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Note that jC =0 (measurements m and n are independent) when ©„,/„ = 90° or 270°, and \CXJis a maximum when ©m/„=0° or 180°.

The above results may be established by use of the covariance analysis introduced in Section 12.3. The derivation is summarized here. "

The covariance matrix, P, which defines the attitude uncertainty determined from measurements m and n, can be obtained from the following equation:

where M and V are the initial estimates of the square of the errors in attitude and measurements, respectively, and G is given by

where m and n are the two measurements and x and are any two orthonormal components on the celestial sphere (such as acosS and S where a and S are the right ascension and the declination of the attitude). Because Um and Un are uncorrected, the uncertainty matrix, (/, is diagonal. By definition,

9m

3 m

dx

3v

dn

dn

dx

3y

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