Formal Specification and Quantitative Analysis of a Constellation of   Navigation Satellites
  Navigation satellites are a core component of navigation satellite based systems such as GPS, GLONASS and Galileo which provide location and timing information for a variety of uses. Such satellites are designed for operating on orbit to perform tasks and have lifetimes of 10 years or more. Reliability, availability and maintainability (RAM) analysis of systems has been indispensable in the design phase of satellites in order to achieve minimum failures or to increase mean time between failures (MTBF) and thus to plan maintenance strategies, optimise reliability and maximise availability. In this paper, we present formal models of both a single satellite and a navigation satellite constellation and logical specification of their reliability, availability and maintainability properties respectively. The probabilistic model checker PRISM has been used to perform automated analysis of these quantitative properties. 
Zhaoguang Peng, Yu Lu, Alice Miller, Tingdi Zhao, Chris Johnson
cs.SY