10.2.5 Results of variance-component estimation

If the number of redundant observations is sufficiently large, the test value, i.e. the quotient of the a posteriori standard deviation and the a priori standard deviation, should approach 1.0 within each observation series. The greater the redundancy of the group, the more reliable will be the estimation of the a posteriori variance. At a redundancy of about 20, estimations will be rather reliable, while a redundancy of 3 must be regarded as very low. If low redundancies occur, it is advantageous to use existing empirical values for the a priori standard deviations of the group, and to neglect the derived test value.

The greater the redundancy in the group, the more closely should the test value approach 1.0. A range of 0.95 to 1.05 is considered as a close approximation. Further changes of weight will then hardly influence the adjustment result.

If the test value deviates from 1.0 there may either be gross observation errors within the group, or the standard deviation has not been correctly estimated, and must therefore be corrected. All observations of the corresponding group should be considered in such a change.

An example of variance-component estimation is given below:

A posteriori variance-component estimation for all observation groups Test value = s(a posteriori) / s(a priori) Group Test Value No. of Obs. Redundancy ---------------------------------------------------------------------------------------------- Photo coordinates : 1.04 86046 51132.14 Camera data incl. vector e' : 0.74 3 3.00 Coordinates of control points : 1.31 150 138.74 Control points in X : 0.79 50 47.06 Control points in Y : 1.24 50 46.80 Control points in Z : 1.75 50 44.87 Photo positions and orientations : 0.67 1434 1359.83 Photo orientation in phi : 0.91 478 441.98 Photo orientation in omega : 0.51 478 442.38 Photo orientation in kappa : 0.51 478 475.46 Exterior orientations incl. GPS : 0.85 1434 1068.30 GPS position in X : 1.26 478 291.35 GPS position in Y : 0.80 478 344.53 GPS position in Z : 0.45 478 432.43 ---------- ---------- Sum of all observations : 1.02 89067 A posteriori variance-components of photo measurements as function of photo radius Radius 0.0 23.7 28.8 32.9 37.3 41.5 45.9 50.6 61.1 Group 1 2 3 4 5 6 7 8 No. of points 5378 5378 5378 5378 5378 5378 5378 5377 Mean redundancy 0.58 0.51 0.50 0.58 0.64 0.64 0.64 0.64 Test value 0.62 0.84 0.89 1.01 1.12 1.16 1.22 1.18 Normalized 0.60 0.81 0.86 0.98 1.08 1.12 1.18 1.14

If the test value is approximately 1.0, possible observation errors within the group will become very prominent (see also Section 10.2.4). Single observations within a group, for which an error is indicated during the statistical test, must never be assigned greater standard deviations in order to achieve a 'fine' result. Such observations must be eliminated.

BINGO does not consider possible correlations between given control points. It may therefore be advantageous for the group of control points to use a test value slightly smaller than 1.0 if correlations between the control points are to be expected. This may be so if the block contains a large number of control points. The influence of a neglected correlation may thus be at least partly reduced.

With BINGO version 6.6 an additional variance component test for photo measurements has been introduced. The total photo area is divided into eight concentric areas. The radial distances are estimated in by BINGO to have approximately the same number of photo measurements in each group. If the test value for photo coordinates above is about 1.0, the test values in the eight groups show the precision of photo measurements as function of the photo radius. See example below.

If the test value of photo coordinates is close to 1.0, a normalized test value for the radial groups will be displayed. These values allow comparing various cameras.

In case all eight test values are not close to 1.0, either the camera precision is not homogeneous over the whole image, or there are still systematic image errors.

The radial distances may be alternatively defined by user by means of a GRUP statement.