2.6.1. Free Station Calculator

2.6.1.1. Overview

The Free Station calculator computes the position (E, N, Z) and orientation of a total-station setup from angle and distance observations to known control points — a classic resection / free stationing. The solution is a rigorous iterative least-squares adjustment; with more than the minimum observations you also get the standard error of unit weight and per-observation residuals.

The tool is found under Calculations > Survey Calculator > Free Station.

../../_images/FreeStation.jpg

The Free Station calculator.

2.6.1.2. Inputs

Parameters (top-left editor):

Key

Default

Meaning

Setup name

ST

Name given to the solved station.

Instrument height

0.000

Height of the instrument above the setup point (metres).

Known points grid — one row per control point:

Name · E (X) · N (Y) · Z · Use

Observations grid — one row per pointing:

Target · Hz (gon) · Zenith (gon) · Slope dist · Target ht · Use

Rules:

  • All angles are in gon (400-gon circle). A zenith of 100 gon is a level sight. There is no DMS input in this calculator.

  • The Use checkbox includes/excludes a row without deleting it (new and imported rows are ticked by default).

  • Every Target must match a name in the Known points grid (case-insensitive); otherwise Compute stops with a message.

  • Minimum data: 2 known points and 1 observation (more observations give redundancy and meaningful statistics).

  • Decimal comma and decimal point are both accepted in numeric cells.

2.6.1.3. What Compute does

Each observation row is expanded into three least-squares observations:

direction        Hz                                     (gon)
horiz. distance  Slope * sin(zenith)                    (m)
height diff      Slope * cos(zenith) + Hi - Ht          (m)

The engine (IQcalc resection + 3D network adjustment) then:

  1. Computes an initial position automatically — by two-circle trilateration when two or more distances to control exist, else from a direction+distance polar, else from the centroid of the controls. You never enter approximate coordinates.

  2. Runs an iterative weighted least-squares adjustment with the setup as the only free station and the controls held fixed, solving E, N, Z and the orientation unknown.

2.6.1.4. Results

The results panel reports:

Station ST
  E = 1040.0000
  N = 1030.0000
  Z = 112.0000
  Orientation = 30.0000 gon
  sigma0 = 1.234e-05
Residuals:
  C1       dir  v=  -0.0001  std=   0.00
  C1       dist v=   0.0002  std=   0.00
  ...

  • Orientation is the orientation correction of the horizontal circle, in gon.

  • sigma0 is the standard error of unit weight. All observations are currently weighted equally (angles in gon and distances in metres are pooled), so treat sigma0 as a relative quality indicator, not a rigorous unit-consistent estimate.

  • Residual rows are tagged dir (direction), dist (horizontal distance) or dz (height difference).

  • If the solve fails, the panel shows Solve failed (status N) where N is: 1 = insufficient data, 2 = divergent, 3 = singular (e.g. no usable control), 5 = max iterations.

The sketch pane shows the controls (blue), the solved station (red) and the sight rays; scroll to zoom, drag to pan.

2.6.1.5. Import / Export

Import… and Export… use a tagged CSV format (comma or tab separated; # starts a comment line):

# Free Station data (tagged CSV). Lines: SETUP / PT / OBS.
SETUP,ST,1.550
PT,C1,1000.000,1000.000,110.000,1
PT,C2,1080.000,1010.000,111.500,1
OBS,C1,229.0334,102.6087,50.0420,1.500,1
OBS,C2,329.0334,97.3913,50.0420,1.500,1

  • SETUP,name,instrumentHeight

  • PT,name,E,N,Z[,use]

  • OBS,target,Hz,Zenith,Slope,TargetHt[,use]

The trailing use flag is optional (default 1). Import replaces the current job (both grids are cleared first). Export writes the same format, so exported files re-import unchanged. Sample files are installed under testfiles/surveycalculator/ (e.g. freestation_3pts.csv).

2.6.1.6. Notes

  • Coordinates follow the IQcalc convention E = X, N = Y, Z = up, metres.

  • The height-difference sign convention is dZ = Slope·cos(zenith) + InstrumentHeight − TargetHeight.

  • The OUTLIER tag in the residual list is reserved; automatic outlier flagging is not active in the current version — judge residuals manually.