On the internal stability of GPS solutions

Abstract.Internal stability is referred to as the uniform asymptotic stability of Kalman filtering solutions, addressing the effects of initial-state errors, observation sample rates, lengths of observation sessions and so on. This paper presents the theory of the internal stability of GPS solutions, including mathematical definitions, properties and theorems addressing the dependence of internal stability of the filtering solutions on the controllability and observability of a GPS dynamic positioning system. The theory has been applied in analysing the stability performance of different GPS positioning modes, and the actual GPS positioning results have demonstrated graphically the asymptotic convergence of those stable solutions versus observation tracking time/filtering time-steps. The internal stability is therefore considered as an important performance criterion to evaluate different GPS positioning solutions.