Simple non-iterative calibration for triaxial accelerometers

Abstract

For high precision measurements, accelerometers need recalibration between different measurement occasions. In this paper we derive a simple calibration method for triaxial accelerometers with orthogonal axes. Just like previously proposed iterative methods, we compute the calibration parameters (biases and gains) from measurements of the Earth gravity for six different unknown orientations of the accelerometer. However, our method is non-iterative, so there are no complicated convergence issues depending on input parameters, round-off errors etc.The main advantages of our method are that only from the accelerometer output voltages it gives a complete knowledge of whether it is possible, with any method, to recover the accelerometer biases and gains from the output voltages, and when this is possible, we have a simple explicit formula for computing them with a smaller number of arithmetic operations than in previous iterative approaches. Moreover, we show that such successful recovery is guaranteed if the six calibration measurements deviate with angles smaller than some upper bound from a natural setup with two horizontal axes. We provide an estimate from below of this upper bound that, for instance, allows 5 degree deviations in arbitrary directions for the Colibrys SF3000L accelerometers in our lab. Similar robustness is also confirmed for even larger angles in Monte Carlo simulations of both our basic method and two different least square error extensions of it for more than six measurements. These simulations compare the sensitivities to noise and crossaxis interference. For instance, for 0.5 % cross-axis interference the basic method with six measurements, each with two horizontal axes, gave higher accuracy than allowing 10 degree deviation from horizontality and compensating with more measurements and least squares fitting.

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

“…Then, from the equations (30d), (30e) and (30f) in Appendix A we obtain that u 4 = u 5 = u 6 = 0 and therefore det(U) = 8u 1 u 2 u 3 as well as Ω ′ = 1+ for m = 1, 2, 3 by (4a) and (4b) respectively. These formulae coincide with the ones for b m and g m derived in the six-parameter calibration method for accelerometer with orthogonal axes that was proposed in [17].…”

“…The following theorem is an extension from six to nine parameters of a similar theorem in [17]. It coincides with calibration that was proposed in [15,16] for estimating the elements of the matrices F and F B in the model (2), but here we do instead give explicit formulae for the parameters α m , b m , g m for comparisons with six-parameter methods like the one in [17]. Similarly to that paper we also derive specific necessary and sufficient conditions that, in absence of noise, tell directly from the accelerometer output voltages whether the parameters α m , b m , g m can be uniquely determined.…”

“…For triaxial accelerometers with orthogonal axes, the authors presented a noniterative accelerometer calibration method in [17]. In this paper, we generalize that method to triaxial accelerometers with non-orthogonal input axes.…”

“…In this paper, we generalize that method to triaxial accelerometers with non-orthogonal input axes. We do this in a manner similar to [15,16], but with a generalization of equivalence results in [17] that allows us to provide simple necessary and sufficient conditions on the accelerometer outputs, which in absence of noise guarantee that the accelerometer parameters can be uniquely determined. We also give closed form expressions for the parameters α m , b m , g m rather than for the elements of the matrices F and F B in the model (2) below and we do Monte Carlo simulations of the acceleration measurement error after calibration to investigate how sensitive the methods are to the noise level and to the choice of accelerometer orientations for the calibration.…”

“…• deviations of the accelerometer orientations from the horizontal plane in [17]. For the nine-parameter calibration we need nine calibration measurements and we will compare the two setups …”