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A precise statement of the attitude uncertainty for Gaussian errors requires the specification of three independent numbers, e.g., the size and eccentricity of the error ellipse and the orientation of the long axis relative to some arbitrary direction. As in the case of quantized measurements, we would like to characterize the uncertainty by a single number. Again there is no precise way to do so, because specifying the ellipse is the only unambiguous procedure. One option for a single accuracy parameter would be to use Eq. (1 l-29a) to obtain o,. This is then the long axis of the error ellipse and corresponds approximately to Umax for quantized measurements.

An alternative one-parameter estimate for the attitude uncertainty would be the radius of a small circle on the celestial sphere which had the same integrated probability as the corresponding error ellipse. A numerically convenient approximation to this radius is given by

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