A new LS adjustment has been introduced that integrates more seamlessly with n4ce, with enhanced features but retaining the look of the Legacy version. Access to both New and Legacy versions is provided.
In this Article...
Post Calculation – Analysing the Results
Getting Started
To start the newer version right-click over the Survey job folder name and select Least Squares… New.
The adjustment process is known as Least Squares Variation of Coordinates and requires approximate coordinates to be calculated from known stations and/or fixed bearings. This is called pre-calc and involves forward calculating these approximations from known positions. If the pre-calc can’t find sufficient data to complete pre-calc a warning will be given, and you will be invited to inspect your data.
Your data is prepared like any other adjustment, with control measurements being denoted with a -99 (STN) Point number. Control bearing measurements with a -88 (BKB) Point Number will be ignored.
Multiple control observations will be averaged with rounds of angles being adjusted to be on face left. This gives a spread about a mean value which is compared against a Standard Error for that measurement. If any of these spreads exceed these tolerances a warning message will be given.
A tabbed display window will then appear with headings identifying different page contents. This is where you can set up your control including fixed bearing in the Control List tab. The program requires at least one fixed station and a fixed bearing or two fixed stations. Pre-calc takes place after this information has been entered.
You may wish to check the Av Data tab to see if there are any meaned observations that have been flagged out of tolerance. Below we can see a potential issue with a Hz distance highlighted in red. Hovering over it will display a tooltip showing you the meaned offset. A tolerance check of 5mm was used here and can be seen in the Settings tab.
Note: Individual readings can be isolated and removed from consideration in the Raw Data tab. If this results in meaned offsets within tolerance the cell no longer highlights in red.
The Control List tab displays all the stations identified within the project and if found in the Project Tree Stations folder, with their Status. The next thing is to enter or derive the approx. stations coordinates of the unknowns from fixed values, which can also be typed in. If using just one fixed station, you will have to enter an Orientation Bearing.
Setting the Control Data
The LS process minimises the sum squares of residual changes to approx. coordinate values. To start the process off these approx. values are required, which is done automatically through pre-calc. We need a minimum of two known stations (fixed) or one known station and a fixed bearing. All the information required to do this is within the Control List tab.
Once entered the program will compute the initial approximations and display them as shown below. In this example A is a fixed station and a bearing A to I5 has been set to 45deg.
If stations exist on the Project Tree, these will come through as either Fixed or Approx. Pre-calc should take care of any remaining Unknowns. The Status of a station can be changed, as shown below. Unknown will let the program decide its value automatically.
If you are using a fixed fixed bearing you have to Identify the From and To stations, followed by bearing in DEG.MMSS format. Checks are made for angles > 360 and mins/secs >59. To fix the Z value, double-click on the cross under Fix Z and this will change to a tick.
Settings
Before any LS adjustments are carried out, you are directed to the Settings tab. This is where you set defaults for standard errors (weights), warnings and corrections. The standard errors relate to the measuring precision of your instrument, which can be improved by taking multiple rounds of readings on both left and right faces to remove systematic instrument errors.
The left Warning Tolerances are used to flag potential excessive meaned reading spreads pre-adjustment and the right warning tolerances are used to flag excessive corrections to readings post-adjustment. The latter is particularly useful when identifying rouge readings.
Since the adjustment process is iterative and may not converge to a solution, two checks are available to prevent divergence. These are in Adjustment Settings and in normal use the values shown below are typical.
Adjustments can be set to 3D, or 2D if the check button is not set. Weights by Count should be used if there are inconsistent multiple readings. For example, a single reading may have a greater influence over multiple readings due to similar weight.
Corrections can be applied for OS UTM or Local Scale Factor, Curvature and refraction and Mean Sea Level.
Note: If you change the settings without saving, they will not be available next time you go into LS.
The Standard Errors shown above will apply to all readings of that type unless you change them individually in the Av Data Tab, as shown below. Here we are changing the Vt Wt from 5” to 10” for readings I1 to I3. It’s usual to allocate larger weights to vertical angles than horizontal angles.
The Raw Data tab allows you to identify and remove individual readings where they are flagged as possible discrepancies in the Av Data tab, as the distant reading I3 to I4 flagged shown in red above.
This has the same effect as adding “,I” to the reading allowing you to remove possible rouge readings and see if the adjustment can improve. Simply double-click on the observation you wish to remove or recover. The remaining meaned multiple reading will be updated.
Map Tab
Before carrying out an adjustment, the map tab will display the pre-calc position of the stations and lines showing the to and from observations. If there is insufficient fixed data, the program will take the first reading from the first station as fixed at a bearing of 0⁰0’0”. You can use this interface to view the data associated with each reading and modify the starting positions and bearing before computing the LS adjustment.
Hovering over lines between the stations will bring up information as a tooltip, namely the stations it is going to/from, the number of readings, and the maximum standard errors for the averaging.
Click your mouse and a query box appears asking if you want to remove the to/from station readings from the LS computation. This will only work if the network is still computable without these readings, assuming there is sufficient fixed data to perform the calculation.
If you select No a popup box appears with the raw data and averaged data between these stations as shown below. Readings can be modified as already identified. Select OK to accept any changes or Cancel to ignore any changes. We don’t keep a log of any changes!
