Optimal Set of Angular Positions of Inertial Measurement Units for Accelerometer Calibration on a Stationary Bench

Abstract

The mathematical model of instrumental errors of a three-accelerometer module has been analyzed in application to the determination of the apparent acceleration vector. To this end, the vector calibration method is used on a stationary testing bench with the gravitational acceleration as a reference. The instrumental errors of each accelerometer in the module are determined by a set of parameters, which are refined at calibration. This set consists of two angular errors of the sensitivity axis orientation, the deviation of the scaling coefficient, and bias. An approach has been proposed to determine the optimal set of angular calibration positions for the accelerometer module to achieve the best accuracy for estimating the listed parameters of the instrumental error model. The improvement is achieved due to a smaller condition number of an intermediate matrix arising when solving the calibration system of linear equations by the least squares method. The decrease in the condition number reduces the influence of unaccounted factors, such as instrumental noise and alignment error, on final parameter estimate. The approach has been tested through a computer simulation by adding noise to the array of measurements and comparison with a nonoptimal set of angular calibration positions.