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I have a list of coordinates from Kenya. The coordinates were recorded in old survey maps using Cassini-Soldner Projection, with Clarke 1858 Datum. The approximate geographic coordinates (WGS84) of the area where the coordinates are apparently located are lat: -1.46 and lon : 36.9.

As an example, one set of the coordinates is (X: 150052.09 , Y: 4690.62). My interest is to convert these set of coordinates to UTM projection.

  • this question might help: gis.stackexchange.com/questions/65868/… – nmtoken Jun 12 '17 at 20:45
  • Your data does not seem to fit together. The Cassini projections of Kenya were centered on 33/35/37/39 degrees East and the equator. A point at latitude -1.46 would be 163 km south of the equator, which is nowhere near your positive Y coordinate. Are you sure these are meters? – AndreJ Jun 13 '17 at 15:39
  • From the survey plan, the coordinates are indicated as shown above. – oloo Jun 13 '17 at 21:10
  • @AndreJ can you help with the parameters for coordinates centered on 33° and 35° meridians. Might help a great deal. Thanks – Leo Sep 19 '18 at 12:41
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You can find details on the transformation from Cassini-Soldner to ARC1960 UTM in this article:

http://cae.uonbi.ac.ke/sites/default/files/cae/cae/Gordon%20Okumu%20Wayumba%20F80-81401-2009.pdf

In Table 4.8, a set of four reference points is given, with an equation to transform from Cassini to UTM:

E= b * n + a * e + ∆E                                                
N= a * n - b * e + ∆N 

Where a= Scos (θ),    b= S sin(θ) 
N and E are the local UTM coordinates
(n,e) are local Cassini  coordinates 

Computed values are given in Table 5.8:

Parameter  Value  Accuracy  Units 
S  1.0000169  ±0.000002  - 
θ  -0.000886  ±0.000002  rad 
∆N  10000167.51  ±0.35  m 
∆E  277419.49  ±0.35  m 

I get a standard deviation of the four points of 10 meters with those values.

Alternatively, you may use:

E = d * n + f * e + ∆E
N = a * n - b * e + ∆N

with:

a    1.00023
b   -0.00077
∆N  10000201.67
d   -0.00086
f    1.00033
∆E    277420.75

Quality of the reference points is now within 2 meters.

These transformations are valid for the Cassini Soldner projection centered on the 37° meridian, against UTM 37S based on ARC1960 datum (not WGS84!).

For the 39° meridian, transformation parameters are given in table 5.3:

PARAMETER  VALUE 
a  1.002248791 
b  0.0007371372 
∆N  10001507.607 
∆E  500339.6901 

Again, only valid for transformation to UTM zone 37S. Appendix 11 and 12 of the document have coordinates for both systems, and here the standard deviation is under 1 meter.

  • Thank you so much for this elaborate answer, the points appear close to where they should be. Just one more question, what is the source of this second batch of parameters? – oloo Jun 14 '17 at 8:13
  • I did some linear regression playing with the parameters in a LibreOffice Calc sheet, like I did in gis.stackexchange.com/questions/76368/…. You will get other values if you have more points, or use GPS data. Don't expect too much accuracy on those old surveying data. – AndreJ Jun 14 '17 at 10:01

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