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Interval Global Positioning with road Surface (iGPS) is a new method to obtain a robust and continuous positioning in urban areas by tightly- coupling precise 3-D drivable area maps with GPS pseudorange measurements. Map and GPS measurements are represented by geometric constraints, thus turning the localization problem into a constraint satisfaction problem whose solution is the confidence domain of position. Interval analysis is employed to solve the problem by using contractions and bisections of a prior position box. If more than 3 satellites are visible, the method is robust to erroneous pseudorange measurements. The system is also able to compute multiple position hypotheses where there are ambiguities. An experimental validation using real GPS pseudorange measurements and a precise 3-D map is reported to illustrate the performance of the method with real data in an urban area, and with reduced satellite visibility. Confidence domains are consistent with the ground truth throughout the 1 km trial, and a 6.5 m 95% accuracy is achieved with at least two satellites in view.