Software for numerically stable covariance analysis

This paper discusses the merits of applying a subroutine library to develop general-purpose covariance analysis software and provides the raison d´etre for using the library in specialized quick-look covariance studies. Attention is centered on the features of one such library, the Estimation Subroutine Library (ESL)*, used by Interstate Electronics in developing covariance analyses for various navigation studies. The general formulation of navigation covariance analysis and one Interstate ESL application (gyrocompassing of an inertial navigation system) are described. Section I of this paper furnishes some insights into the general problem of numerically stable covariance analysis. Section II briefly reviews key formulae and relations useful in covariance analysis for system performance. Section III is a general discussion of computer subroutine libraries and ESL capabilities in particular. Interstate Electronics application of the ESL to navigation covariance analysis is described in Section IV. In Section V, the methodology is applied to analyze the performance characteristics of a gyrocompassed inertial navigation system (INS). Section VI summarizes the results of ESL application to software development at Interstate. Interstate Electronics is actively pursuing ESL applications to navigation systems analysis, specifically for evaluating reference instrumentation subsystems for the Trident II Strategic Weapon System. The ESL is used in both the design and evaluation of instrumentation-system error models by filtering and smoothing actual weapon system data, and as an aid in the evaluation of reference instrumentation systems through covariance analysis.