Thanks a lot to all of you for your hints and pointers to such interesting information!
In fact for practical purposes, I will experiment with GPS first and see how this works (from a first impression, the acceleration data from the phone seem extremely "hyper-sensitive", so it might anyway turn out to be impossible calibrating them...) On the other hand, the Kalman filter looks very interesting (and the whole topic of estimation/prediction is, of course) , and it's something I like especially about this list that you so often get pointed to fascinating things (in fact, Racket & functional programming being "just a hobby" for me, perhaps the main reason I follow this list - and try to find a bit of spare time for Racket programming myself - is that it's so intellectually stimulating and pointing to all kinds of topics (mathematical etc.) I've been ignorant of for too long :-; Sigrid On Tue, Nov 30, 2010 at 4:02 PM, Will M. Farr <wmf...@gmail.com> wrote: > In particular, combining noisy measurements in the context of an ODE that > describes the evolution of a system (in this case, you measure a = dv/dt = > d^x/dt^2, and want to "integrate" to find x(t)) is often done using a Kalman > filter: > > http://en.wikipedia.org/wiki/Kalman_filter > > This is also almost certainly the approach you would take if you want to > combine data from a GPS unit with the accelerometer data. ?Kalman filters are > often used in commercial inertial navigation systems (i.e. in planes) to > track position as well. ?The literature on the subject is *very* extensive, > if you enjoy that sort of reading. ?Alternately, from the basic description > it can be fun to work out a lot of the simple results yourself (depending, of > course, on how much you enjoy math and what your level of experience with > statistics and differential equations are). ?In practice (from someone who is > not in the field of inertial navigation, but has heard talks about it) it > seems like the "tuning" of the filter is as much art as science, so I > wouldn't necessarily assign too much weight to the prior literature in your > case. The black art of tuning applies mostly to PIDs as mentioned in another thread, and should be a part of every PhD :P But for a good introduction to applied Kalman filtering, check out Probabilistic Robotics from the library and it will show you how to proceed. I will however take one last opportunity to repeat my original advice of just using GPS for estimating a person's velocity. Frankly, the gain in accuracy from integrating data from a cheap accelerometer into a Kalman filter with GPS data is often not worth it. Only do so after the GPS has proven too inaccurate. Anthony
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