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m/nl

as can be obtained from Eq. (11-29) when o2 approaches zero. An alternative physical interpretation of UA, as defined by Eq. (11-31), is to note that UA is the exact formula for the attitude component inclined at 45 deg to both the semimajor and semiminor axes of the error ellipse (see Eq. (11-19)).

Another option for a single accuracy parameter would be to use the radius of a circle with the same geometrical area as the error ellipse. That is,

Equation (11-33) is analogous to Eq. (11-15) for the quantized measurements. Note that this representation also gives a poor estimate of the attitude uncertainty when o,»o2 because ^„^„->0 when o2->0. Again, when o,»o2, Eq. (11-32) should be used for one-parameter attitude uncertainty. The application of a three-dimensional analog of Umem to three-axis attitude is discussed in Section 12.3. Throughout the rest of this chapter, we will use UA as defined by Eq. (11-31) as our one-parameter estimate of the attitude uncertainty, unless stated otherwise.

11.3.2 Attitude Accuracy for Measurements With Correlated Uncertainties

Whenever there exists a systematic error which can introduce uncertainties in both measurements m and n, then the measurement uncertainties contain a correlated component. For example, a sensor mounting angle bias will produce a correlated uncertainty component when using the Earth-width/Sun-to-Earth-in rotation angle method.

When attitude is determined from two measurements with a correlated uncertainty component, the measurement uncertainty matrix given in Eq. (11-25) will contain off-diagonal terms. That is, t/ =

where

0 0

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