Uncertainty Propagation in a Non-linear Regression Analysis: Application to a Ballistic Absolute Gravimeter (IMGC-02)

Today's most accurate measurements of the gravitational acceleration are based on interferometric reconstruction of the vertical trajectory followed by a test body launched in a vacuum chamber. The gravity value g is one of the parameters of a model function derived from the law of motion of the body, and is estimated by a least squares adjustment. In this paper we present the regression analysis applied to the IMGC-02 absolute gravimeter and the associated uncertainty propagation We also show how a suitable choice of the reference height z, at which g is calculated, can yield a minimum-variance estimate. This choice is based on the covariance matrix of the parameter estimates provided by the adjustment algorithm.