Studying the Сonsistency of Extended Kalman Filter in Pedestrian Navigation with Foot-Mounted SINS

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Abstract
—The paper focuses on pedestrian navigation with foot-mounted strapdown inertial navigation systems (SINS). Zero velocity updates (ZUPT) during the stance phase are commonly applied in such systems to improve the accuracy. Zero velocity data are processed by the extended Kalman filter (EKF). Zero velocity condition is written in two forms: in reference and body frames. The first form traditional for pedestrian navigation is shown to provide an inconsistent EKF. The second form provides a correct ZUPT algorithm, which is naturally written in so-called dynamic errors. The analyzed algorithm for data fusion from two SINS is based on the bound on foot-to-foot distance. It is shown how EKF inconsistency can be manifested, and how it can be avoided by proceeding back to dynamic errors. The results are obtained analytically using observability theory and covariance analysis.

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