I am trying to estimate the 3D position of a point in space by measuring acceleration.This can easily be done by computing the integral of the integral over time of each component of the acceleration vector.
The question is how to statistically characterize the noise. If I assume uncorrelated zero-mean Gaussian noise on the acceleration, the error on the velocity will be a zero-mean Brownian motion, and the error on the position will be the integral of a Brownian motion.
Do anyone know any literature on how to statistically characterize the integral of Brownian motion?
I thank you in advance
Hi, I hope these texts will be useful for you.
Regards.
http://www.stat.purdue.edu/~chen418/study_research/StochasticCalculus-note1.pdf
https://books.google.es/books?hl=es&lr=&id=hGP1BwAAQBAJ&oi=fnd&pg=PR7&dq=characterize+the+integral+of+Brownian+motion&ots=vfrtyHv90O&sig=2QGnIGznIwgr7JNeF1GGQMPqiNU#v=onepage&q=characterize%20the%20integral%20of%20Brownian%20motion&f=false
Using only accelerometers will not bring you anywhere. First you should correct for gravity, then the double integration will explode any inaccuracy. The solution is to combine accelerometers with other sensors, like gyroscopes and magnetic sensors, maybe a GPS receiver.
Such a device 'Xsens' is commercially available.
Dear Hof,
I agree that using the accelerometer alone will not be sufficient, indeed it will be combined with another measurement. This is why I am asking for a statistical characterization of the error in case I used the accelerometer only.
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