Measurement weighting strategies for satellite attitude estimation

Most attitude estimation algorithms (e.g, q-Method, QUEST, FOAM, etc.) permit vector observations to be weighted using scalar weights. From a theoretical standpoint, the best choice of weights is clear: when weights are proportional to inverse variance, the Wahba problem solutions are equivalent to the maximum likelihood solution. In practice, the true covariance may be difficult to determine online, and engineers may have to rely on heuristic estimates of the `goodness' of any particular measurement. In this paper, we examine several strategies for determining effective weighting for vector observations and discuss the effects of weighting schemes on system performance. Noise equivalent angle estimates provide the most direct approximations of the measurement covariances needed for optimal weighting. We demonstrate how simple lab measurements can be used to evaluate the variation of centroid noise with star brightness and position in the field of view. We evaluate appropriate fitting functions for the noise estimates and compare the relative merits of scalar and vector measurement weighting. Comparing the noise calibration results from multiple instruments provides insight into the expected performance loss that may be experienced if a per-unit calibration is replaced by simpler relations.