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