Set inversion via interval analysis for nonlinear bounded-error estimation
Automatica (Journal of IFAC) - Special section on fault detection, supervision and safety for technical processes
Brief paper: Robust set-membership state estimation; application to underwater robotics
Automatica (Journal of IFAC)
A solution to the ill-conditioned GPS positioning problem in an urban environment
IEEE Transactions on Intelligent Transportation Systems
Indoor location tracking in non-line-of-sight environments using a IEEE 802.15.4a wireless network
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Tightly-coupled GIS data in GNSS fix computations with integrity testing
International Journal of Intelligent Information and Database Systems
Guaranteed robust nonlinear estimation with application to robot localization
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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A Robust Set-Inversion via Interval Analysis method in a bounded-error framework is used to compute three-dimensional location zones in real time, at a given confidence level. This approach differs significantly from the usual Gaussian error model paradigm, since the satellite positions and the pseudorange measurements are represented by intervals encompassing the true value with a particular level of confidence. The method computes a location zone recursively, using contractions and bisections of an arbitrarily large initial location box. Such an approach can also handle an arbitrary number of erroneous measurements using a q-relaxed solver and allows the integration of geographic and cartographic information such as digital elevation models or three-dimensional maps. With enough data redundancy, inconsistent measurements can be detected and even rejected. The integrity risk of the location zone comes only from the measurement bounds settings, since the solver is guaranteed. A method for setting these bounds for a particular location zone confidence level is proposed. An experimental validation using real L1 code measurements and a digital elevation model is also reported in order to illustrate the performance of the method on real data.