Free Station Network Adjustment

GNSS & Optics Geocom

 

A free station is defined as the setup of a total station over an unknown point, from which observations are made to known points, with the objective of determining the coordinates of the instrument station and establishing its orientation. This method is applied to obtain the determination directly in the field: after performing a free station setup, the total station is automatically positioned and oriented.

This method is especially useful in confined spaces, such as tunnels, for example, where observations are made to points materialized on the tunnel walls. It is also used in geomonitoring where it might be used to track the same point where the total station was set up. Generally speaking, the method is widely accepted in a variety of surveying applications. For this reason, this article aims to demonstrate a precise coordinate densification methodology where monumentation can be complex, along with adjusting a network based entirely on free stations using a variety of observations made with the total station.

However, the problem with point densification using this technique is the determination of the total station's orientation, which depends on the quality and quantity of fixed points involved in the solution and the station's location relative to these points. Furthermore, it is not a technique accepted by the industry for densifying points like a traverse or a network due to the potential loss of orientation that can occur in chained station setups.

 

This document aims to present a new way of densifying, demystifying the free station or trisection, through the support of good field technique, cycle measurements, appropriate accessories, planning, and least squares network adjustment in software like Trimble Business Center.

Free station and cycle measurement

For this article, a Trimble SX12 scanning total station (1" angular accuracy and 1 mm + 1.5 ppm distance accuracy) was used along with a TSC7 controller with Trimble Access as field software. Essentially, a series of free stations were performed, which will be adjusted in a block once this data has been imported into TBC.

 

Figure 2. Free station or trisection in Trimble Access

 

Each free station setup was configured to observe 4 cycles in direct and reverse automatically using the automatic aiming system (Autolock), considering that prisms were used. Additionally, after performing the free station setup, positions are densified, given that the total station is already oriented, to perform the station change by performing another free station setup until the circuit is closed.

 

Monumentation

Each point was monumented using Rothbucher prisms, which are used for geomonitoring and for surveying, either for precise determination or construction layout. The accessory used on this occasion is a magnetic base prism that rotates 360° clockwise and 180° on its vertical axis, providing an efficient orientation level when aiming at the total station. In this way, the prism is mounted on a metal base whose shape matches the prism's base. This metal base can be anchored to different surfaces using epoxy glue, screwed onto wood, rock, concrete, or metal.

 

 

Network Design

The network considers an origin point called E1 along with the fixed orientation E1-P1. Both E1 and the E1-P1 azimuth constitute the datum. In this way, points Px correspond to the prism positions while points ELx are the positions of each free station.

 

 

In sequential terms, the following applies:

● E1 is the network origin and E1-P1 is a fixed azimuth.
● From E1, 4 cycles are observed in direct and reverse to points P1, P2, P3, and P10.
● The instrument is moved to EL2, observing 4 cycles in direct and reverse under a trisection to points P1, P3, and P4.
● From EL2, 4 cycles are observed in direct and reverse to points P5 and P6.
● The instrument is moved to EL3, observing 4 cycles in direct and reverse under a trisection to points P3, P5, and P6.
● From EL3, 4 cycles are observed in direct and reverse to point P7.
● The instrument is moved to EL4, observing 4 cycles in direct and reverse under a trisection to points P6 and P7.
● From EL4, 4 cycles are observed in direct and reverse to points P1 and P8.
● The instrument is moved to EL5, observing 4 cycles in direct and reverse under a trisection to points P1 and P8.
● From EL5, 4 cycles are observed in direct and reverse to points P2 and P10.

 

 

Adjustment in Trimble Business Center

Each free station produces its own solution regarding the total station's position and orientation determination. However, when all data converges into a block, it is possible to adjust by least squares, similar to any network with redundancy greater than 1.

It is also important to check the consistency between TBC and Trimble Access. Regarding position and orientation determination, both TBC and Trimble Access show the same results.

 

 

It is important to review the observations to eliminate those that deviate from expectations. For this purpose, there is a tool called mean angles where observations can be removed.

Finally, the least squares adjustment is executed, obtaining the following coordinates along with their respective precisions:

 

Figure 11. Adjusted network

 

Conclusions

The results obtained from this experience allow for an interesting analysis of the observation technique and the accessories required for the activity. With this type of methodology, systematic errors are completely eliminated: prism height and installation remain unaltered throughout the entire lifespan of the network.

Furthermore, the prism constant is fundamental for position determination, being a recurring source of error. The one used for Trimble is indicated as an offset (-16.9 mm) in the following figure:

 

Observations by cycles to prisms using Trimble SX12's Autolock Advanced auto-aiming technology allow for fast and redundant measurements. In this experiment, 4 observation cycles in the trisection took approximately 4 minutes, with high-precision position and orientation determination as shown in the following figure:

 

The network design, or operatively, performing these measurements in a network fashion, linking at least two origin points and two advance points from each position, allows for creating a link with sufficient information redundancy for a network adjustment in TBC. The results obtained from this experience exceed expected expectations. The analysis of the captured data is crucial when adjusting the network, as TBC provides warnings for observations with higher errors. Given the amount of captured information, it is possible to discard out-of-range observations and re-perform the network adjustment.

Finally, the results obtained from the fieldwork and office analysis allow us to conclude that the quality of the results makes it possible to use this network as control points for a construction project and to use it for layout tasks, topographic control, and high-precision surveying.