[FoRK] kalman filters

Damien Morton dmorton at bitfurnace.com
Tue May 12 18:06:49 PDT 2009

On Wed, May 13, 2009 at 9:39 AM, Stephen Williams <sdw at lig.net> wrote:
> I want to solve a similar problem soon.
> The acceleration is given in 3D.  You get a series of vectors that allow you
> to fit an arc.  Too bad the Wiimote, and I think the iPhone don't seem to
> have gyros in addition to the MEMS accelerometers.  The iPhone should also
> have a compass.

The iPhone does have a camera, and I had the idea of using some kind
of optical flow computation to get some additional motion estimate
from the camera - just enough to tell you rough gyro-like numbers.

I though the WiiMote had a low res IR camera in the nose?

> Just looking at the Wiimote as an example:
> http://blogs.msdn.com/coding4fun/archive/2007/03/14/1879033.aspx
> http://www.wiibrew.org/wiki/Wiimote#Accelerometer
>>  Accelerometer
>> ADXL330 in a Wii remote
>> Coordinate system used by Wii Remote
>> The Wii Remote includes a three-axis linear accelerometer located on the
>> top suface of the circuit board, slightly left of the large A button. The
>> integrated circuit is the ADXL330 (data sheet), manufactured by Analog
>> Devices. This device is physically rated to measure accelerations over a
>> range of at least +/- 3g with 10% sensitivity.
>> Since the accelerometer actually measures the force exerted by a set of
>> small proof masses inside of it with respect to its enclosure, the
>> accelerometer measures linear acceleration in a free fall frame of
>> reference. If the Wii Remote is in free fall, it will report zero
>> acceleration. At rest, it will report an upward acceleration (+Z, when
>> horizontal) equal to the acceleration due to gravity, g (approximately 9.8
>> m/s²) but in the opposite direction. This fact can be used to derive tilt
>> from the acceleration outputs when the Wii Remote is reasonably still.
>> XX, YY, and ZZ are unsigned bytes representing the acceleration in each of
>> the three axis, where zero acceleration is approximately 0x80. The
>> coordinate system is shown in the diagram above (note that this is different
>> from the coordinate system used by GlovePIE). Additionally, the BB BB
>>  Buttons bytes also include the LSBs of the acceleration values in the
>> unused bits
> So, a series of acceleration points at certain time steps allows integration
> to a set of fixed points in space. This talks about it but doesn't solve it
> completely:
> http://www.mathhelpforum.com/math-help/advanced-applied-math/51269-finding-distance-traveled-accelerometer-readings.html
> According to this a Kalman filter won't help when you only have a single
> sensor:
> http://answers.yahoo.com/question/index?qid=20070814120651AAsUZwW
> Good demo of a Kalman filter for gyro+accel:
> http://tom.pycke.be/mav/92/kalman-demo-application
> Partially helpful.  Note that you cannot fly properly without either a gyro
> or ground vision.
> http://tom.pycke.be/mav/69/accelerometer-to-attitude
> Nice:
> http://en.wikipedia.org/wiki/Kalman_filter
> http://blog.medallia.com/2007/08/iphone_accelerometer_source_co.html
> http://blog.medallia.com/2007/08/fun_with_the_iphone_accelerome.html
> sdw
>> Fourth thought is to create a simulated robot arm, and use inverse
>> kinematics to torque the joints to match the observed acceleration. I
>> can simplify the problem to 2D, which will help. Getting really
>> complicated here.
>> I'm wondering if there might be a simpler way. In the end, all I want
>> to do is take the accelerometer data and produce a value for casting
>> velocity (I am assuming that the launch angle is perfect).
>> Any suggestions welcome!
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