A report discusses the design of fast stochastic observers for spacecraft pointing control. In this special context, "observers" signifies mathematical algorithms, implemented on computers aboard spacecraft, through which one processes sensory data (principally, the outputs of star trackers and gyroscopes) to estimate the states (attitudes and angular velocities) of the spacecraft. The development in the report was motivated by the presence of an attitude-dependent bias error in the star-tracker measurement associated with NASA's upcoming SIRTF (Space Infra-Red Telescope Facility) space telescope. This attitude-dependent bias term lies outside of basic linear estimation assumption, and the well-established Kalman theory is no longer optimal. The attitude-dependent bias term forces a step response through the dynamics of the onboard estimator each time the spacecraft is repositioned. If an optimal Kalman filter were used, its sluggish dynamics would create a long undesirable lingering output drift in the pointing response. While this drift error is small (e.g., at the arcsecond level) it cannot be ignored for space telescope applications, and is the main reason that Kalman filters are routinely replaced by simple observers on important missions with stringent pointing requirements such as the Hubble Space Telescope and SIRTF.
In this report, a theoretical analysis of an attitude estimator comprising three decoupled single-axis observers leads to a globally optimal solution for designing a constrained stochastic observer of second-order form. This stochastic observer minimizes the variance of the attitude estimate, subject to a constraint that its poles lie to the left of a specified vertical line in the complex Laplace-transform s-plane. This so-called "fast observer" design allows the step response of the onboard estimator to be sped up with minimal degradation in the variance of the state estimate. Examples are presented to illustrate the optimal tradeoff between observer speed and estimation error.
This work was done by David S. Bayard of Caltech for NASA's Jet Propulsion Laboratory. To obtain a copy of the report, "Fast Observers for Space Telescope Pointing Control with Application to SIRTF," access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Information Sciences category.