist.

Only racing laps can be chosen as reference or comparison; caution laps are shown with their delta to the fastest lap for context.

Resolution of a lap time

The crossing interpolation resolves the crossing to a fraction of a sample interval; with ~0.2 m positional noise at 35 m/s the crossing time noise is of the order of 5–10 ms. Because the reference and the comparison lap cross the same gate with the same receiver, GPS latency cancels in the delta.

Verified

• Hamilton County HERO9 heat: 8 racing laps 20.70–21.49 s, one caution, two partials; I-35 HERO11 heat: pace laps classified caution, green laps racing. Lap times match the independent heading-based reconnaissance within 0.3 s.
• Synthetic oval: exact lap count and times; an infield excursion produces no lap; a stop on track → pit; a slow lap → caution. Also covered by unit tests of the gate geometry and by regression tests (lap count, classes, times ±5 ms).