2.7.5 Properties of Standard Ellipses

The positional error c02-math-0787 of a station is directly related to the standard ellipse, as seen in Figure 2.7.5. The positional error is the standard deviation of a station in a certain direction, say c02-math-0788. It is identical with the standard deviation of the distance to a known (fixed) station along the same direction c02-math-0789, as computed from the linearized distance equation and variance-covariance propagation. The linear function is

2.7.84 equation

Because of equations (2.7.70) and (2.7.71), the distribution of the random variable c02-math-0791 is multivariate normal with

2.7.85 equation

The variance of the random variable c02-math-0793 follows from the law of variance-covariance propagation:

The variance ...

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