Athletics: 100 m Hurdles
It’s a numbers game (if you don't like numbers, jump this section)
As the "extreme case", consider 100 m hurdles: over a total distance of 100 m there are 10 hurdles, evenly spaced at 8.5 m (13m runup and 10.5m home stretch). The best women cover this distance in well under 12.5 seconds. Tobi Amusan (NGR) holds the world record at 12.12 seconds, from 2022 (Source). For the sake of simplicity, suppose the athlete runs at a constant speed of 8 m/s. Thus, the hurdle-to-hurdle time is 1.0625 seconds (8.5 m divided by 8 m/s). Between each hurdle the athlete does four steps. Ignoring that the one step over the hurdles lasts approximately twice as long, the average step duration is approximately 0.26 seconds. In other words, we have step frequency of 3.76 Hz (steps per second). This means that, when measuring at 10 Hz, we have a bit more than two samples per second. In a perfect world, according to the Nyquist-Shannon theorem, this is enough and, simplified, no more information is gained at a higher rate. However, is it truly enough considering that when we start looking more closely, during each step we have contact phase and a flight phase? Suddenly for each of these phases we have less than two samples. But shouldn't we not also have at least to samples during each of these phases? Whoops, we have a problem: the motion is much faster than the step frequency! Sampling at 10 Hz is too slow and cannot measure the whole movement!
An example from a short hurdles training session
First, let's start without the centre-of-mass model, looking just at how fast the sensor is moving. The figure below compares the ground speed measured at 10 Hz (i.e., 10 samples per second) with the GNSS (black line, each sample is marked with a small dot) with the 200 Hz speed from the sensor fusion (blue line). Both lines follow approximately the same pattern. Until about second 2.0 we have zero speed: the athlete is at the start and waits for the signal. Then we have the acceleration phase for about 2 seconds, followed by the steady state phase with the hurdles for the rest of the time.
The GNSS ground-speed signal appears very noisy and shows regular spikes. These spikes are measurement artifacts caused by the abrupt changes in the athlete's upper-body inclination when jumping over each hurdle. For a very short moment, the sensor suddenly "sees" a different portion of the sky and receives a different combination of satellite signals. This makes the receiver briefly "think" it has moved much faster than it actually has, which shows up as a sharp speed spike in the data.
The 200 Hz speed signal looks much smoother and more regular. However, it still appears noisy, and you can only vaguely recognize the individual steps. This residual noise is mainly caused by the additional motion of the upper body, especially when clearing each hurdle (in this example, the average time from hurdle to hurdle was 1.15 seconds).
Now let's see what happens when we apply our centre-of-mass body model. The first figure below shows the raw 10 Hz GNSS ground speed in grey and the 200 Hz centre of mass ground speed in green. Because the difference may be hard to see, we also display the plot side by side to highlight it (second figure below). Suddenly, the structure in the 200 Hz data emerges: individual steps become easy to identify, and the steps over the hurdles stand out with a clear, repeatable pattern in the athlete's speed between the hurdles. Doing sensor fusion and applying a centre-of-mass model completely changes the signal: noise and measurement errors are removed, the individual steps appear.
You may ask why there are such large speed fluctuations of almost 5 km/h within each step? The main reason is air-drag: you can only accelerate when your foot is pushing on the ground. But when running / sprinting, during approximately 50% of the step, no foot is touching the ground. You are in the so-called flight phase. The air-drag slows you down and makes you lose speed. Air-drag increases with the square of the speed: the faster you go the more speed you lose. And, of course, the longer you take going over a hurdle the more speed you lose, too.