In this study, we investigate the problem of detecting time epochs when zero-velocity updates can be applied in a foot-mounted inertial navigation (motion tracking) system. We examine three commonly used detectors: the acceleration moving variance detector, the acceleration magnitude detector, and the angular rate energy detector. We demonstrate that all detectors can be derived within the same general likelihood ratio test framework given the different prior knowledge about the sensor signals. Further, by combining all prior knowledge, we derive a new likelihood ratio test detector. Subsequently, we develop a methodology to evaluate the performance of the detectors. Employing the developed methodology, we evaluate the performance of the detectors using leveled ground, slow (approx. 3 km/h) and normal (approx. 5 km/h) gait data. The test results are presented in terms of detection versus false-alarm probability. Our preliminary results shows that the new detector performs marginally better than the angular rate energy detector that outperforms both the acceleration moving variance detector and the acceleration magnitude detector.

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Abstract-We present an open-source, realtime, embedded implementation of a foot-mounted, zero-velocity-update-aided inertial navigation system. The implementation includes both hardware design and software, uses off-the-shelf components and assembly methods, and features a standard USB interface. The software is written in C and can easily be modified to run user implemented algorithms. The hardware design and the software are released under permissive open-source licenses and production files, source code, documentation, and further resources are available at www.openshoe.org. The reproduction cost for a single unit is below $800, with the inertial measurement unit making up the bulk ($700). The form factor of the implementation is small enough for it to be integrated in the sole of a shoe. A performance evaluation of the system shows a position errors for short trajectories (<100 [m]) of ± 0.2-1 % of the traveled distance, depending on the shape of trajectory.

The implementation challenges of cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging are discussed, and work on the subject is reviewed. System architecture and sensor fusion are identified as key challenges. A partially decentralized system architecture based on step-wise inertial navigation and step-wise dead reckoning is presented. This architecture is argued to reduce the computational cost and required communication bandwidth by around two orders of magnitude while only giving negligible information loss in comparison with a naive centralized implementation. This makes a joint global state estimation feasible for up to a platoon-sized group of agents. Furthermore, robust and low-cost sensor fusion for the considered setup, based on state space transformation and marginalization, is presented. The transformation and marginalization are used to give the necessary flexibility for presented sampling-based updates for the inter-agent ranging and ranging free fusion of the two feet of an individual agent. Finally, the characteristics of the suggested implementation are demonstrated with simulations and a real-time system implementation.

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