Analysis Parameters

Use this dialog to define which parameters apply to the various controls and analyses in a surveying application layer.

Where do I find the dialog?

Select the surveying application layer in the vertical list, right-click (or double-click), and choose Properties.... Then go to the Analysis Parameters tab.

Control of Sets

You can choose between two control methods:

• Statistical test
• Maximum spread between full sets

When you reduce sets, key values for set control are calculated depending on the selected control method. The values are shown in the lists for conventional observations, and the result is also displayed in the summary.

You can also check Reduce first horizontal direction to 0. This option is off by default and is only necessary if the horizontal scale has been adjusted between measurement sets. It is not recommended otherwise.

Info

See the general documentation for further details.

Control of Standard Deviation of the Weight Unit

This test is one of several global tests that treat the entire system as a whole. The test provides an indication of how the adjustment has performed. Significant upward deviation usually indicates gross errors in the measurements or that the weighting is too optimistic, meaning the measurement uncertainty is greater than assumed. If this is the case, you should perform further analyses.

This is a chi-square test, and Gemini calculates the values for the control value range (confidence interval) based on the selected test level. The result is shown in the summary.

Gross Error Search

There are various methods for detecting and identifying gross errors in the observation material before adjustment calculation.

Gemini supports two methods:

• Multiple t-test
• Datasnooping (Baarda)

Multiple t-test is commonly used in Norway, while datasnooping is described in Swedish standards.

Multiple t-test

By comparing the observations with each other, you can search for gross errors in the observation material. This is done in a Multiple T-test. A (gross) error is estimated in each observation included in the adjustment. At the selected significance level, a Student's T-test is applied, and the observation that most strongly exceeds the significance threshold in free adjustment is rejected.

In gross error search, free network is the default choice, and you can select the test level you want to use.

The error probability \(\alpha\) for testing a single observation is given as a number between 0 and 1. The typical value is 0.001 (1 ‰). This should be small so that the total error probability when testing all observations (\(n\)) is acceptable.

The total error probability can be estimated as \(1-(1-\alpha)^n\).

If the number of observations is less than 50, it may be more appropriate to estimate the error probability using the formula:

\(\alpha=(1-(1-\alpha_{tot})^{1/n})\)

Where:

• \(n\) : Number of observations
• \(\alpha_{tot}\) : Total error level (0.05)
• \(\alpha\) : Error probability for a single test

For datasets with fewer than 50 observations, the program calculates the error probability for a single observation. The calculated value is shown in the summary.

Example:

Test level 5 % and minimum test level for single observation 0.1 %

Number of observations	Error probability for 1 observation	Total error probability
20	0.26 %	5 %
50	0.10 %	5 %
600	0.10 %	5 %

Datasnooping

In the datasnooping method, you search for observation errors in the measurement data, not typing errors. In Swedish standards, standardized residuals/BVH ratios are considered.

Values above 2 (1.96) for standardized residuals (Baarda parameter) are marked as potential gross errors.

Values for MDE (Baarda) and External Reliability (Baarda) are calculated and shown in the analysis list. These are also shown in the list of observations and in the report.

Test of Known Points (Global Test)

This test determines whether there is constraint in the reference network. Weighted sum of squared errors from free and constrained adjustment and the number of overdeterminations (excess measurements) are input data for the test value. This is an F-test.

Test Level

The error probability \(\alpha\) in the global test is a classic F-test. The probability is given as a number between 0 and 1. Typical value is \(\alpha=0.05\) and maximum number of free points is 20.

General

• The global test can be run in plan, height, or all three dimensions, depending on which dimension is active when you start the test.
• In the global test, the sum of squared errors from free and constrained adjustment are compared, and an F-distributed test statistic is calculated and evaluated against a statistical F-value.

Test for Coordinates

Here you specify the selected error probability for forming a confidence interval around free points. The interval is oriented towards the existing position.

Typical test value: 0.05.

