Quantifying the Uncertainty of the Relative Geometry in Inertial Sensors Arrays

We present an algorithm to estimate and quantify the uncertainty of the accelerometers' relative geometry in an inertial sensor array. We formulate the calibration problem as a Bayesian estimation problem and propose an algorithm that samples the accelerometer positions' posterior distribution using Markov chain Monte Carlo. By identifying linear substructures of the measurement model, the unknown linear motion parameters are analytically marginalized, and the remaining non-linear motion parameters are numerically marginalized. The numerical marginalization occurs in a low dimensional space where the gyroscopes give information about the motion. This combination of information from gyroscopes and analytical marginalization allows the user to make no assumptions of the motion before the calibration. It thus enables the user to estimate the accelerometer positions' relative geometry by simply exposing the array to arbitrary twisting motion. We show that the calibration algorithm gives good results on both simulated and experimental data, despite sampling a high dimensional space.

Automated summary

This algorithm presents an approach to estimate and quantify the uncertainty of accelerometer geometry in an inertial sensor array using Bayesian estimation and Markov chain Monte Carlo sampling. By identifying linear substructures and leveraging information from gyroscopes, it allows for accurate calibration without making assumptions about motion. Despite sampling a high dimensional space, the algorithm provides good results on both simulated and experimental data.