Doppler experiment
Contents
Introduction
Increasingly, we are seeing FlySight used to score Speed Skydiving competitions. There has been some concern within the Speed Skydiving community that these devices may not be accurate at such high speeds. In particular, it has been suggested that the dynamic model imposes some kind of limit at 100 m/s. An engineer from u-blox has responded to this concern as follows:
The 100 m/s figure is part of sanity check and not an absolute limit. As long as speed does not exceed 600 m/s you should still get valid position data.[1]
The “sanity check” is imposed only if the signal degrades past some point—i.e., if the number or geometry of satellites or signal strength fall below some threshold. If the sanity check is imposed, we should see this reflected in the accuracy estimates reported by the u-blox module:
Similar degradation of accuracy estimates is to be expected regardless of which sanity check limit is exceeded.[2]
To address these concerns, we have developed a Doppler speed measurement system to measure the relative speed of the jumper directly. To use this system, a transmitter with very accurate frequency is placed on the jumper. A receiver is then placed on the ground. Any motion of the jumper toward or away from the receiver will cause a shift in the received frequency.
We can then use position and velocity data from FlySights on the jumper and on the ground to calculate an expected Doppler shift. This expected shift can be overlaid on the received signal to determine if the two are in agreement.
Theory
Doppler shift occurs when the source of a wave is moving relative to an observer. In the illustration below, a source on the jumper periodically emits a pulse. Each pulse moves uniformly outward from the original location of the source. However, since the source itself is moving, these waves do not share a common center. The effect is that the waves “pile up” in front of the jumper and are “stretched out” behind him. An observer in front of the jumper will hear this as an increase in the frequency of the source.
A common example of this effect is the change in pitch heard as a siren passes us on the road. The same effect is observed with radio waves. When the source of a radio wave is moving toward the observer, that observer will detect a slight increase in the frequency of the source. Because the jumper will be moving at much less than the speed of light, we can approximate the Doppler shift using this equation:
\sum_{k=1}^N k^2
