On-the-fly geometric calibration of inertial sensor arrays

We present a maximum likelihood estimator for estimating the positions of accelerometers in an inertial sensor array. This method simultaneously estimates the positions of the accelerometers and the motion dynamics of the inertial sensor array and, therefore, does not require a predefined motion sequence nor any external equipment. Using an iterative block coordinate descent optimization strategy, the calibration problem can be solved with a complexity that is linear in the number of time samples. The proposed method is evaluated by Monte-Carlo simulations of an inertial sensor array built out of 32 inertial measurement units. The simulation results show that, if the array experiences sufficient dynamics, the position error is inversely proportional to the number of time samples used in the calibration sequence. Further, results show that for the considered array geometry and motion dynamics in the order of 2000° /s and 2000° /s
²
, the positions of the accelerometers can be estimated with an accuracy in the order of 10
^-6
m using only 1000 time samples. This enables fast on-the-fly calibration of the geometric errors in an inertial sensor array by simply twisting it by hand for a few seconds.