Statistical Characterization of Attitude Determination Algorithms using Two Noisy Vector Measurements
Using Monte Carlo simulations, we analyze the statistical characteristics of three common spacecraft attitude determination algorithms using two input vectors convolved with zero-mean, uncorrelated Gaussian measurement noise. Our results suggest the attitude error distributions associated with a spherical-noise sampling model are robustly non-Gaussian but highly structured. By inspecting attitude error histograms corresponding to a variety of input variance noise distributions, we isolate two driving factors, the relative measurement noise variance and relative true measurement geometry, which appear to correlate with observable morphological variability between error histograms. For practical measurement conditions we find calculated error histograms can be parameterized by generalized Gamma distributions, and for at least one significant class of measurement conditions these distributions are entirely described by a single scale parameter which is a linear function of the input variance. We furthermore find that both geometric estimates of the attitude via TRIAD and quaternion solutions to Wahba’s problem are largely similar both in accuracy and distributional morphology, converging at the distributional level for relative input noise variance ratios as low as 25:1.
Frueh, Purdue University.
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