Piecewise In-Plane Calibration for Drilling Inclinometer System

Tilt measurement is commonly achieved by sensing the gravity, its accuracy heavily depends on the calibration procedure. This article investigates accelerometer calibration scheme of a drilling inclinometer and proposes a novel piecewise in-plane calibration scheme to update the calibration coefficients from the results of the ellipsoid fitting (EF) and the plane fitting (PF). According to the motions rotating around the inclinometer frame, the proposed scheme utilizes the maximum likelihood to estimate the adjustment for calibration coefficient, as a modification to the EF + PF scheme. The simulation and experimental results demonstrate that, compared to existing methods in drilling applications, the proposed scheme significantly reduces the error of tilt measurement. Specifically, the proposed inclinometer system achieves an error of less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 0.0011^{\circ }~\pm ~0.0108^{\circ }$ </tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\sigma \text {)}$ </tex-math></inline-formula> for the axial tilt angle and less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 0.0931^{\circ }~\pm ~0.0735^{\circ }$ </tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\sigma \text {)}$ </tex-math></inline-formula> for the tool face angle.