Spherical calibration and reference alignment algorithms

Abstract

Inclinometer and directional field sensor readings can have gain, offset, and non-orthogonality errors, as well as reference alignment rotation errors. When a series of readings are taken by a three axis sensor with a variety of different orientations, the resulting dataset looks like a perfect hypothetical sphere in the absence of any errors; with errors as mentioned above the dataset looks like an offset, rotated, ellipsoidal quadratic surface. This invention provides a simple method of removing the above errors from a tilt reference device. A disclosed algorithm is divided into two distinct components: the ellipsoidal quadratic surface component, which covers gain, offset, and axis misalignment; and the rotation component, which covers rotation relative to a set of reference axes. The solution presented here addresses both components combined, or separated and for inclinometers, magnetometers and rate sensors.