code to convert the (Easting, Northing) MUTM data (datum : Everest-1830) to Latitude Longitude in datum WGS-84

gistfile1.txt

//test data
// 632750,3024751,1230 and zone 88 (3 degree UTM zone)
data = {
  "N" : 3038250,
  "E" : 617000,
  "ht": 1230,
  "zone": 88
};
//parameters of Everest-1830
everestParams = {
  "e" : 0.08147298125166744,
  "f" : 0.0033244493186534527,
  "e2": 0.0066378466740345775,//square of the eccentricity
  // "e2": 0.00667054,
  "a": 6377276.345,//semi major axis of Everest-1830
  // "a": 6377563.396,
  "if": 300.8016980102568,
  "fE": 500000,
  "phi0": 0,//latitude of the natural origin
  // "fE": 400000,
  "fN": 0,
  "k0": 0.9999,
  // "k0": 0.9996012717,
  "M0": 0 //for latitude of origin 0
};
//parameters of wgs-84
wgsParams = {
  "a" : 6378137.0,
  "e" : 0.08181919092890624,
  "e2": 0.006694380004260827,
  "f" : 0.0033528106718309896
};
//transformation parameters
transformParams = {
  "dx" : 282,
  "dy" : 726,
  "dz" : 254
};

//calculations used in the formula
function esquareby4(){
  return (everestParams["e2"]/4)
};
function threee4by64(){
  return (3*(everestParams["e2"])*(everestParams["e2"])/64);
};
function fivee6by256(){
  return (5*(Math.pow(everestParams["e2"], 3)/256));
};
function capitalM1(){
  return (everestParams["M0"] + ((data["N"] - everestParams["fN"])/everestParams["k0"]));
};

//mue1
function mue1(){
  var numerator = capitalM1();
  var denom = everestParams["a"] * (1- esquareby4() - threee4by64() - fivee6by256());
  // console.log(numerator/denom);
  return (numerator/denom);
};
//calculations
function rootoneminuse2(){
  return Math.pow((1-everestParams["e2"]), 0.5);
};
function e1(){
  return ((1 - rootoneminuse2())/(1 + rootoneminuse2()));
};
function threee1by2(){
  return (3* e1()/2);
};
function twenty7e1cubeby32(){
  return (27* Math.pow(e1(), 3)/32);
};
function sinmue1(x){
  var xmue1 = x * mue1();
  return Math.sin(xmue1);
};
function twenty1e1squareby16(){
  return (21* Math.pow(e1(), 2)/16);
};
function fifty5e1power4by32(){
  return (55 * Math.pow(e1(), 4)/32);
};
function hundred51e1power3by96(){
  return (151 * Math.pow(e1(),3)/96);
};
function thousand97e1power4by512(){
  return (1097 * Math.pow(e1(),4)/512);
};

//phi1
function phi1(){
  return (mue1() + ((threee1by2() - twenty7e1cubeby32()) * sinmue1(2)) + ((twenty1e1squareby16() - fifty5e1power4by32()) * sinmue1(4)) + (hundred51e1power3by96() * sinmue1(6)) + (thousand97e1power4by512() * sinmue1(8)));
};

//v1
function v1(){
  var numerator = everestParams["a"];
  var denominator = Math.pow((1 - everestParams["e2"] * Math.pow (Math.sin(phi1()), 2)), 0.5);
  return(numerator/denominator);
};

//row1
function row1(){
  return(v1()*v1()*v1()*(1 - everestParams["e2"])/(everestParams["a"]*everestParams["a"]));
};

//T1
function T1(){
  return (Math.pow(Math.tan(phi1()), 2));
};

//e'2
function edash2(){
  var numerator = everestParams["e2"];
  var denominator = (1- everestParams["e2"]);
  return (numerator/denominator);
};

//c1
function C1(){
  return (edash2() * (Math.pow(Math.cos(phi1())),2));
};

//D1
function D(){
  return ((data["E"] - everestParams["fE"])/(v1() * everestParams["k0"]));
};

//calculations
function Dsquare(){
  return Math.pow(D(),2);
};
function C1square(){
  return (Math.pow(C1(),2));
};


