John-Olof Nilsson

Zero-Velocity Detection—An Algorithm Evaluation

In this paper, 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 (LRT) framework, given the different prior knowledge about the sensor signals. Further, by combining all prior knowledge, we derive a new LRT 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 (approximately 3 km/h) and normal (approximately 5 km/h) gait data. The test results are presented in terms of detection versus false-alarm probability. Our preliminary results show 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.

Evaluation of zero-velocity detectors for foot-mounted inertial navigation systems

A study of the performance of four zero-velocity detectors for a foot-mounted inertial sensor based pedestrian navigation system is presented. The four detectors are the acceleration moving variance detector, the acceleration magnitude detector, the angular rate energy detector, and a novel generalized likelihood ratio test detector, refereed to as the SHOE. The performance of each detector is assessed by the accuracy of the position solution provided by the navigation system employing the detector to perform zero-velocity updates. The results show that for leveled ground forward gait at a speed of 5 km/h, the angular rate energy detector and the SHOE give the highest performance, with a position accuracy of 0.14% of the travelled distance. The results also indicate that during leveled ground forward gait, the gyroscope signals hold the most reliable information for zero-velocity detection.

Foot-mounted INS for everybody - an open-source embedded implementation

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

Cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging

800, with the inertial measurement unit making up the bulk (

Foot-mounted inertial navigation made easy

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.

Aligning the Forces - Eliminating the Misalignments in IMU Arrays

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.

Performance characterisation of foot-mounted ZUPT-aided INSs and other related systems

Despite being around for almost two decades, foot-mounted inertial navigation only has gotten a limited spread. Contributing factors to this are lack of suitable hardware platforms and difficult system integration. As a solution to this, we present an open-source wireless foot-mounted inertial navigation module with an intuitive and significantly simplified dead reckoning interface. The interface is motivated from statistical properties of the underlying aided inertial navigation and argued to give negligible information loss. The module consists of both a hardware platform and embedded software. Details of the platform and the software are described, and a summarizing description of how to reproduce the module are given. System integration of the module is outlined and finally, we provide a basic performance assessment of the module. In summary, the module provides a modularization of the foot-mounted inertial navigation and makes the technology significantly easier to use.

Time synchronization and temporal ordering of asynchronous sensor measurements of a multi-sensor navigation system

Ultralow-cost single-chip inertial measurement units (IMUs) combined into IMU arrays are opening up new possibilities for inertial sensing. However, to make these systems practical for researchers, a simple calibration procedure that aligns the sensitivity axes of the sensors in the array is needed. In this paper, we suggest a novel mechanical-rotation-rig-free calibration procedure based on blind system identification and a Platonic solid printable using a contemporary 3-D printer. The IMU array is placed inside the Platonic solid, and static measurements are taken with the solid subsequently placed on all sides. The recorded data are then used together with a maximum-likelihood-based approach to estimate the interIMU misalignment and the gain, bias, and sensitivity axis nonorthogonality of the accelerometers. The effectiveness of the method is demonstrated with calibration results from an in-house developed IMU array. MATLAB scripts for the parameter estimation and production files for the calibration device (solid) are provided.

Joint state and measurement time-delay estimation of nonlinear state space systems

Foot-mounted zero-velocity-update (ZUPT) aided inertial navigation system (INS) is a conceptually well known with publications in the area typically focusing on improved methods for filtering and addition of sensors and heuristics. Despite this, the performance characteristics, which would ultimately justify and give guidelines for such system modifications of ZUPT-aided INSs and other related systems, are in some aspects poorly documented. Unfortunately, the systems are non-linear, meaning that the performance is dependent on the system set-up, parameter setting, and the true trajectory. This complicates the process of evaluating performance and partially explains the few publications with detailed performance characterisation results. Therefore in this article we suggest and motivate methodologies for evaluating performance of ZUPT-aided INS and other related systems, we apply them to a suggested baseline set-up of the system, and study some aspects of the performance characteristics.

Fusing the information from two navigation systems using an upper bound on their maximum spatial separation

In this article we propose a filter based method to solve the time synchronization and minimum delay temporal ordering problem of asynchronous sensor measurements. A problem which inevitably arise in the sensor fusion of a multi-sensor navigation system implemented in realtime on a general purpose operation system (OS) without using functionality dedicated to realtime applications. The time synchronization is done up to a constant error by linear filtering of time stamps given to each measurement. The filtered time stamps together with predicted future time stamps are then used in a measurement temporal ordering algorithm to achieve a minimal delay temporal ordering subject to a user specified jitter tolerance. Finally, experimental time synchronization and temporal ordering results from the system implemented with a typical set of navigation sensors are presented.