Formal modelling and quantitative analysis of satellite navigation systems

Satellites now form a core component for space based systems such as GPS and GLONASS 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 modelling of both a single satellite and a satellite navigation system 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.

[1]  Edmund M. Clarke,et al.  Symbolic model checking for sequential circuit verification , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[2]  Alan J. Hu,et al.  Protocol verification as a hardware design aid , 1992, Proceedings 1992 IEEE International Conference on Computer Design: VLSI in Computers & Processors.

[3]  David J. Sherwin,et al.  System Reliability Theory—Models and Statistical Methods , 1995 .

[4]  Joost-Pieter Katoen,et al.  Safety, Dependability and Performance Analysis of Extended AADL Models , 2011, Comput. J..

[5]  Gavin Lowe,et al.  Breaking and Fixing the Needham-Schroeder Public-Key Protocol Using FDR , 1996, Softw. Concepts Tools.

[6]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[7]  Catuscia Palamidessi,et al.  Model Checking Probabilistic and Stochastic Extensions of the π-Calculus , 2009, IEEE Transactions on Software Engineering.

[8]  Natarajan Shankar,et al.  PVS: A Prototype Verification System , 1992, CADE.

[9]  R.M. Alkan,et al.  GPS, GALILEO and GLONASS satellite navigation systems & GPS modernization , 2005, Proceedings of 2nd International Conference on Recent Advances in Space Technologies, 2005. RAST 2005..

[10]  Robert K. Brayton,et al.  Verifying Continuous Time Markov Chains , 1996, CAV.

[11]  Leang-San Shieh,et al.  An alternative Kalman innovation filter approach for receiver position estimation based on GPS measurements , 2007, Int. J. Syst. Sci..

[12]  Marco Pistore,et al.  NuSMV 2: An OpenSource Tool for Symbolic Model Checking , 2002, CAV.

[13]  Corrado Priami,et al.  Stochastic pi-Calculus , 1995, Comput. J..

[14]  J. Aronson.  Safety , 2009, BMJ : British Medical Journal.

[15]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[16]  E. Denney,et al.  Verification of autonomous systems for space applications , 2006, 2006 IEEE Aerospace Conference.

[17]  Gerard J. Holzmann,et al.  The SPIN Model Checker , 2003 .

[18]  Maged Dessouky,et al.  Minimizing the cost of availability of coverage from a constellation of satellites: Evaluation of optimization methods: Regular Paper , 2004 .

[19]  Horst Czichos.  Scope of Technical Diagnostics , 2013 .

[20]  Gerard J. Holzmann,et al.  The Theory and Practice of A Formal Method: NewCoRe , 1994, IFIP Congress.

[21]  C. W. Johnson.  The Natural History of Bugs: Using Formal Methods to Analyse Software Related Failures in Space Missions , 2005, FM.

[22]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

[23]  Michael R. Lowry,et al.  Formal Analysis of a Space-Craft Controller Using SPIN , 2001, IEEE Trans. Software Eng..

[24]  Thomas A. Henzinger,et al.  Reactive Modules , 1999, Formal Methods Syst. Des..

[25]  John Rushby,et al.  Formal Methods and their Role in the Certification of Critical Systems , 1997 .

[26]  Marta Z. Kwiatkowska,et al.  PRISM: Probabilistic Symbolic Model Checker , 2002, Computer Performance Evaluation / TOOLS.

[27]  Christel Baier,et al.  Approximate Symbolic Model Checking of Continuous-Time Markov Chains , 1999, CONCUR.

[28]  Gerard J. Holzmann,et al.  Design and validation of computer protocols , 1991 .

[29]  Enrico Tronci,et al.  MODEL CHECKING SATELLITE OPERATIONAL PROCEDURES , 2011 .

[30]  Chris W. Johnson,et al.  A Probabilistic Model Checking Approach to Analysing Reliability, Availability, and Maintainability of a Single Satellite System , 2013, 2013 European Modelling Symposium.

[31]  Somesh Jha,et al.  Verification of the Futurebus+ cache coherence protocol , 1993, Formal Methods Syst. Des..

[32]  Christel Baier,et al.  Principles of model checking , 2008 .

[33]  Joost-Pieter Katoen,et al.  Formal correctness, safety, dependability, and performance analysis of a satellite , 2012, 2012 34th International Conference on Software Engineering (ICSE).

[34]  David Notkin,et al.  Model checking large software specifications , 1996, SIGSOFT '96.