Study on Misalignment Angle Compensation during Scale Factor Matching for Two Pairs of Accelerometers in a Gravity Gradient Instrument.

A method for automatic compensation of misalignment angles during matching the scale factors of two pairs of the accelerometers in developing the rotating accelerometer gravity gradient instrument (GGI) is proposed and demonstrated in this paper. The purpose of automatic scale factor matching of the four accelerometers in GGI is to suppress the common mode acceleration of the moving-based platforms. However, taking the full model equation of the accelerometer into consideration, the other two orthogonal axes which is the pendulous axis and the output axis, will also sense the common mode acceleration and reduce the suppression performance. The coefficients from the two axes to the output are δO and δP respectively, called the misalignment angles. The angle δO, coupling with the acceleration along the pendulous axis perpendicular to the rotational plane, will not be modulated by the rotation and gives little contribution to the scale factors matching. On the other hand, because of coupling with the acceleration along the centripetal direction in the rotating plane, the angle δP would produce a component with 90 degrees phase delay relative to the scale factor component. Hence, the δP component coincides exactly with the sensitive direction of the orthogonal accelerometers. To improve the common mode acceleration rejection, the misalignment angle δP is compensated by injecting a trimming current, which is proportional to the output of an orthogonal accelerometer, into the torque coil of the accelerometer during the scale factor matching. The experimental results show that the common linear acceleration suppression achieved three orders after the scale factors balance and five orders after the misalignment angles compensation, which is almost down to the noise level of the used accelerometers of 1~2 × 10−7 g/√Hz (1 g ≈ 9.8 m/s²).