It is likely that networks of any size will be estimated using software. To do otherwise would be tedious in the extreme. A rigorous solution can only be achieved if all the gross errors in the observations have been removed from the data set first. This can be a tedious process if there are many of them and the geometry of part of the network is weak. The following contains some hints on how to deal with these situations.
First check the data for correct formatting and that there are no ‘typos’. When data is manually entered through a keyboard, errors will often be made. It is much easier to check input data independently before processing than to use software outputs to try to identify the source of blunders. Once obvious errors have been removed and the estimation attempted there will one of two outcomes. Either it converges to a solution, or it does not. If it does not converge to a solution then either there are too many gross errors or there is very weak geometry somewhere in the network, or both. Weak geometry occurs when the locus lines from observations associated with a particular point lie substantially parallel to each other in the region of the point. See Section 7.3.1 for a discussion of locus lines.
It is likely that the software will allow for setting the convergence criteria, either in terms of the largest correction to a provisional coordinate in successive iterations or the maximum number of iterations to be performed. Set the convergence criteria to be rather coarse initially, say to 0.01mor 0.001mand the number of iterations to the maximum allowed, or at least the maximum you have patience for. If convergence has not been achieved then it is not possible to identify suspect observations. One possible check for gross errors in the coordinates of fixed points or the provisional coordinates of free points is to use the input coordinates to plot a network diagram to see if there are any obvious errors.
As a very general rule of thumb, points should be within about one third of the shortest distance in the network of their true value to ensure convergence. Imprecise coordinates of free points coupled with weak geometry may cause the estimation to fail. Obviously it would be possible to compute better provisional coordinates by the methods described in Chapter 5 and of course better coordinates will improve the likelihood of convergence. However, whether it is worth the effort may be questionable. If there are no obvious errors in the plot and convergence has not been achieved, compare the observation values with their dimensions on the plot to identify large gross errors in any of the observations.
If the estimation still fails then it is likely that there are problems associated with the geometry part of the network. These are harder to identify but the following may help. Check to see if there are any points are connected to the rest of the network by only two observations. If there are then check the locus lines at the point associated with the two observations to see the quality of their intersection. If that does not resolve the problem investigate points with three observations and so on. If this still does not resolve the problem and achieve convergence then more drastic action is called for.
There may be problems associated with the coordinates of the fixed points, the coordinates of the free points, or the observations and all problems cannot be resolved simultaneously. Isolate the problems of the coordinates while you resolve the problems with observations by temporarily making all but one point free and adding a realistic fixed bearing to the set of observations. If convergence can now be achieved then there was a problem with one of the fixed coordinates which needs to be resolved.
If convergence was not achieved there is at least one, and probably more than one, gross error in the observations. Convergence needs to be forced. This can be done by removing the fixed bearing and temporarily treating all the coordinates except those of one fixed point as observations of position where the observations have a suitable standard error. Start with a large and therefore weak value for the standard error of a coordinate. If you are confident that you know the coordinates of a point to 10 m, say, use that. If convergence is achieved relax the standard error to 100 m or 1000 m and so on until you have the largest value where convergence is still achieved. If convergence is not achieved reduce the standard error to 1 m, 0.1 m, 0.01 m or whatever is needed to make the estimation converge.
Once convergence has been forced it is possible to investigate the observations in spite of the now highly distorted nature of the network. Examine the estimation output and identify the observation with the statistic of residual divided by its own standard error remembering that most of the coordinates are now
also ‘observations’. You now have the choice of investigating the observation by reference to the source data, such as a field sheet, and correcting a transcription error. If that was not the problem then you can remove the suspect observation from the data set.
If you do, that may remove a suspect observation but it will not solve the problem with it. A better approach is to give that single observation, temporarily, a very large standard error. If the observation was an angle then 100 000 would be appropriate, if a distance then a standard error of the average distance between stations to one significant figure would suffice. The effect of this is make the observation of no practical significance to the estimation but the estimation process can still compute a residual for the observation.