The effect of star tracker model choice on satellite attitude stability analysis

Two nonlinear models (one dynamic and one instantaneous) are derived for gimbaled star trackers utilized as attitude sensors. Both models are linearized and are shown to produce the same linear model; in fact, it is the model used by Doolin and Showman in the design and analysis of their "paired-tracker" system. A comparison of the linear and nonlinear tracker-error processor models for some values of the attitude angles within the range of interest indicates that the linear model produces substantial errors, and its utility for stability analysis is questionable. Using the NASA Orbiting Astronomical Observatory coarse pointing mode attitude control system as an example, it is shown that the instantaneous nonlinear tracker model has distinct advantages over the dynamic model. In particular, the system\´s state equation is of fixed dimension regardless of the number of star trackers used; the stability of the linear part can be determined by analyzing each of the three attitude channels separately; the system is readily shown to be locally asymptotically stable; and, in principle, its domain of asymptotic stability can be estimated by a straightforward procedure.