Speed

Which speed

The GoPro receiver reports a 2-D speed with every position. Reconnaissance on the real files showed it behaves like a receiver velocity solution: smooth and unbiased against the positions (1 s window bias −0.02…+0.09 m/s), while sample-to-sample position differencing at 18 Hz is unusable (RMS disagreement 3.2–3.8 m/s, "roughness" 7.4 vs 0.13). The reported speed is therefore the primary channel and position-derived speed is the independent witness (the consistency check in GPS validation).

Definitions

• $v_{raw}$: reported 2-D speed with its quality flags.
• $v_{valid}$: $v_{raw}$ with SPEED_SPIKE, NO_FIX, PRELOCK samples removed; gaps up to 0.5 s linearly filled and flagged INTERPOLATED; longer gaps left open.
• $v_{analysis}$: zero-phase Butterworth low-pass of $v_{valid}$ — order 2 applied forward and backward (second-order sections, effective order 4, no phase lag) with cutoff 1.0 Hz, computed on a uniform time grid per contiguous run and mapped back to the samples, then resampled onto the 1 m track grid. This is the speed on every chart and in every metric.
• Longitudinal (path) acceleration: $a_{long} = dv_{analysis}/dt$ by Savitzky–Golay derivative with window 0.7 s and polynomial order 2. Positive = accelerating.

Why 1.0 Hz

Selected during development, on the real recordings, from candidates 0.5 / 1.0 / 2.0 Hz: the lowest cutoff whose residual is near-white and whose brake/acceleration events shift by less than 3 m against the 2 Hz candidate; a one-sample injected spike changes the maximum speed by < 0.1 m/s. The heading window (1.0 s) was chosen for Cornering G noise of 0.02–0.04 g (1σ) on straights with no corner bias; the longitudinal window (0.7 s) reproduces a synthetic ramp within 3 %.

Metrics

metric	definition	units shown
Max / min / average speed (lap)	max and min of $v_{analysis}$ in the lap; average = centerline length / lap time	mph
Entry / exit speed (segment)	$v_{analysis}$ at the first / last grid point of the segment	mph
Minimum speed (segment)	lowest $v_{analysis}$ in the segment and its track position	mph, m
Speed loss	entry − minimum	mph
Brake point	first position where $a_{long} < -$2 m/s² is sustained for 0.3 s	m of track position
Acceleration point	first position after the minimum speed where $a_{long} > +$1 m/s² is sustained for 0.5 s	m of track position

Positions are track progress s in metres from the start/finish gate (the "s coordinate", not seconds).

Display conversions

mph = m/s × 3600 / 1609.344 (exact). Nothing else is recomputed in the browser: the values shown at the cursor are the engine's grid values at the nearest 1 m grid point.

Limitations

• The receiver's speed trails true motion by 0.15–0.40 s (the GPS lag, measured per session against the accelerometer). It is constant within a session and common to both laps of a comparison, so it does not affect deltas; it does shift brake points slightly later on the video.
• Speeds below 3 m/s carry no heading (Cornering G undefined); lap detection ignores samples below 3 m/s at the gate.
• Reported speed above 80 m/s (179 mph) or a physically impossible step is rejected as a spike.

Verified

• Per-s standard deviation of speed across racing laps < 2 m/s on the straights of both reference recordings.
• $|a_{long}| < 12$ m/s² everywhere on the reference recordings; minimum-speed locations fall inside the corner arcs.
• Tests: filter unit tests (impulse symmetry, unit DC gain, SG derivative of a known polynomial), synthetic ramp within 3 %, regression tests (max/min/avg ± 0.05 m/s).