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Re: accelerometer gravity correction

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  • Re: accelerometer gravity correction

    I am posting this to the list, because it may be of general interest.

    Lisa Carnes wrote:
    > If the orientation of the accelerometer is changed, then gravity
    > vector becomes a problem, and the mathematics are hairy. Does anyone
    > have any advice?

    There is no fundamental solution to this problem: Einstein in his
    general
    theory of relativity (1916) hypothesized that it is not possible to
    distinguish
    between accelerations of the reference frame and being in a
    gravitational
    field. That theory is widely accepted. Also this idea seems consistent
    with
    the structure of the equation that describes the output of an
    accelerometer.
    You can find that equation in:

    Bogert, A.J. van den, L. Read and B.M. Nigg "A method for inverse
    dynamic analysis
    using accelerometry". J. Biomech. 29: 949-954, 1996.

    We have some advantage in that we know the magnitude of the
    gravitational field,
    only its orientation relative to the sensor is unknown. But I still
    think the
    contributions from gravity and from acceleration are inseparable.

    In my own work I circumvented the problem by doing an analysis (inverse
    dynamics)
    that did not require a separation of the contributions by accelerations
    and
    gravity.

    If you need pure acceleration information, you could assume that the
    accelerations are large compared to the acceleration of gravity, so
    you would ignore gravity. This assumption may be OK for impact
    situations (tibial acceleration 4-10 g). But probably not for upper
    body movement.

    [By the way, if you make the opposite assumption: accelerations are
    much smaller than 1 g, the signal is only dependent on orientation of
    the
    sensor with respect to gravity. The accelerometer then becomes an
    inclinometer.]

    Or you can measure the orientation of the accelerometer and use
    that information to calculate the contribution of gravity and
    subtract that from the signal. This was done by Wu and Ladin in
    their "kinematometer". See:

    Z. Ladin & G. Wu (1991) Combining position and acceleration
    measurements for joint
    force estimation. J. Biomech. 24: 1173-1187.

    G. Wu & Z. Ladin (1993) The kinematometer--an integrated kinematic
    sensor for
    kinesiological measurements. J. Biomech. Eng. 115:53-62.

    If you can make certain assumptions about the system (e.g. there
    is a point with zero acceleration) separation of acceleration and
    gravity is also theoretically possible. See:

    A.T.M. Willemsen, J.A. van Alste and H.B.K. Boom (1990) Real-time gait
    assessment
    utilizing a new way of accelerometry. J. Biomech. 23: 859-863.

    Ton van den Bogert

    --

    A.J. (Ton) van den Bogert, PhD
    Department of Biomedical Engineering
    Cleveland Clinic Foundation
    9500 Euclid Avenue (ND-20)
    Cleveland, OH 44195, USA
    Phone/Fax: (216) 444-5566/9198

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