Consistent local mapping using the invariant extended Kalman filter

Abstract

Recent advancements in non-linear filtering techniques provide for an opportunity to improve and rid past consistency issues in large scale simultaneous localization and mapping based on the extended Kalman filter as the chosen optimization method. This is important for the multitude of industries that rely on such algorithms when the Global Positioning System or other means of extracting absolute measurements of one's whereabouts is not available. Especially in robotics and augmented reality is exact and reliable localization information crucial for operation as well as acquiring the structure of the environment.

In this study, the invariant extended Kalman filter is rigorously investigated for its ability to correctly model uncertainty of the estimated states by avoiding the unfortunate mathematical properties of the current state of the art implementations of filter-based simultaneous localization and mapping

that is, the need to linearize around the true trajectory but as this information is obviously unknown, one must evaluate the linearization around the estimate instead which can lead to inconsistencies.

This enables robust and consistent fusing of local maps via the means of the information filter formulation which will save tremendous computational effort and reduce memory requirements. In order to use the non-linear uncertainty presentation for local mapping a novel extension of the framework of local mapping using the extended information filter is presented and tested in simulation and on a real data set using a camera and inertial measurements.