High integrity GNSS location zone characterization using interval analysis

Robust Set Inversion via Interval Analysis methods in a bounded error frame is used in this paper 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 pseudo-ranges measurements are represented by intervals enclosing the true value with a particular confidence. The method computes a location zone recursively, using contraction and bisections of an arbitrarily big initial location box. Such an approach also enables to consider the presence of an arbitrary number of erroneous measurements using a q-relaxed solver, and allows integration of geographic and cartographic information such as digital elevation models or 3-dimensional maps. With enough data redundancy, inconsistent measurements can be detected and even rejected.The integrity risk of the location zone is only brought by the measurement bounds settings, since the solver is guaranteed. A way to set these bounds for a particular location zone confidence is proposed. An experimental validation using real L1 code measurements and a digital elevation model is also reported to illustrate the performance on the method with real data.