Adjustment Combinations Tool

• Combinational Theory
• How Does This Apply To Network Adjustment?
• Why Not Just Use All Known Control?
• How Solutions Are Ranked
• Summary

Combinational Theory

You could decide to put only three on the project. Or you could add a fourth or fifth to finish the project sooner. Some of the possible combinations are listed below:

• Tom, Mary, Dave
• Tom, Mary, Alice
• Tom, Mary, Andy

• Tom, Mary, Dave, Alice
• Tom, Mary, Dave, Andy

• Tom, Mary, Dave, Alice, Andy

               N!

	-----------------

	K! * (N - K)!

! = factorial
N = total number of qualified people available (in this case, five)
K = number of qualified people for any given solution

The answer to this example is: 10 + 5 + 1 = 16

Note:		5! = 5 * 4 * 3 * 2 * 1
		4! = 4 * 3 * 2 * 1
		3! = 3 * 2 * 1

How Does This Apply To Network Adjustment?

The Adjustment Combinations Tool can be used when you are ready to perform a constrained adjustment. Before using this tool, you should have performed repeated free adjustments and removed any possible bad observations. If you have several control stations tied to your network, several possible combinations of control station scenarios exist. You could use all the control you have, or you might decide to use a subset of your total control.

If you had several control stations, in normal practice you might perform several constrained adjustments, altering which stations are set up to be controlling for each adjustment. After finding the most favorable results, you would perform your final constrained adjustment and be done. This process could require days or weeks worth of work if you had to manually change the configuration of control for each combination. Plus, you might leave one of the possible combinations out, never knowing if it would have been the best solution. With the Adjustment Combinations Tool, COLUMBUS performs these iterative steps for you quickly, easily, and without leaving any possible solution untested!

Example: You have a 3D network consisting of 50 stations and hundreds of observations. You have completed the free adjustment process and have removed all poor quality observations. Of the 50 stations in your network, you have known 3D coordinates for four of the stations and known 1D height for three additional stations.

Within COLUMBUS you would select these stations to be fixed in 3D and 1D, respectively. From within the Set Up Adjustment Combinations dialog box, you would then specify which combinations of control configurations are desirable in any final solution. This is accomplished by setting up the minimum and maximum number of control station types you want to have in each acceptable configuration.

For any constrained 3D network, you need a minimum of three fixed combination parameters (two fixed parameters are required for 1D or 2D networks). Stations fixed in 1D or 2D count as one parameter. Stations fixed in 3D count as two parameters - since they have both a 1D and 2D component. A constrained 3D network would require (at a minimum) any of the following:

One 1D fixed station + one 3D fixed station
One 2D fixed station + one 3D fixed station
Two 1D fixed stations + one 2D fixed station
Two 2D fixed stations + one 1D fixed station
Two 3D fixed stations

By selecting the minimum and maximum number of control stations you are willing to accept in any possible solution, the range of possible solutions is decreased or increased, respectively.

For this example, we have decided that each solution must have at least one station fixed in 1D and one station fixed in 3D. You would declare this by setting the Minimum boxes for 1D and 3D stations to the number '1'. Additionally, we have decided we want a maximum of two 1D stations in any given solution. You would declare this by setting the Maximum box for 1D stations to the number '2'. Finally, for any given solution, we want no more than two stations to be fixed in 2D (a 3D stations can be used as a 1D, as a 2D, or as a 3D control station). You would declare this by setting the Maximum box for 2D stations to the number '2'.

The edit boxes would then look like this:

Station Type	Minimum	Maximum
1D	1	2
2D	0	2
3D	1	4

For the settings above, each combination solved by COLUMBUS will have:

At least one station fixed in 1D
At least one station fixed in 3D
No more than two stations fixed in 1D
No more than two stations fixed in 2D
No more than four stations fixed in 3D

As you can see, there are many possible solutions even with as few control stations as described above. To perform this task manually would be mind-boggling and time-consuming. The risk of not attempting each solution could be the difference between an acceptable survey and one which requires more work.

Why Not Just Use All Known Control?

By solving all possible combinations, you have the best opportunity to eliminate control which may be introducing significant errors into your project.

How Solutions Are Ranked

The A Posteriori Variance Factor ranking is always performed. The closer the A Posteriori Variance Factor is to 1.0, the better the ranking for a given solution. This test does not require a final inverse on each solution, which results in faster processing times for larger networks.

The Residual Distribution Test is optional. It will give you a numerical indicator as to how evenly the Standardized Residuals (for all observations) are distributed about their mean. Since this test requires additional statistical information found within the final inverse for each solution, it will lengthen processing times for large networks when enabled.

Summary

The Adjustment Combinations Tool can save you days of work spent processing different constrained network scenarios looking for the Best-Fit Solution!