The Limits of In-Run Calibration of MEMS and the Effect of New Techniques

Inertial sensors can significantly increase the robustness of an integrated navigation system by bridging gaps in the coverage of other positioning technologies, such as GNSS or Wi-Fi positioning [1]. A full set of chip-scale MEMS accelerometers and gyros can now be bought for less than $10, potentially opening up a wide range of new applications. However, these sensors require calibration before they can be used for navigation[2]. Higher quality inertial sensors may be calibrated "in-run" using Kalman filter-based estimation as part of their integration with GNSS or other position-fixing techniques. However, this approach can fail when applied to sensors with larger errors which break the Kalman filter due to the linearity and small-angle approximations within its system model not being valid. Possible solutions include: replacing the Kalman filter with a non-linear estimation algorithm, a pre-calibration procedure and smart array [3]. But these all have costs in terms of user effort, equipment or processing load. This paper makes two key contributions to knowledge. Firstly, it determines the maximum tolerable sensor errors for any in-run calibration technique using a basic Kalman filter by developing clear criteria for filter failure and performing Monte-Carlo simulations for a range of different sensor specifications. Secondly, it assesses the extent to which pre-calibration and smart array techniques enable Kalman filter-based in-run calibration to be applied to lower-quality sensors. Armed with this knowledge of the Kalman filter's limits, the community can avoid both the unnecessary design complexity and computational power consumption caused by over-engineering the filter and the poor navigation performance that arises from an inadequate filter. By establishing realistic limits, one can determine whether real sensors are suitable for in-run calibration with simple characterization tests, rather than having to perform time-consuming empirical testing.