Experimental-based Cramér-Rao lower bound estimation of triaxial accelerometer calibration methods using Monte Carlo simulation

Low-cost accelerometers can be found in many systems requiring accurate attitude estimation. Their unique thermomechanical responses necessitate frequent recalibrations to maintain a certain level of performance. Established accelerometer calibrations are the six position and multi-position methods requiring static conditions. This paper presents a Monte Carlo simulation comparing these for a sensor with a comprehensive set of calibration errors in the model. Precision of the simulations are compared with the Cramér-Rao lower bound (CRLB) and, for the first time, the CRLB for the six-position method is defined. For the multi-position method, calibration accuracy of six algorithms is assessed by Monte Carlo simulation. The precision of the best performing algorithm is compared with the CRLB using experimental data. The effect of parameter initialisation on the algorithms is observed via simulation and experimentally with two algorithms shown to have sensitivity to initialisation. The types and order of positions sampled in the multi-position method are analysed for the case when only the minimum number are available. Cardinal positions are shown to be best in terms of calibration accuracy and precision. • Accuracies of the six and multi-position methods are assessed via Monte Carlo simulation of sensors with realistic errors. • Precision of the six-position method is compared with the Cramér-Rao lower bound for the first time. • Calibration accuracies of multi-position method algorithms are evaluated and two found to be sensitive to initialisation. • Sampling cardinal positions is shown to give best calibration accuracy on average with their order being unimportant. • The precision of the simulated and experimental multi-position calibrations are compared with their Cramér-Rao lower bound.