Mathematical modelling and design of optimal satellite constellations with multi-fold continuous coverage for position location and navigation

Abstract

<p>The demand for significant improvements in navigation systems, which must include more accurate and reliable position location, has been continuously growing in the last decade and is expected to increase rapidly in the near future. The need for this advanced position location and navigation system extends, not only to the airspace, but also to the surface of the earth where ships, land vehicles and aircraft in distress exist. Investigations have shown that satellite-based systems offer a number of unique advantages which meet the required characteristics of the future position location and navigation system. Whether the satellite system is designed to serve the entire earth or a certain portion of the earth, it is required that one or more satellites be visible simultaneously to the user. This necessitates the use of a satellite constellation which provides a multi-fold continuous coverage pattern. In this thesis, a detailed study of coverage patterns and design of satellite constellations for position location and navigation is presented. The metod employed relies on mathematical modelling and computer search f or the configurations of the optimal constellations. The selected optimization criterion is based on minimizing the cost through the minimization of the total number of satellites and satellite altitude. Several new mathematical models have been developed which eliminate the need for computer modelling. Computer search has been conducted based on the different models to determine the optimal satellite constellation for multi-fold continuous coverage. Results are presented throughout the thesis. Specifically, the analysis has led to the development of the following: 1. A mathematical model for a constellation of satellites in an equatorial orbits. 2. Two different mathematical models for a constellation of satellites in a network of polar orbits. A major development is the concept of the interaction between orbits to maximize the coverage. 3. Two mathematical models for a satellite constellation in a hybrid network which combines a network of polar orbits with an equatorial orbit. This type of constellation has not received attention in the open literature to date. 4. A model for a satellite constellation in a network of inclined orbits providing single-fold continuous coverage. 5. Five different satellite constellations in synchronous orbits for three-fold continuous coverage of the Atlantic Ocean. Finally, conclusions and a number of recommendations for future research are provided.</p>