3D Adjustments

3D Adjustments - Introduction

In addition to the 1D-Vertical and 2D-Horizontal least squares adjustment modes, there are two 3D adjustment modes as follows:

1. 3D Terrestrial + GPS - Lat, Long & Ht - This mode allows the combination of any 1D or 2D terrestrial observations with any 3D spatial observations such as slope distances and GPS coordinate and baseline vector observations. Adjustment to network points is made in terms of local geographic/geodetic, or easting, northing and 'up' (ENU) coordinates, thus misclosures and parameter terms for GPS coordinate and baseline vector observations are determined by transformation from XYZ into ENU components for derivation of the coordinate parameter coefficients. This should be the 3D adjustment mode used for most typical survey requirements
   
2. 3D Spatial/GPS - XYZ - This mode is for slope distances and GPS observations only, where the adjustment to network points is made directly in terms of XYZ Cartesian spatial coordinates, followed by transformation to the local job datum. If an adjustment is set for this mode and one or more partially-fixed points are specified as control, the mode will be forced back to 3D-Terrestrial mode because control points must be in latitude, longitude and height components when only partially fixed. If there are terrestrial observations set 'Active' when the 3D-Spatial mode is set, the terrestrial observations will be ignored and excluded from the adjustment.

   CAUTION - In 3D Spatial/GPS - XYZ mode the adjusted points' standard deviations and error ellipses are determined and reported in the Cartesian XYZ coordinate frame and may be misleading if casually applied to the adjusted points in the normal geodetic system

Thus adjustments to network points for GPS observations will be made in either cartesian XYZ or local geodetic space with these two modes, depending on the mode selected and the presence of fully- or partially-fixed control points.

Note that if the network consists entirely of GPS observations and they have been imported or entered from a single source where adjustment has already been made to the network of observations by the GPS processing software from which they were derived, there may be little point in further attempting to adjust these observations amongst themselves. However, transformation or localisation into the local datum may still be required.

Observed Coordinates - In some cases, observed coordinates exported from proprietary post-processing GPS software may be unadjusted positions. Unless their standard deviations are relaxed, it is probably inappropriate to include these observations (Coord. Observations tab) in an adjustment since they may distort the adjustment and the statistical results for the network. Similarly, unless observed coordinates are adjusted values, using them to compute localisation parameters is not recommended. Refer to Leica SKI point classes for more information. To remove observations from the network, either disable individual observations, or un-tick the Active checkbox for the whole observation type, but note that a localisation cannot be computed from these points if the Observed Coords. type is set in-active.

Horizontal Distances in 3D adjustments - Horizontal distances can be included for adjustment in 3D but are better suited to shorter distances only (not geodetic), since the length determined for any specific line may vary depending on which end of the line the observed slope distance is reduced to horizontal. It is doubtful if horizontal distances are ever 'observed' as such since they will always have been reduced from measured slope distances.

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Network Pre-Analysis

Where GPS and terrestrial observations are combined into a single network, separate 2D adjustment of the terrestrial observations and another 3D adjustment of the GPS observations should first be done to check for (and more easily eliminate) observation anomalies, errors and outliers before combining all observations into a single 3D network adjustment - this will also help to avoid errors being hidden and compensated by the adjustment. Further, to check for internal consistency, adjustment should first be made with minimum constraints to avoid placing strain on the observations - for more information refer to the Constraints and Minimally-constrained network sections in the Network Adjustment - Least Squares topic.

"Combining GPS and terrestrial data requires a common coordinate system. When the original GPS vectors do not form a network, the 3D network adjustment cannot be performed. In this case, in order to integrate the GPS measurements with the terrestrial observations and to perform a combined network adjustment, the GPS measurements should be transformed to this common system." Derivation of some geometric parameters of GPS measurements - Adel Alfrehat, Janka Sabov�nd Marcel Mojzes, Acta Montanistica Slovaca, Volume 10 (2005), No. 3, 310 - 316

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Three situations for 3D adjustments

1. 3D adjustment of terrestrial observations ONLY (no GPS) - When there are no GPS observations used, no localisation will be required and the adjustment will be done in the local ENU system where parameters coefficients are derived from coordinate differences in the local system.
   
