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An ultrawideband 3-D positioning technique is described here for locating wireless sensor nodes in extreme multipath environments. These typically form part of a network of sensors used to monitor salient parameters such as temperature and humidity in large industrial storage vessels. The novelty of this approach is twofold. First, a leading ultrawideband pulse edge detection method is combined with a series of spatially diverse measurements to isolate the line-of-sight component from the unwanted multipath interference from the vessel walls. Second, a new location algorithm based on the statistical analysis of spherical function intersection points is applied to the received time-domain data to improve the estimation of the time of flight at each measurement location. These two features combine to facilitate both precision positioning and cumulative error source estimation and yield resolutions approaching 2 cm in rich scattering environments. The results of the application of the new spherical technique compares favorably with those obtained using a conventional hyperbolic positioning method where it was demonstrated to provide a marginally superior resolution for the applied experimental conditions.