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.We derive necessary and sufficient conditions on the accelerometer output that guarantee that the nine parameters can be uniquely determined from the calibration measurements in an idealized scenario with no noise or quantization errors. The method is based on measurements of the Earth gravity with the accelerometer placed at rest in at least nine different orientations.The choice of orientations is important for measurement accuracy. We compare two different setups, one called A090-45, which is based on 90 and 45 degree rotations of the accelerometer and one called A0max sep that has maximized smallest angle between any two of the orientations. For the A090-45 setup we have constructed a simple test equipment for quick positionings of the accelerometer. For the A0max sep setup, a similar equipment is more complicated to construct, but equally simple to use.We have done Monte Carlo simulations with accelerometer orientations deviating at most D degrees from the desired A090-45 or A0max sep and with D ranging from 1◦ to 30◦. For real-world noisy environments and D up to 18◦, our simulations showed slightly smaller errors for the A0max sep than for the A090-45 setup. For noise standard deviation typical for our field measurements, the measurement errors after nine-parameter calibration were about 100 times smaller than those for six-parameter calibration both for the A0max sep setup and, as long as D ≤ 13◦ for the A090-45 setup. For the A090-45 setup, however, we found that combinations of large noise levels and/or large D can makesix-parameter calibration the better choice.