   
2. 3D adjustment of combined terrestrial and GPS observations - The adjustment will be done in the local ENU system as previously, except that it will ALSO be necessary to localise the GPS coords and transform the vector observations to the local XYZ system BEFORE adjustment
   

   Note (Cases 1 and 2) - Although the 3D adjustment is performed in the local geodetic system, both the geodetic and geocentric coordinates are required to compute the coefficients and observation adjustments.
   

   
   
3. 3D adjustment of GPS coord or vector observations ONLY (no terrestrial) - If the 'observed' coords and vectors are GPS, then the corresponding ellipsoid datum will be ITRF/WGS84 and the adjustment can be done simply with Cartesian XYZ coordinates. The adjusted points can then be localised to the job datum when adjustment is finished. Although it would be possible to localise the observations in this case BEFORE adjustment, it is programmatically simpler and more efficient to adjust in Cartesian XYZ first and THEN localise the adjusted coordinates to the local system.

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Combining GNSS and terrestrial observations

Combining terrestrial observations with GNSS and immediately adjusting the whole network with the 3D Terrestrial + GPS option can result in a poor or un-converged adjustment if there are 'incompatible' observations present. In such a case an important point to start preparing for the adjustment is to isolate the broad observation types and compute separate 1D, 2D and 3D preliminary adjustments as follows:

1. First disable the GNSS observations (GPS Vectors and/or Coord. Observations) and any 3D terrestrial observations (Slope Distances and/or Zenith Angles) by un-crossing 'Active' on the corresponding tabs, and adjust the remaining terrestrial observations in 2D. Eliminate outliers, correct errors, adjust settings, and fine tune until a satisfactory 2D adjustment is made
2. Next disable the 2D terrestrial observations and activate the 3D observations made in-active in step 1 and adjust in 3D. Again eliminate outliers, correct errors, adjust settings, and fine tune until a satisfactory adjustment 3D is made
3. Finally activate all the observation types and adjust again in 3D

If there are no conflicts, the adjustment should be satisfactory but once again may need fine-tuning and refinement of parameters and settings as in the preceding steps.

However if the adjustment now immediately diverges or there are excessive residuals, corrections, observation outliers, large error bars or ellipses, unacceptable variance factor or other statistical values, etc, then incompatibilities exist between the 2D and 3D observations which must be identified and eliminated. For example:

• Check whether or not horizontal distances have been reduced to ellipsoid, particularly at high terrain elevations (see the Reduce Dists to Spheroid checkbox on the General tab). If the network extends over a large area it is better to not reduce any slope distance and vertical angle observations into horizontal and vertical components but to retain them as valid observations in 3D space
• Did the networks that were computed separately in steps 1 and 2 above appear to be be the same and with matching points in exactly the same positions? If not then there may be observations with points numbered incorrectly
• GNSS baseline vector observations will normally be very reliable but should still be checked by applying loop checks during adjustment (Check loops checkbox) to verify there are no miscloses. Outlier-test errors and excessive corrections or residuals appearing in either the vector observations, or in terrestrial observations connected to the same points, may indicate either incorrectly-numbered points or incorrectly-reduced terrestrial observations (eg Height Difference observations - see next item)
• Have Height Difference or vertical component observations been reduced accurately? While approximate instrument and reflector heights have little effect on reduction of distances to horizontal, the corresponding derived vertical components may be significantly in error. In this case, to include approximate vertical measurements in the network will severely conflict with 3D observations such as GNSS baseline vectors; however their effect can be compensated by modifying the vertical centring standard deviations to more realistic values consistent with their accuracy, but then their usefulness for inclusion in the network is doubtful
• Disabling observation types in turn using the 'Active' checkbox can help to isolate anomolous observations
• Clustering of large error ellipses and error bars (corresponding to excessive corrections, computed standard deviations etc) around certain points in the plotted network provides a quick visual indication of the possible location of a problem

For related information please refer to these Help topics:

or to the Least Squares Adjustment - Tips and Suggestions FAQ topic:

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Localisation of point coordinates or GPS vector observations

Normally localisation will be used for post-processed GPS baseline and point observations so that observations made on the GPS WGS84 or ITRF datum can be localised onto the job datum prior to least squares network adjustment. However localisation may also be necessary in other situations, such as to derive transformation parameters to transform points on a foreign datum (entered as points on the Coord Observations tab with the coordinate system defined by the Coord Obs. Type drop-down list) to the current job datum.

For further details regarding localisations refer to Localisation (Site Calibration).

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