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A GPS does nothing more than provide a location fix; an X-Y-Z (latitude, longitude, elevation) position. This is the basic measurement, known as a fundamental unit. Speed, heading, course, eta, etc. are all derived, or computed values using your delta position over a given amount of time, usually fractions of a second. Most GPSs provide speed data not as instantaneous readings for every delta, rather they use moving averages over say 5 or 10 discretized movements to compensate for GPSs inherent errors. Remember, most of the GPSs we use are in the range of +/-2 meters with WAAS enabled, but more often +/-5 meters accuracy. This is where we see occasional spikes of troughs in velocity indications. If, for instance, one positional fix is -15 meters, and the next of +15 meters, that's a total error of about 90 feet. This error over say even 250 milliseconds amounts to about 30mph error. All it takes is the gain or loss of a few milliseconds during clock re-sync (because the internal GPS clocks are synced with satellite time at set intervals), or the loss/acquisition of satellites giving slight positional errors, and you'll see some weird indicated speeds.
Like from going under a bridge?