If you hover over a station its positional and status will be displayed, as shown below.
Clicking the mouse button will bring up a dialog with station data, allowing editing. Select OK to update or Cancel to ignore.
Post Calculation – Analysing the Results
Having set appropriate standard errors in Settings and provided sufficient control information, you can now press the Adjust button at the bottom of the screen. The Standard Errors are used to calculate weights and affect the results, as you will see later. If there is a problem with the control provided a message will appear, after selecting Adjust, asking you to return to the Control List tab.
Assuming the calculations have been completed successfully we can now interrogate the results. The starting point for this will be found in the Adj Vals tab, which appears only after you select Adjust. Other tabs also appear, allowing you to interrogate the corrected observations.
The results appear with information allowing you to question their authenticity. The Adj tabs display the reverse calculated observations using the adjusted coordinate values. It’s here that you can interrogate the difference between original and computed observational values. The last tolerances in Settings are used to highlight possible rouge readings.
The Adj Vals tab contains your first look at the adjustment, allowing you to make corrections to Standard Errors in Settings, then repeat the Adjustment – if necessary.
The first port of call is to look at the Total Error Factor or Sigma Zero (16.5) value. This should approximate towards unity and its value is affected by the weights associated with Err Factors/Sd Err values to Hz Distance, Hz Angle and Vt Angles which should fall between 0.5 and 1.5.
The weights for Hz Distance (3) and Hz Angle (10) are within limits but those for Vt Angles (5) need to be increased. Return to the Settings tab and change the Vt Angles SE to 20” then re Adjust.
The results are getting better as the Total Error Factor is now 4.2 but the Vt Angle Err Factor (5.84) is too large.
It may be worth looking at the rest of the results here to see if there is any indication of why the Vt Angle Err Factor is so high. The Adj Vals tab also contains the worst-case corrections (Max Residuals) to the observations and it's showing serious Vt Angle issues between A to I3 (233.4”).
The LS adjustment process calculates the new station coordinate values from the approximates and then reverse engineers the readings comparing them to the originals and calculates the differences. This can identify possible blunders or poor readings, which can be isolated and removed from further repeat calculations but remember the adage “rubbish in – rubbish out”. The LS process cannot correct your mistakes!
The Max RMSE Values also gives you the worst root mean square error at stations for XY&Z. This is the 95% confidence value and clearly, we have a problem with the vertical angle in this survey. Maybe time to do a complete resurvey?
Not all surveys are this bad! Here is one that has more acceptable results, but also look at the Max Residuals and Max RMSE Values. It’s up to you to decide if the survey results are acceptable.
We can see that the Total Error Factor is close to unity and the individual Err Factors are within the range of 0.5 to 1.5. The adjusted stations appear as the above with red highlights indicating where the RMSE values fall outside set tolerances, which in this example were all set to 10mm in XY&Z.
Several other tabs are now available, which allow you to interrogate the resulting corrected observations. In the example below for Hz Angles, the red highlights indicate where tolerance checking has been exceeded. In this case, the Hz angle check was for > 10” difference between the original averaged reading and that calculated from the final adjusted coordinates. The same would apply to the Adj Vt Ang and Adj Hz Dist tabs.
Now that the adjustment has been completed successfully, the Map tab will display the survey with error ellipses, which indicate the likely error magnitude and orientation. Scale and colour options are available here.
Hovering over a station will bring up a tooltip that contains its name, XYZ cords, RMSE, semi and minor error ellipse axis and rotation. The right panel displays the worst-case corrections, colour, and scale settings.
Reporting
The above results can now be exported to a printable report. This allows you to further interrogate the adjustment process in more detail and is created in a PDF format, and hence cannot be edited directly. Press Create Report, which will be greyed out until you do an Adjustment.
Scroll down the report to see the different stage calculations, finishing off with the final adjusted coordinates and RMSE and error ellipse parameters for the adjusted coordinates values.
It’s important to look at the Corrected Observations. If out of tolerance is identified an Asterix will appear in the Std. Resid column. A single * indicates just exceeding the tolerance check, whilst *** indicates serious issues with your data that need checking!
A hard copy of the Map will appear at the bottom of the Report, as shown below, with a coordinate grid for location and scale.
Before leaving and moving on to Reduction, it’s important to note the settings for corrections. These include Scale/OS UTM, Curvature and Refractions and Mean Sea Level. These must be applied before Adjustment in the Settings tab, using check buttons and carry through to Reduction.
Note: Setting corrections from within the LS program, will automatically carry these back to the main program, where reduction takes place.
Exiting the program
You can exit the program at any time by selecting the Cancel button, this will not pass anything back to the main program. You will be asked to confirm exit without saving.
After Adjustment, the Save & Exit button becomes enabled which allows you to pass the information back to the main program. This will record the adjusted coordinate values in the Stations folder, with a status Lst Squares in Type and RMSE values in the Remarks.
You will automatically enter Reduction. Any Corrections used in the least squares process will be carried through to Reductions including those set in the main program before entering LS.
The process will then continue, with a reduced survey that may need editing, some of which can be done under Observations, before passing its data through to a model. Remember that editing can be done both graphically and in spreadsheet form using dual display and edit.
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