Reliability and accuracy prediction for a redundant strapdown navigator

Abstract

A comprehensive approach to the evaluation of the accuracy and reliability of a redundant navigation system is described. A Markov model of the redundant system is used to determine the probabilities of particular operational state time histories. Navigation system accuracies are associated with these state time histories through the use of a modified covariance analysis of the system's navigation errors. Suitable scalar figures of merit are used to assess the impact on performance of significant system parameters. The analysis is applied to a redundant navigator which is used to transfer a payload from launch to geosynchronous orbit. HE accuracy of navigation systems has traditionally been evaluated by means of conventional covariance analysis techniques,1 sensitivity analyses,2 or Monte Carlo simulations.3 These approaches are not well suited, however, to the evaluation of the accuracy of a redundant system. This is primarily due to the fact that the operational state of a redundant system changes at random points in time, resulting in a very large ensemble of operational state time histories which must be considered. An analysis approach which accounts for the effects of the random occurrence of component failures and reconfigurations of the redundant system elements is required. The operational state of a redundant system changes as system components fail and as failure detection and identification (FDI) decisions are made. A Markov model of the redundant system and its associated FDI algorithms can be used to determine the probabilities of particular operational state time histories. These probabilities can be used to identify the members of the ensemble of operational state time histories which most strongly influence system performance. A linearized stochastic sensitivity analysis4 can then be used to determine the statistics of the navigation system errors for each of the operational state time histories of interest. The many factors which influence the accuracy of a redundant navigation system also influence the system's reliability. Conventional reliability prediction methods5 must be augmented, therefore, in order to include these effects. A Markov model is well suited to this purpose. System reliability can be predicted by summing the probabilities of all operational state time histories which end in severely degraded performance. The use of Markov modeling techniques to predict system performance also provides insight into the sensitivity of this performance to significant features of the system design. These techniques thus provide a systematic method of evaluating design tradeoffs and for choosing parameters such as FDI thresholds by examining the effects of these tradeoffs and choices on system accuracy and reliability. The redundant inertial measurement unit (RIMU)6 considered in this paper consists of five gyros and five accelerometers in a conical configuration. Three power supplies