Definition of Error
- If (X, Y, Z) is the true value of a point, and (XA, YA, ZA) the approximate value
- Use the Euclidean metric E2 = [(X- XA)2 + (Y- YA)2 + (Z- ZA)2] to determine an error ball of radius E; for two dimensional systems, set the Zs to 0
- There two types of geodetic points: (lat, lon, h) or for the map projections (lat, lon, 0).
- Except for UTM, the forward transformations are exact
- Generate a known set of points {(lat, lon, h)}
- When the exact transformation is available, generate the corresponding exact set of points {(X, Y, Z)}
- E, in terms of position errors, can always be calculated in two or three dimensions
- Because there is no exact transformation in either direction
- Angular measures can be converted to distance measures using s = r•ø
- Again, start with a known set of exact points {(lat, lon)}
- Given the approximate point (latA, lonA), compute e2 = [(lat - latA)RM]2 + [( lon - lonA)RN]2
- Where RN is the radius of curvature in the prime vertical, and RM is the radius of curvature in the meridian
- e is the (approximate) radius of the positional error ball
- When the angular errors are small, the error measure e is nearly E