1 rGHS)

m/nl

This approximation is good for 0|»s02. That is, if Um and Un are the 3a uncertainties in m and n, then the probability that the attitude will lie within UA of the estimated value, if 0|?»02, is 0.989. If 0|»a2, then the approximation of Eq. (11-31) is less accurate, being a 37% overestimate for the lo uncertainty radius and a 16% underestimate for the 3o uncertainty radius. As o, becomes much larger than o2, the error ellipse becomes very elongated and any single number representation becomes less meaningful. In this case, the best choice for the one-parameler attitude uncertainty would be the semimajor axis of the error ellipse, which is approximately

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