Internal Reliability

Internal reliability must be based on the same adjustment that was used when rejecting observations. It is therefore appropriate to calculate internal reliability in connection with gross error search.

• Internal reliability can be performed in plan and height separately, or together in a 3D calculation. You must select the calculation type before starting.
• To perform internal reliability, you must have made a selection.

Freeing the network is the default choice for internal reliability. Gemini then performs a gross error search to estimate the Largest Remaining Gross Error, \(\nabla_0\). In the same routine, redundancy is also calculated, and the result is written to an XML file and displayed on the screen.

Test Level

The error probability \(\alpha\) when estimating the largest remaining gross error:

\(\nabla_0=\hat\nabla\pm m_{\hat\nabla}T_{\alpha/2,p}\)

Where:

\(m_{\hat\nabla}\) : Estimated standard deviation (mean error) of the gross error

\(T_{\alpha/2,p}\) : T-distribution table value for error probability \(\alpha\) and \(p\) number of overdeterminations.

Typical value: \(\alpha=0.05\) (5 %)

Document Baarda Values (MPF and BYP)

Check the field if you want Minimum Detectable Error and Baarda External Reliability to be listed along with the other measures. This only affects documentation, not the calculation itself.

Info

See the general help for a description of the values.

External Reliability

External reliability can be performed in plan and height separately, or together in a 3D calculation. You must select the calculation type before starting. If you use correlated satellite observations in the calculation, final calculation and documentation should be done in 3D.

To perform external reliability, you must create a selection of points.

Usually, any constraint in the network should be reflected in the external reliability measures. The Largest Remaining Gross Error must then be based on observations and reference in the existing network – constrained calculation.

Test Level

The error probability \(\alpha\) when estimating the largest remaining gross error:

\(\nabla_0=\hat\nabla\pm m_{\hat\nabla}T_{\alpha/2,p}\)

Where:

\(m_{\hat\nabla}\) : Estimated standard deviation of the gross error

\(T_{\alpha/2,p}\) : T-distribution table value for error probability \(\alpha\) and \(p\) number of overdeterminations

Typical value: \(\alpha=0.05\) (5 %)

More

• Number of sectors around center point: For the nearest points in each sector, the largest effect of a remaining gross error on the distance and direction is calculated. Note: The product of the number of sectors and the number of points in each must not exceed 40.
• Number of points in each sector: Specifies how many of the nearest points in each sector should be subject to external reliability analysis. Note: The product of the number of sectors and the number of points in each must not exceed 40.
• Maximum distance from center point: If the distance from the center point to the nearest point in the sector is large, this neighbor point becomes less interesting. You can define the maximum distance to the point. If the distance is greater, it is not selected as a neighbor.
• Minimum distance from center point: Eccentric bolts are close to the center point and should not be used together with these due to poor reliability. Their reliability is therefore not interesting to calculate.

Display Type

In the analysis list, you select which external reliability measure you want to list. At the same time, this is what is displayed on the screen. The value range between the largest and smallest value for each reliability measure is called the variation width.

• Point deformation: Largest change in a point position that a possible remaining gross error can cause to the point. A vector indicates the direction, while the color symbolizes the relative size.
• Direction and angle deformation: Worst direction and angle deformation to the nearest neighbor points that a possible remaining gross error can cause in the point. An arc symbolizes the angle and a double line the direction, while the color of the symbol shows the relative size.
• Height deformation: Worst deformation in height difference to the nearest neighbor points that a possible remaining gross error can cause in the point. A double line symbolizes the height difference against a neighbor point, while the color of the symbol shows the relative size.
• Distance and scale deformation: Worst distance and scale deformation to the nearest neighbor points that a possible remaining gross error can cause in the point. An arc symbolizes the distance difference and a double line the distance, while the color of the symbol shows the relative size.

Control of Leveling

Here you select which standard you want to use for leveling.

Norwegian standards:

• Bruksnett I
• Bruksnett II
• Bruksnett III

Swedish standards:

• Anslut I
• Anslut II
• Anslut III