Angle of arrival geolocation using non-linear optimization

This paper addresses the problem of object localization using only angle-of-arrival (AoA) data from satellites. Traditionally, this is performed by a triangulation algorithm (TA) that minimizes the distances between the estimated object location to all lines-of-sight representing measurements of the object. However, when observing objects from satellites, the differences in distance from each satellite to the object can be significant. The error this induces in measurements from farther-distant satellites results in an inordinate impact on the geo-location error. To overcome this problem, we introduce a non-linear optimization (NLO) approach that models the measurement error at each satellites as a probability density function. By finding the most-probable geo-location of the object, this systematic error is eliminated. We found that the NLO provides a more accurate estimate of the object's location than the TA in 93% of instances. In addition, we analyze the uncertainty estimates generated by both the TA and NLO approaches. The NLO estimates of uncertainty are also considerably more accurate than the TA estimates in all cases.