Site localization (calibration)
Fits local site coordinates to grid coordinates through control points seen in both, by a similarity (scale, rotation, shift) or affine transform, with residuals, their root mean square, and a check for a feet-and-meters mix-up.
Experimental: not yet fully verified. How results are checked
The fit has a scale of 0.999968514, and its residuals average 0.0013 m (root mean square).
| Point | Northing residual | Easting residual | Horizontal residual |
|---|---|---|---|
| CP1 | 0.0007 m | -0.0009 m | 0.0011 m |
| CP2 | -0.0005 m | 0.0008 m | 0.0010 m |
| CP3 | 0.0008 m | -0.0012 m | 0.0014 m |
| CP4 | -0.0010 m | 0.0013 m | 0.0016 m |
- Scale offset
- Rotation
- Root-mean-square residual
- Northing shift
- Easting shift
- a
Provenance
- Computed by
- survey.gnss.localization 1.0.0, core 0.1.0
- Model
- Least squares on centroid-reduced coordinates. Similarity: E = a·e + b·n + tE, N = c·e + d·n + tN with d = a and b = −c, scale √(a² + c²), rotation atan2(c, a). Affine: E = a·e + b·n + tE, N = c·e + d·n + tN, scale √|ad − bc|. Local and grid values are compared in meters
- Accuracy
- Exact least squares; the transform is only as good as the control points and holds within their extent
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Least squares on centroid-reduced coordinates. Similarity: E = a·e + b·n + tE, N = c·e + d·n + tN with d = a and b = −c, scale √(a² + c²), rotation atan2(c, a). Affine: E = a·e + b·n + tE, N = c·e + d·n + tN, scale √|ad − bc|. Local and grid values are compared in meters
Show your work
Rotation
atan2(c, a) from the least-squares coefficientsa = 0.999625908, c = 0.02617389= 1.499872°Scale
a = 0.999625908, c = 0.02617389= 0.999968514
The same steps an agent gets from the MCP server with explain: true.
Accuracy: Exact least squares; the transform is only as good as the control points and holds within their extent
Worked example: Four control points, similarity. Source: Built at scale 0.99997 and 1.5° rotation with a few millimeters of noise; least squares after Ghilani and Wolf (2021).
You enter
- Expected combined factor
- 0.99997
- Control points
- CP1, 5000 ft, 5000 ft, 1520129.021 ft, 3139867.253 ft CP2, 6000 ft, 5200 ft, 1521133.878 ft, 3140041.010 ft CP3, 5400 ft, 6100 ft, 1520557.663 ft, 3140956.371 ft CP4, 4700 ft, 5800 ft, 1519850.067 ft, 3140674.813 ft
You get
- Scale
- 0.999968514
- Scale offset
- -31.5
- Rotation
- 1.499872°
- Root-mean-square residual
- 0.0013 m
- Northing shift
- 461,772.006 m
- Easting shift
- 955,547.9987 m
- a
- 0.999625907781
- b
- -0.02617389049
- c
- 0.02617389049
- d
- 0.999625907781
- Transform
- similarity
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Changes
- 2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog
Checked against: 7 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapters 10 (traverse computations), 12 (area), 24 (horizontal curves), 25 (vertical curves), 26 (volumes).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.