GPS Satellite Surveying, 4th Edition

2.7.5 Properties of Standard Ellipses

The positional error 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 . It is identical with the standard deviation of the distance to a known (fixed) station along the same direction , as computed from the linearized distance equation and variance-covariance propagation. The linear function is

2.7.84

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

2.7.85

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

2.7.86

The variance ...