//the latitude
function phi(){
  // debugger;
  var firstTerm = phi1()*180/Math.PI;
  var secondTermpart1 = v1() * Math.tan(phi1()) / row1();
  var secondTermpart2_1 = Dsquare()/2;
  var secondTermpart2_2 = (5 + 3 * T1() + 10 * C1() - 4 * C1square() - 9 * edash2()) * (Dsquare()/24);
  var secondTermpart2_3 = (61 + 90 * T1() + 298 * C1() + 45 * T1() * T1() - 252 * edash2() - 3 * C1square()) * (Math.pow(D(), 6)/720);
  var secondTermpart2 = secondTermpart2_1 - secondTermpart2_2 + secondTermpart2_3;
  var secondTerm = secondTermpart1 * secondTermpart2;
  // debugger;
  return (firstTerm - secondTerm);

};


//central meridian
function lamda0() {
  if (data["zone"] == 87) {
    return 81;
  }
  else if (data["zone"] == 88) {
    return 84;
  }
  else {
    return 87;
  }
};

//FOrmula of D for ZOned UTM
function DLamda(){
  // return D();
  return ((data["E"] - everestParams["fE"] - (88 * Math.pow(10,4)))/(v1() * everestParams["k0"]));
};

//longitude
function lamda(){
  var firstTerm = lamda0();
  var secondTerm1 = DLamda();
  var secondTermpart2 = (1 + 2 * T1() + C1()) * (Math.pow(DLamda(), 3)/6);
  var secondTermpart3 = (5 - 2 * C1() + 28 * T1() - 3 * C1() * C1() + 8 * edash2() + 24 * T1() * T1()) * (Math.pow(DLamda(), 5)/120);
  var secondTermDenom = Math.cos(phi1());
  var secondTermNum = secondTerm1 - secondTermpart2 + secondTermpart3;
  var secondTerm = secondTermNum/secondTermDenom;
  return (firstTerm + secondTerm);
};



//transformation using molodensky 3 parameters
//transformation OF Everest Lat/lng to WGS lat/lng
function sinLat(){
  return Math.sin(phi());
};
function cosLat(){
  return Math.cos(phi());
};
function sinLng(){
  return Math.sin(lamda());
}
function cosLng(){
  return Math.cos(lamda());
};
function ssqlat(){
  return Math.pow(sinLat(),2);
};
function adb(){
  return 1/(1 - everestParams["f"]);
};
function rn(){
   return (everestParams["a"]/(Math.pow((1-everestParams["e2"] * ssqlat()),0.5)));
 };
 function rm(){
   return (everestParams["a"] * (1 - everestParams["e2"])/Math.pow((1 - everestParams["e2"]*ssqlat()),2));
 };
 function da(){
   return (wgsParams["a"] - everestParams["a"]);
 };
 function df(){
   return (wgsParams["f"] - everestParams["f"]);
 };
 function dlat(){
  //  debugger;
   return ((((((-transformParams["dx"] * sinLat() * cosLng() - transformParams["dy"] * sinLat() * sinLng()) + transformParams["dz"] * cosLat()) + (da() * ((rn() * everestParams["e2"] * sinLat() * cosLat()) / everestParams["a"]))) + (df() * (rm() * adb() + rn() / adb()) * sinLat() * cosLat())))/ (rm() + data["ht"]));
 };
 function dlng(){
   return(-transformParams["dx"] * sinLng() + transformParams["dy"] * cosLng()) / ((rn() + data["ht"]) * cosLat());
 };







var dlng1 = dlng(); //change in longitude from transformation
var dlat1 = dlat(); //change in latitude from transformation

var dlat1_dg = dlat1 * 180/ Math.PI;
var dlng1_dg = dlng1 * 180/ Math.PI;

var phi2 = phi(); //Everest Lat
var lamda1 = lamda(); //Everest Long

var new_lat = phi2 + dlat1_dg; //
var new_lng = lamda1 + dlng1_dg;

console.log('WGS-lat');
console.log(new_lat);
console.log('WGS lng');
console.log(new_lng);

console.log('Everest-1830 lat');
console.log(phi2);
console.log('Everest-1830 lng');
console.log(lamda1);