The mean of the residuals should be near zero, because the p, can be either positive or negative. A large value for k indicates that unmodeled biases are probably present in the observations. A large value of op indicates that the observation noise is large.

•Alternatively, a fractional rms residual, r^, may be calculated using all observations, as follows:

Example of a Simplified Batch Least-Squares Application. Consider a spacecraft that is spinning uniformly about the axis A, which may be expressed in rectangular celestial coordinates (Section 2.2) as

A = AxX + AyY + AtZ. or in terms of right ascension, a. and declination, ¿¡, as

Suppose that A is fixed in inertia! space during an interval spanned by a series of observations from an onboard sensor, and that an initial estimate for A is available using attitude solutions from previous intervals. Suppose, also, that the observations consist of arc lengths, 0„ between A and a known time-varying reference vector, U(/)> such as the nadir vector. We choose

0 0

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