Linear Covariance Analysis for Gimbaled Pointing Systems

Abstract

Linear covariance analysis has been utilized in a wide variety of applications. Historically, the theory has made significant contributions to navigation system design and analysis. More recently, the theory has been extended to capture the combined effect of navigation errors and closed-loop control on the performance of the system. These advancements have made possible rapid analysis and comprehensive trade studies of complicated systems ranging from autonomous rendezvous to vehicle ascent trajectory analysis. Comprehensive trade studies are also needed in the area of gimbaled pointing systems where the information needs are different from previous applications. It is therefore the objective of this research to extend the capabilities of linear covariance theory to analyze the closed-loop navigation and control of a gimbaled pointing system. The extensions developed in this research comprise two areas. The first is related to generalizing the linear covariance controller models. Previous controller models have been somewhat limited in their applicability to controllers with internal states, a common features in gimbaled pointing systems. This research extends the controller model to allow for accurate modeling of such controllers. The second extension is related to characterizing the frequency content of the pointing errors. In previous applications of linear covariance, the focus has been on computing the total error at some critical mission time. No consideration was given to the bandwidth of the error, i.e. whether the error varied slowly or quickly with time. The analysis method developed in this research enables the designer to identify not only the magnitude of the error sources, but the portion of the spectrum to which they contribute. This knowledge is extremely valuable in areas such as satellite imagery, weapon stabilization, and remote sensing. In summary, the objective of this dissertation is to increase the utility of linear covariance analysis for systems with a wide variety of controllers and for whom the spectrum of the errors is critical to performance. The extended theory is applied to a model of a gimbaled pointing system and validated by direct comparison to conventional analysis techniques. The results show excellent correlation with conventional methods, but at the drastically lower computational load typical of linear covariance analysis. This efficiency enables comprehensive trade studies, allowing the system designer to span the entire design space and select the system configuration with the lowest cost and complexity that still meets mission requirements