Abstract: | Onboard measurements of periodic x-ray signals from highly stable, rapidly spinning stars called pulsars, enable determination of spacecraft position, velocity, and attitude states. Due to the short period of pulsar signals, X-ray pulsar based navigation (XNAV), may result in position ambiguity within the Solar System and typically requires an initial position estimate in order to determine spacecraft position. This dissertation presents a method to determine spacecraft position using XNAV in the absence of any prior state information, a scenario sometimes referred to as the cold-start problem or the lost in space scenario. In these scenarios, the spacecraft cannot communicate with Earth-based systems, nor is any prior state information available, excepting the current time. A position determination capability under these conditions may provide navigation redundancy for high-value missions (e.g. human missions to Mars), improved spacecraft autonomy, or improved deep-space navigation accuracy for low cost missions such as cubesats. In order to solve the cold-start problem, a model is developed to find candidate spacecraft positions for a given XNAV measurement. Combinations of pulsars are explored to find sets of pulsars which minimize the number of candidate solutions within a given domain. Through proper pulsar selection it is possible to find a single candidate position within a given domain solving the initial position determination problem without prior information.
This investigation includes a comprehensive survey of XNAV technology across a range of topics from advances in pulsar modeling, timing models, algorithms to estimate the pulsar phase, navigation filters, and hardware. By observing x-ray signals from pulsars, XNAV may be used to improve the navigation capabilities of spacecraft. XNAV is a particularly strong candidate for deep space applications because it is more accurate than ground based systems beyond 15~AU. XNAV may allow for more spacecraft autonomy, and improved robustness and accuracy when integrated with other navigation technology. Several flight experiments have been conducted to test the feasibility of XNAV technology on Earth orbiting spacecraft. As hardware and signal processing algorithms improve, XNAV will become a more desirable space technology option for future space missions.
The majority of current XNAV system concepts require an initial position estimate to resolve ambiguity in the state determination process. Without prior information there are many candidate positions which may produce the same measurement as the true spacecraft position. If position ambiguity can be resolved, XNAV may enable full state estimation without prior information, a valuable capability for future space missions. Candidate spacecraft positions may be found by searching for intersections between pulsar wavefronts. An efficient numeric scheme for determining candidate spacecraft positions is developed for an arbitrary number of observed pulsars in two and three dimensions. Results indicate that, as the error in the measurement is reduced by an order of magnitude, the number of candidate solutions is also reduced by an order of magnitude. However, increasing the number of pulsars observed by one pulsar reduces the number of candidate solutions by two orders of magnitude.
Pulsar selection criteria to minimize the number of candidate solutions over a given domain are developed in terms of relative direction, period, and phase accuracy. Results indicate that smaller angular separation between the observed pulsars and increased period of the observed signals reduces the number of solutions in a given domain. Further, phase measurement accuracy should be improved simultaneously for all observed pulsars rather than focusing on improving observation of a single pulsar. These selection criteria are verified by evaluating the number of candidate solutions for all permutations of 34 candidate pulsars. Combinations of 3, 4 or 5 pulsars are evaluated to determine which set minimizes the number of candidate positions within a given domain.
By selecting an appropriate set of pulsars for a desired domain size, a single candidate position may be found within the domain. The trajectories of NASA's Insight, Juno and New Horizons missions are considered to represent Mars, Jupiter, or outer Solar System missions. In these cases results are presented for combinations of 5, 7 or 8 pulsar observations in the presence of measurement error. For all three cases a single candidate position is found to within the predefined measurement uncertainty. These results demonstrate feasibility of using XNAV for initial position determination without prior information for a variety of missions within the Solar System. |