Best-Fit Computing - COLUMBUS Network Adjustment Software

Real-World Applications of COLUMBUS

Outlier Detection Using Automated Search

One of the many challenges facing surveyors is the identification of bad observations (measurements) in their field data. Loop closure computations can help to isolate poor quality measurements (outliers) under ideal conditions, such as in a strictly GPS survey. COLUMBUS provides tools to perform loop closures in both GPS, terrestrial, and mixed surveys.

However, even after all known poor quality observations have been removed, occasionally a few remain hidden in the network.

During a least squares network adjustment, any remaining poor quality observations will degrade the quality of your adjustment. One of the downsides of the least squares method is its inherent need to warp your survey to accommodate all measurements — including bad measurements. When this happens, you generally have an idea that some bad measurements exist, but it's not always clear where they are in your survey.

What to do

Check your data first. Before you can go looking for possible outlier observations, it is important to do the following:
  1. Check your measurements for obvious blunders.

  2. Ensure that your network has adequate redundancy and geometry (minimize very short legs adjacent to long legs, etc.).

  3. Double-check the expected errors (standard deviations) you have assigned to each observation. Assigning inappropriate standard deviations to an observation may make it look bad (after adjustment) or could make a nearby observation look bad. If your chord distances have been carefully measured to +/- 0.005 meters, don't assign them a standard deviation of 0.025 meters. Assigning the appropriate standard deviations to each observation type is absolutely essential to finding poor quality observations and achieving the desired adjustment results.

  4. For 3D networks using terrestrial measurements, be sure to include instrument and target heights for each set of measurements. If the observations have already been reduced to mark-to-mark, instrument and target heights are not required. Reduction of measurements to mark-to-mark should be performed using geodetic reduction techniques, not simple trigonometry (unless the stations are very close together; for example, less than a few hundred meters).

The Standardized Residual

Outlier detection techniques during adjustment utilize statistical analysis to identify and isolate bad measurements. Many different outlier detection schemes exist, but only a few really seem to work on a consistent basis.

The National Geodetic Survey (NGS) recommends using the Standardized Residual ratio test as a means for examining each observation in the adjusted network. The Standardized Residual is the ratio of the:

observation residual

observation residual standard deviation

The observation residual is the difference between the measured observation and the adjusted observation. It is the correction applied to the original observation to arrive at the adjusted observation. The larger the corrections, the larger the error in your network. The residual standard deviation is a by-product of the least squares adjustment process: it is the computed standard deviation of the residual. At the 68.3% confidence level you can expect the true residual (for the observation) to be between:

residual (plus or minus) its standard deviation

Also note that the ratio is a unitless value; the units are cancelled by forming the ratio. Thus, all observation types, whether linear or angular, are comparable to one cutoff value (see below).

For each observation in the adjusted network, the absolute value of the Standardized Residual is compared against a cutoff value (set up by you or computed automatically by COLUMBUS). If the observation's Standardized Residual (its absolute value) is larger than the cutoff value, that observation is tagged as a possible outlier.

To set up the cutoff value in COLUMBUS, use the Options | Network Options | Outlier Constants dialog box in the Standardized Residual field. If set to zero, the constant is calculated using the TAU statistic. The TAU statistic is a function of the number of observations, the degrees of freedom, and the confidence level setting (68%, 95%, 99%, etc.) for the network. By setting the value to a positive non-zero number, you control the cutoff value. Over time (and with the same instruments and field crew) you might get comfortable with a value which works for you. Whether you enter your own value or let COLUMBUS compute the TAU-statistic, the resulting cutoff is always displayed in the Network Processing Summary view after the adjustment has completed.

Eliminate external factors first

Outlier observations should always be isolated and removed before performing a fully-constrained adjustment. We recommend you perform repeated minimally-constrained (free) adjustments to isolate outliers. For a 3D Geodetic network, this means holding only one station fixed in 3D or one station fixed in 2D and one station fixed in 1D. Only in this way can you eliminate the introduction of errors from prior surveys into you current project. By only fixing one station, you can be sure any blunders in your survey are due to the current observation set (and not some additional control, which you may not have established).

Process of elimination

Because outlier observations tend to distort a network, one bad observation can make others look bad, too. Therefore, when searching for outliers, the following process is recommended:

  • Adjust the minimally-constrained (free) network and examine all outliers which fail the Standardized Residual Test.
  • Remove the observation (or baseline, in the case of GPS) for which the Standardized Residual is the largest (observations can be de-selected within the Network | Observations dialog before re-adjustment).
  • On each subsequent adjustment, the largest offender is again removed.
This process is repeated until no more outlier observations are found (based on the Standardized Residual test).

Research suggests that the worst outlier may be causing other observations to be seen as outliers. Often by simply removing a few of the worst offenders, all the remaining outlier observations disappear. This is the result of good observations being distorted by the adjustment that included bad observations.

An automated approach

As you can see from the discussion above, the process of identifying and removing outliers is an iterative one. So why not just let the computer do the work? This process can be automated in COLUMBUS.

The automated approach requires very little additional work from you. It is very similar to performing the manual process described above, except the automated approach finds and removes the bad observations for you.

To use this feature, simply select your Network Stations, one fixed station, and network observations in the usual way. Set up the Standardized Residual cutoff value in the Options | Network Options | Outlier Constants dialog to either zero (let COLUMBUS calculate the cutoff) or some non-zero value. Enter the Network | Adjustment (Free - Eliminate Outliers) dialog and follow the directions. For additional information see the help screen within this dialog.

About the process

Sometimes when using this option in networks with low degrees of freedom (or some other situation), you may get a partial solution which terminates the process. This simply means not all outlier observations could be removed while still being able to adjust the network. The process may have removed more observations than the minimum observation required to have a valid network (for example, degrees of freedom may have dropped to zero or below).

Whether you get a partial solution or a complete solution, you can look at the Results | Best Free Solutions view to see a summary of the observations which were removed on subsequent adjustments. The Network Processing Summary view will indicate if a partial or complete solution has been found. Sometimes you may not get even a partial solution. In this event, you need to fix the reported error before continuing.

If you obtained a complete solution ("All Found Outlier Observations Successfully Removed" message), you can then look at the final network adjustment results,accessed from the RESULTS menu (just like when completing the normal network adjustment process).

Additionally, you can save the final network configuration with the Network | Save Network command, or you can proceed to do a constrained adjustment by closing the current adjustment, selecting additional fixed stations and then selecting the Network | Adjustment command.

As long as you do not re-enter the Network | Observations dialog and "Select ALL", the observations removed will not be included during any immediate adjustments. If you are curious, enter the Network | Observations dialog and scroll down to see which observations are now "de-selected". These observations were removed during the iterative process just completed. They have not been removed from memory, only temporarily disabled while this file is loaded and you have not re-selected them.

Questions or comments

If you have any questions, comments or problems using the automated technique or performing the operation manually, please contact us and mention the article title. It is always helpful if you can send us your project data file, saved as an ASCII (Text) file when possible.

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