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Symbols and names used in adjustment statistics.
| Symbol | Description |
|---|---|
| v, V | residual, vector of residuals |
| p, P | observation weight, matrix of weights |
| [pvv] | sum of weighted residuals v’Pv.
The summation symbol [.] used to be popular in geodetic literiture, namely in connection with description of normal equations, during pre-computer era. It was introduced by Carl Friedrich Gauss who also introduce symbol P for weights (Latin pondus means weight). Letter V for adjustment reductions comes from German Verbesserung. We use [pvv] symbol only in html and text adjustment output. Sic transit gloria mundi. |
| Ax = b, P | design matrix, right-hand side (rhs) and weight matrix P |
| r | redundancy, typically number of columns minus rows of A |
| Nx = n | normal equations,
N = A’PA,
n = A’Pb.
The method of least squares can be solved directly from Ax=b. which is generally a more numerically stable solution |
| Q = inv(N) | cofactor matrix for adjusted unknowns (matrix of weight coefficients, cofactors, of adjusted unknowns) |
| Q_L = AQA’ | cofactor matrix for adjusted observations |
| f[%] | degree of control of an observation in the network, spans from 0% (uncontrolled, e.g. observed direction and distance to an isolated adjustment point) to 100% (fully controled, e.g. measured distance between two fixed points) |
| m0 | a priori reference standard deviation. |
| m0’ | a posteriori estimate of reference standard deviation |
| m0” | minimal a posteriori estimate of reference standard deviation after removal one observation (removal of the observation leading to minimal value of m0”) |
| g | position of approximate coordinates xy of the adjusted point with
respect to its confidence ellipse (g < 1 approximate coordinates
are located inside the ellipse; g = 1 on the ellipse; g > 1
outside the ellipse). Zero value of g indicates that approximate and adjusted coordinates are identical. This situation typically happens when iterative adjustement is needed due to poor initial linearization (initial approximate coordinates are too far from the adjusted) and the iterative process ends up with identical approximate and adjusted coordinates. |
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