Non-iterative calibration for accelerometers with three non-orthogonal axes, reliable measurement setups and simple supplementary equipment

Abstract

The input–output relationship of an accelerometer depends on parameters that are sensitive to temperature and air humidity. High accuracy field measurements therefore require simple in-field estimation of these parameters. We present an extension of a simple non-iterative six-parameter calibration method for triaxial accelerometers with orthogonal input axes to a nine-parameter method that also handles non-orthogonal axes and cross-axis interference. The method is based on measurements of the Earth gravity with the accelerometer placed at rest in at least nine different orientations. The main difference from previous work is that we derive necessary and sufficient conditions on the accelerometer output that tell whether calibration is possible, model the joint effect of non-orthogonal axes and cross-axis interference, provide closed form expressions for computing the parameter values and do a closer investigation and comparison of different ways to choose the accelerometer orientations for successful calibration. We compare two different setups, one called A90 − 450, which is based on 90° and 45° rotations of the accelerometer and one called Amax sep0 that has the maximized smallest angle between any two of the orientations. For the A90 − 450 setup we have constructed simple test equipment for quick positioning of the accelerometer. For the Amax sep0 setup, similar equipment is more complicated to construct, but equally simple to use. In Monte Carlo simulations with accelerometer orientations deviating at most D degrees from the desired A90 − 450 or Amax sep0 setup, equipment with D < 10° was enough for reliable calibration. For noise standard deviation typical for field measurements and for D up to 18°, our simulations showed slightly smaller errors for the Amax sep0 than for the A90 − 450 setup. The measurement errors after nine-parameter calibration were about 100 times smaller than those for six-parameter calibration both for the Amax sep0 setup and, as long as D ⩽ 13°, for the A90 − 450 setup. For the A90 − 450 setup, however, we found that combinations of large noise levels and/or large D can make six-parameter calibration the better choice.