Summary
Figure 30-15. Example Summary
The summary section lists a general summary of the USMN calculation with the current settings. Each time the USMN network point list is updated or edited these value should be used as a review of the overall solution. The summary provides the following results:
Pointing Error:
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Overall RMS. The RMS deviation of each measured point to the solved network points.
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Average. The average of each measured point to the solved network points.
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Max. Largest Point Error for the network. The point name with this showing this error is listed in parenthesis.
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System Solution Time. Time to arrive at the network solution.
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Robustness Factor. Is an indicator of the numeric instability of the solution and is the inverse of the Conditioning Number.
To understand the Condition Number, it becomes necessary to know a bit about singular value decomposition, singular values, eigen vectors, and eigen values – the sort of stuff that causes eyes to glaze over. The short description is that the process of numerical error minimization produces a system of matrices that are subjected to Jacobian operators and SVD to produce a set of orthogonal gradient vectors defined in solution parameter space that provide a direction towards a minimum (hopefully the global minimum) in solution space. Once the solution has moved to the solution point, these gradient vectors should be such that any movement away from the solution point will make the error worse. Ideally there will be as many orthogonal unique gradient vectors as there are solution parameters – the direction of steepest gradient will be a combination of these vectors.
The influence of each of these vectors is scaled by singular values, a large value means that small changes in the associated vector direction will have large impact on the solution result.
A small value means that the associated vector direction will have less impact on the solution result – in other words, the solution could wander further along this direction without substantially changing the solution result. Consider a point on a plane, (Tx, Ty, and Rz) are still unconstrained and could take on any value and still retain its status as a planar point – in solution space, a similar condition specific to a particular solution parameter means that that particular solution parameter (or some combination of solution parameters) is redundant.
The ratio between the largest and the smallest singular value is the Condition Number – condition numbers nearer to unity are more robust and those that are very large are not as robust. A condition number of 10000 (robustness = 0.0001) means that the largest contributing vector has 10000 times more effect than the smallest. This means that If the smallest of the solution gradient vectors was only dependent upon one of the solution parameters which was not otherwise used by any of other solution gradient vectors, then that parameter could vary significantly without significantly changing the solution results – this would be a poorly resolved parameter. Even worse would be that one or more of the solution gradient vectors might not affect the solution result at all – each of these vectors will result in a negative integral robustness contribution.
A small Robustness (large Condition Number) value greater than zero is considered satisfactory for USMN.
A negative Robustness Factor indicates a reduced number of degrees of freedom in solution parameter space, along the solution gradient, at the solution point. Generally this means that redundant solution parameters exist relative to measurements. Alternately, an insufficient number of measurements exist to resolve solution parameters.
For example, a Robustness Factor equal to -3 would mean that three of these vectors had no effect on the solution, at the solution point specifically. This could indicate that the measurements taken are in- sufficient to resolve all of the solution parameters or that the solution is at a singular location. In either case a closer inspection of the results is recommended.
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Unknowns. The number of instruments in the network that are free to move times the 6 degrees of freedom considered in the solution (the first instrument in the list is not counted).
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Equations. The sum of the number of points from each of the instrument used in the network, times 3 to provide a 3 dimensional solution.
Uncertainty Magnitude:
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Average. Average of the uncertainty magnitudes for each of the included network points
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Max. Largest point uncertainty for the network. The point name with this showing this error is listed in parenthesis.
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Confidence Interval. The Sigma uncertainty interval used for the calculation.
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Samples. Number of samples used for each point in the computation.
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WCF. Working Coordinate Frame used to determine XYZ un- certainty.
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Uncertainty Analysis Time. Time to compute the uncertain- ties for the network.
It also provides access to information about scale bars included in the USMN calculation.