# [racket] what initial velocity to use when calculating velocity from acceleration (peripherally moby-related...)

 From: Anthony Cowley (acowley at seas.upenn.edu) Date: Tue Nov 30 16:51:05 EST 2010 Previous message: [racket] what initial velocity to use when calculating velocity from acceleration (peripherally moby-related...) Next message: [racket] big-bang! Messages sorted by: [date] [thread] [subject] [author]

```On Tue, Nov 30, 2010 at 4:02 PM, Will M. Farr <wmfarr at 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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