Non-Linear Optimization Applied to Angle-of-Arrival Satellite-Based Geolocation

Geolocation is a common application for satellite systems. This involves estimating an object\u27s location (herein called the subject) based on noisy satellite data. Many geolocation methods exist; however, none are tailored specifically for the unique problems faced by satellite systems. Some satellites are so far from the subject being localized that by the time the satellite receives a signal from the subject it might have moved appreciably. Furthermore, some satellites or terrestrial sensors may be much closer to the subject than others. Therefore, sensors may need to be weighted based upon their distance to the subject being localized. In addition, even if a subject can be localized, the confidence in this localization may be unknown. Non-linear optimization is proposed, implemented, and analyzed as a means of geolocating objects and providing confidence estimates from passive satellite line-of-sight data. Non-linear optimization requires an initial estimate. This estimate is provided by a triangulation method. The non-linear optimization then improves upon this estimate iteratively by finding estimates that are more likely to have produced the observed line-of-sight measurements. The covariance matrix of the geolocation parameters being estimated is naturally produced by the optimization which provides quantified confidence in the geolocation estimate. Simulations are developed to provide a means of evaluating the performance of the non-linear optimization algorithm. It was found that non-linear optimization can reduce the average error in geolocation estimates, provide improved estimation confidence, and accurately estimate its geolocation confidence for some subjects. The results from the theoretical development of the non-linear optimization algorithm and its simulated performance is quantified and discussed