This topic applies to ArcEditor and ArcInfo only.

A single observation (bearing and distance) from an existing survey point can be used to compute the coordinates for a new survey point. However, relying on a single observation is risky, since there is no way to tell whether the measurement is correct. A second measurement from the same or another existing survey point will confirm, or check, the coordinates defined by the first measurement. Generally, the more measurements fixing the coordinates of a survey point, the more reliable the coordinates. These additional measurements are called redundant measurements.

Weighted average

All measurements contain some degree of error. Therefore, each measurement will compute slightly different coordinates for the same survey point. For practical reasons, there should be one coordinate location for a survey point. A single, best estimate coordinate can be derived by computing a weighted average of the additional or redundant measurements, with each weight defined by the measurement accuracy.

 Computing a weighted average

Although the weighted average approach works for a single point, it is not sufficient to compute the coordinates for multiple points in a network such as the parcel fabric. A more advanced method is needed to account for the numerous possible measurement paths between the points. The techniques and algorithms in a least-squares adjustment provide the most rigorous and widely accepted solution for processing a network of measurements and points.

 Multiple points in a network

A least-squares adjustment is a mathematical procedure based on the theory of probability that derives the statistically most likely coordinate location of points defined by multiple measurements in a network. In mathematical terms, a least-squares adjustment defines a best-fit solution for weighted measurements by finding a minimum for the sum of the squares of the measurement residuals. A measurement residual is the amount needed to correct a measurement for it to fit into the best-fit solution found by the least-squares adjustment.