Simple non-iterative calibration for triaxial accelerometers

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's 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 from just 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° 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-squares error extensions of it for more than six measurements. These simulations compare the sensitivities to noise and cross-axis 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° deviation from horizontality and compensating with more measurements and least-squares fitting.