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Casting Doubt On the Hawkeye Ball-Calling System
Human judgment by referees is increasingly being supplemented (and sometimes overridden) by computerized observation systems. nuke-alwin writes "It is obvious that any model is only as accurate as the data in it, and technologies such as Hawkeye can never remove all doubt about the position of a ball. Wimbledon appears to accept the Hawkeye prediction as absolute, but researchers at Cardiff University will soon publish a paper disputing the accuracy of the system."
Why not use a radio transmitter in the tennis ball (or soccer ball or whatever) to record its exact position? I am certain this has been discussed and I wouldn't be surprised if it's already in use. The article's "Hawkeye" just works by optical analysis.
It's been tried in soccer. The latest attempts were prior to the last couple of World Cups IIRC, but the systems were plagued with problems, not the least of which was the survival of the transmitter.
http://www.gizmag.com/go/2790/
"Anyone that has ever gotten an idea based on any of my work and done something better with it-good for you."--J.Carmack
For those that didn't care to RTFA, the study is in the journal 'Public Understanding of Science' and (gooly who would have guessed) doesn't have anything to do with the summary written. They argue that uncertainties in measurement that normally don't impact the layman now need to be presented in an understandable way. They worry that people will wrongfully become too trusting of the systems that do have appreciable error in rare circumstances.
To inject my own opinion on the matter, I've had a little bit of experience with Vicon motion capture systems which appear to use similar technology to the Hawkeye system. The main problem with the system (when it works) isn't any problem with accuracy or precision. In fact, it's awesome. The problem is that the output is a little noisy and suffers from occasional jumps and hiccups. With proper filtering these are eliminated and the output is amazing. I can only imagine the problem is much easier when you're tracking a single ball rather than tens of tiny reflective makers such as with the Vicon system.
You gotta find first gear in your giant robot car
If the errors are random and follow a normal distribution (two big ifs, I admit) then even in one dimension, the error is reduced by a factor of 1/sqrt(N) where N is the number of measurements.
The same general idea applies to higher dimensions. If you can avoid systematic errors then the more measurements you take, the more accurate your final result will be. If you are interested in the gory details of the higher dimensional case, you should take a look at singular value decomposition.
We don't see the world as it is, we see it as we are.
-- Anais Nin
Since we're only dealing with three dimensions, why would any number of satellites > 3 be more precise for GPS?
;-)
Because we are dealing with reality as well - where no measurement is perfect.
Geometrically, three sats indeed are enough, but in reality:
More measurements -> smaller error bars -> better position.
The alternative to more sats would be not to move and to take more measurements over time.
But that would render GPS useless for most applications
Additional trouble with the "stay and wait" method: Those nasty satellites move over time,
introducing different errors that can not be eliminated as easily by simple averaging.
That's also why ultra precise GPS surveying records the satellite data and waits for the week it takes
to make the actual orbital data (as measured, and not just as predicted) available before computing
the position, thereby elimiating (well, at least reducing) another source of error.
In statistics, the only thing beating multiple measurements is even more measurements.
Because that's not the issue. You'll always have uncertainty in systems. The study argues that the public perceives these systems as infallible, and therefore believe that technology can provide a final, absolute arbitration. The study is commenting on this tendency in lay people (i.e., people without specialized knowledge of the system), and warns against the corollaries that stem from such assumptions. Also, the title is bad: they are merely looking at the issue through the lens of Hawk-Eye, they're not looking at Hawk-Eye specifically. You may note that there is no analysis of the hawk eye system beyond a basic discussion of its function.