Eccentricity discrimination of hyperbolic localizations to minimize positioning uncertainty. Free

Conventional hyperbolic positioning locates a source at the intersection of hyperbolas that are based on time difference of arrival (TDOA) of a signal at each receiver pair. There are times when the intersections of these hyperbolas may delineate regions of uncertainty rather than a point, causing inaccurate locations due to the ambiguity of source positions. Localization accuracy can be improved by selecting hyperbolas based on their eccentricity (i.e., curvature). Since the eccentricity of a hyperbola is greater than 1, localization curves with eccentricity equal to or less than 1 are discarded as candidates of greater uncertainty. Curves with eccentricity tending to infinity are also discarded only when no other curves intersect with it. If the separations between receivers and the sound velocity are known, the hyperbolic eccentricity can be used as a function of the TDOA to minimize the ambiguity of source localizations. This method was applied to shallow water scenarios where 2‐D localization approximation was sufficient (minimum three receivers required). Validation results of this method are shown based on bowhead (Balaena mysticetus) vocalizations recorded in the Chukchi Sea in autumn 2009.