The Humble Pedometer
a fantastically simple device, dirt cheap and widely available. sadly however quite unreliable for running.
a sprung weight inside the pedometer closes a switch each time a foot strikes the ground. you have to tell it how far you go for each stride and it will multiply up the stride length by the number of strides it counts to give distance, and subsequently can divide distance by time to give average speed.
it's not difficult to see that this relies on accurate measuring of your stride length and a consistent stride length when you run.
i've used one of these and went through a learning process of adjusting the stride length to give the correct reading on a known course. eventually it was quite good at that course and at least gave me a rough idea of the distance of other courses, still drastically affected by walking, changes of pace and hills.
Global Positioning Systems
something we've all no doubt heard about, and increasingly widely available. some of the older chunky models can now be had for as little as £70 or so.
the geometry is tricky but basically using a network of satellites it can locate you anywhere on the globe to within a quite impressive accuracy (impressive relative to the size of the globe, not always so impressive in relation to the size of your average runner).
some gps related articles:
how stuff works
useful background & history pulled from an advanced driving forum
the boffin chronicles on the runnersworld forum, one of the many sdm/gps related threads that inspired this article.
now you know how it knows where you are... but what you're really interested in is how fast you're going and how far you've been.
lets say for now it checks your position every 5 seconds, it's easy to work out how far it is between these two positions, divide this by time and we have speed (m/s km/h mph whatever) which is directly related to the pace us runners like to use (min/mile min/km). similarly it's easy to add the distance each time step and keep a total distance measurement.
so it does speed and distance, just what we wanted... right? well only kind of.
if this position reading was 100% accurate it would be great, but of course it's not. it varies with the number of satellites in view at any point in time, and not having a clear view of the sky means it could lose it's position altogether.
Positional Accuracy
The accuracy of a gps is dependant on how many satelites it can see, most these days can track up to 12 at once. a good accuracy might be around +/-3m meaning each position it records is within a 3m radius of where you actually are. this is great for most navigation work.
Distance Accuracy
Since position is the main output of a gps, calculating the distance between two points if fairly straightforward. to give total distance for a run it just has to add the distances between all the pointes it records.
you might think that the positional accuracy would skew the accuracy of any distance measurement. however if the positional error is truly randon (i.e. as likely to be 3m in front as 3m behind or 3m to one side etc) then it will be effectively averaged out. which is good!
Speed Accuracy
Again this signal isn't directly available from the gps so must be calculated, fairly simply this is the distance between the two points divided by the time between measurement of the two points.
unfortunatly precisely because the positional error is fairly random this can give poor results. at one extreme one measurement could be 3m behind and the next 3m ahead, giving the distance travelled as 6m too far (as i mentioned above this is likely to average out when added to give total distance). at the other extreme the first measurement could be 3m ahead and the other 3m behind giving a distance 6m less than it actually is. so sample on sample the distance could vary by 12m which depending on the time between measurements will give erratic current speed readings (although the average should be largely correct)
Speed Smoothing
Most systems offer some form of smoothing on the speed signal to average out the erractic speed signal over a few measurements. This may work with varying success but an unavoidable side effect is that it will delay the response of the speed reading, since the speed must be raised for a few measurements before it has any effect on the average. this can make gps speed readouts too slow to be useful for interval work.
Lost Signals
Unfortunately for us the signals are relatively weak by the time they get down from the satellites, this means they are easily blocked by buildings and trees etc.
There's not much you can do about it but it is worth bearing in mind what a gps sdm is going to do when it's satellites get blocked enough for it not to know where it is. The intelligent response is to calculate a direct path between where it lost the signal to where it regained it, if you've gone round a corner or worse, done a u-turn, whilst it has no signal you'll lose some or all of that distance.
I have heard reports that devices that are supposed to record split times or bleep at regular distance intervals start to do strange things if the split occurs during a lost signal. You'd think it's quite straightforward, but apparently not!
Initial reports from fitsense and then nike systems seemed to reflect this but were very positive about the speed reading and quick response when doing intervals.
Looking at fitsense patents there is alot to suggest that they're not integrating acceleration but using it to detect when the foot contacts and loses contact with the ground.
and relating what 'foot loft' time to running or walking speed. it also directly mentions (if i remember rightly) needing to calibrate such systems to the individual runner in both walking and running.
this calibration requirement was born out (as far as i'm aware) in the instructions for the early systems.
Assuming such an algorithm is reliable and calibrated correctly it removes the first potential source of error, integrating the acceleration.
this would give good fast response to speed changes, but could also br susceptible to drifting when integrating for distance (again reflected in initial feedback).
From a technical point of view the 3 accelerometer system has several advantages, tracking a much fuller motion of the shoe, allowing resolution of a 'true' longitudinal acceleration to integrate to speed and distance.
there must also be a wealth of information to be gained from the magnitude & phasing of the vertical / longitudinal acceleration.
and if you can also detect when the foot is on the ground you should be able to compensate for any drift or offset.
since you know you should only be reading gravity directly downwards and no longitudinal acceleration you can detect any misalignment.
additionally since inaccuracy is introduced by the continual integration some of this could be overcome by restarting the integration at the start of each stride.
I'd love to be able to get my hands on the raw data from a footpod and see how much is possible with it!