Efficient Extrinsic Self-Calibration of Multiple IMUs using Measurement Subset Selection

TL;DR

It is hypothesized that utility is insensitive to changes in the parameter estimate for many systems of interest, suggesting that evaluating utility at some initial parameter guess would yield equivalent results in practice.

Abstract

This paper addresses the problem of choosing a sparse subset of measurements for quick calibration parameter estimation. A standard solution to this is selecting a measurement only if its utility -- the difference between posterior (with the measurement) and prior information (without the measurement) -- exceeds some threshold. Theoretically, utility, a function of the parameter estimate, should be evaluated at the estimate obtained with all measurements selected so far, hence necessitating a recalibration with each new measurement. However, we hypothesize that utility is insensitive to changes in the parameter estimate for many systems of interest, suggesting that evaluating utility at some initial parameter guess would yield equivalent results in practice. We provide evidence supporting this hypothesis for extrinsic calibration of multiple inertial measurement units (IMUs), showing the reduction in calibration time by two orders of magnitude by forgoing recalibration for each measurement.

Figures (6)

• Figure 1: The intervals of subset within a roll-pitch-yaw profile, which is used by the calibration process for the baseline (left), \ref{['eq:M-largest']} (middle), and \ref{['eq:Greedy']} (right), are highlighted. The background color highlights the segments selected and used in each calibration process.
• Figure 2: The correlation coefficient of the information as a function of the difference ($\delta \mathbf{\bm{p}}$, $\delta \mathbf{\bm{q}}$) in guessed and reference extrinsic parameters in the multi-IMU system. A coefficient of 1 indicates perfect correlation with the true value, while 0 denotes independence.
• Figure 3: Absolute error in estimated extrinsic parameters for baseline, original greedy, and greedy with utility evaluation at initial calibration parameters over each dataset in simulation.
• Figure 4: Sensor rig used for data collection.
• Figure 5: The correlation coefficient of the information as a function of the difference ($\delta \mathbf{\bm{p}}$, $\delta \mathbf{\bm{q}}$) in guessed and reference extrinsic parameters in the two-IMU system on hardware. A coefficient of 1 indicates perfect correlation with the true value, while 0 denotes independence.