Time difference of arrival geolocation allows for the position estimation of a terrestrial emitter by measuring its signals with 3 or more receivers. This type of geolocation, also known as hyperbolic fix, is used by a variety of satellite and aircraft systems worldwide. Existing systems do not provide continuous coverage of a target area, instead relying on infrequent passes of satellites or keeping aircraft in flight for extended periods of time.
In this study we design constellations of satellites which can provide continuous geolocation services in a specific target region. The constellations are designed using global optimization techniques of exhaustive search and genetic algorithms with the aim of minimizing the lower bound of the geolocation estimation error, which is a variant of the Cramér-Rao lower bound. Additionally, the estimation itself is carried out with a specialized algorithm, the constrained extended Kalman filter.
The design methodology and the efficacy of the estimation algorithm are demonstrated with Monte Carlo simulations of geolocation with one of the resulting constellations. The constellation is shown to provide consistent coverage with a low estimation error, and the estimator is shown to be efficient.