Accommodating Sensor Uncertainty in the Cones Method: Polycones and Fuzzycones

The “cones method” is an analytical algorithm to combine a pair of separate angle observations into a common vector. Two new algorithms have been developed to determine optimum “cones method” solutions when more than two observation angles and estimates of their measurement uncertainties are available. The polycones algorithm consists of determining a simple weighted average of the solution vectors over all possible pairs of measurements with the weights determined from the measurement uncertainty. The Fuzzycones method finds the vector of maximum probability consistent with the measurements and their uncertainties. Both of these methods have been implemented and tested by comparison with simulations of a coarse Sun sensor and attitudes determined for a simulated spinning spacecraft. Compared to the cones method, both algorithms reduce angle errors somewhat for simulated Sun sensors. For the simulated spacecraft, attitude determination with Fuzzycones gives results almost identical to those for the cones method while Polycones gives significantly worse results with the current weighting method. I. Nomenclature q Elevation angle of an arbitrary point on the surface of a unit sphere (-p/2 to p/2)