Conversion of 3 degree UTM zone Easting Northing to WGS-84

Question

In Nepal we use 3 degrees width zone UTM with 3 central meridians 81 E, 84 E and 87 E and datum: Everest-1830. I am trying to convert the Everest-projected coordinates to WGS-84's Latitude and Longitude. I applied reverse of projection for conversion of Everest projected Easting and Northing to Everest's Latitude and Longitude and then transformed to WGS-84's Latitude and Longitude

I used the formula in ogp publications 373-7-2 geomatics guidance note number 7 page number 50 and 54 to calculate latitude and longitude from Easting and Northing Projected coordinates and created code to do so.

But whenever I tested the conversion and input Easting, Northing and height values 617000, 3038250, 1230 respectively of zone 88 (Central meridian 84 degree E, datum : Everest-1830). I get output latitude 27.461834699447184 and longitude 83.86573999170062 (Datum: Wgs-84). But the expected output is latitude: 27.732 and longitude: 85.417.

I must be doing something wrong. Please help me

Answer 1

I guess you stumbled over this note on page 53:

subsequent civilian adoption of the systems usually ignores the zone prefix to easting. Where this is the case the formulas below do not apply: use the standard TM formula separately for each zone

The formulas on page 54 should only be used if the zone number is written before the false Easting, which is not the case here. So I took only the formulas from p 50ff into Libre Office and got these results:

M0  0           
e1  0.0016649922            
mue1    0.4772587465            
M1  3038553.85538554            
T1  0.2701106629            
C1  0.0059292372            
esq 0.0066822021            
D   0.0183352698            
phi1    0.4793002154            
nue1    6381782.36093598            
rho1    6348382.77011411            
phirad  0.4792124095        phi 27.4568485565
lamrad  1.4867384817        lam 85.1838402406

which returns the same lat and lon on the Everest ellipsoid as

cs2cs +proj=tmerc +lon_0=84 +lat_0=0 +k=0.9999 +a=6377276.345 +b=6356075.41314024 +x_0=500000 +units=m +towgs84=282,726,254 +no_defs +to +proj=longlat +a=6377276.345 +b=6356075.41314024 +towgs84=282,726,254 +no_defs -f "%%.6f"<MUTM88.txt >WGS84out.txt

85.183840   27.456849 1230.000000

Transforming to WGS84 returns:

85.181615   27.457128 1188.383496

which is still not exactly what you expected, but more close than your result.