Computing the Rigid-Body Acceleration Field from Nine Accelerometer Measurements

  • Philippe Cardou
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 83)


Among other applications, accelerometer arrays have been used in crashworthiness studies to measure the acceleration field of the head of a dummy subjected to an impact. In previous analyzes, the centripetal component of the rigid-body acceleration was estimated linearly from point-acceleration measurements, that is, by considering the quadratic products of the angular-velocity components as independent variables. Although this assumption greatly simplifies the estimation process, it has two drawbacks: (i) it raises the minimum number of accelerometers from nine to 12, and, when more than the minimum number of accelerometers are available, (ii) it ignores some of the constraints between the kinematic parameters, which would otherwise help in filtering the data. In this paper, we solve the nonlinear problem of estimating the rigid-body acceleration field from point-acceleration measurements. To this end, we partition the associated system of equations into two subsystems, one linear, the other nonlinear. The nonlinear subsystem of three equations in three unknowns represents three quadrics in 3D space, whose intersection contains the rigid-body angular velocity. This intersection is computed using a readily-available technique, which yields eight closed-form solutions to the problem. A criterion for the selection of the proper solution is given. The proposed nonlinear method should prove useful when the number of accelerometers is limited, or to improve the robustness of an array of 12 or more accelerometers by taking into account the constraints between the quadratic terms of the angular velocity.


Angular Acceleration ASME Journal Sensitive Direction Accelerometer Measurement Tangential Acceleration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Philippe Cardou
    • 1
  1. 1.Laval UniversityQuebec CityCanada

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