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Re: accelerometer gravity correction

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  • Re: accelerometer gravity correction

    Necip Berme wrote to Biomch-L:

    > I was expecting Albert King from Wayne State University to respond to the
    > "accelerometer gravity correction" listing. As he has not, I am doing so to
    > set the record straight. In 1970's one of Dr. King's doctoral students
    > showed that nine accelerometers appropriately positioned on a rigid body
    > are necessary and sufficient to separate the effect of gravity from the
    > other acceleration information. Hence, it is possible to calculate the
    > position of a rigid body from acceleration data.

    Dr. Berme is correct and it is important for anyone using 3-D accelerometry
    to know about this work. The full reference is:

    N.K. Mital and A.I. King (1979) Computation of rigid-body rotation in
    three-dimensional space from body-fixed linear acceleration measurements.
    J. Appl. Mech. 46: 925-930.

    Mital and King were able to solve the angular acceleration vector of a rigid body
    from multiple accelerometer signals, and successfully eliminated the effect of
    gravity on that result. Obtaining the attitude then required a double integration
    in order to obtain Euler angles. This works for movements of short duration with
    accurately known initial conditions (initial attitude and angular velocity). For
    movements of longer duration, the end result will drift noticeably due to
    inaccuracies in the initial conditions of the integration. It would be hard to
    predict at which duration this becomes a problem. My feeling is that it is not
    a practical method for most applications. Movement analysis in automobile crash
    testing is probably a feasible application, and I think this is the area that Dr.
    King works in.

    Angular velocity can also be solved directly, using the centrifugal terms in
    the accelerometer signals, but this tends to be noisy for typical movements
    (my own observations). On the other hand, then only a single integration
    is required to obtain Euler angles. Attitude (or Euler angles) can not
    be solved directly from the accelerometer signals. Integration is always

    Once attitude is known, the gravity contribution to the translational
    acceleration of the rigid body can then be calculated and a correction can
    be made to obtain the true translational accelerations. With a further
    double integration, position and velocity of the rigid body will be known.

    There is an even earlier paper where a similar analysis was used, although
    no integrations were carried out. Only angular velocity and angular
    acceleration were needed. Reference:

    T.R. Kane, W.C. Hayes and J.D. Priest (1974) Experimental determination
    of forces exerted in tennis play. In: R.C. Nelson and C.A. Morehouse (eds.)
    Biomechanics IV, University Park Press, Baltimore, pp. 284-290.

    For the sake of completeness, here is a later development of that method.
    The methodology is presented, but to my knowledge it has not been applied
    again. Reference:

    W.C. Hayes, J.D. Gran, M.L. Nagurka, J.M. Feldman and C. Oatis (1983) Leg motion
    analysis during gait by multiaxial accelerometry: theoretical foundations and
    preliminary validations. J. Biomech. Eng. 105:283-289.

    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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