pair<Matrix, Matrix> IB(Matrix R, Matrix D, Matrix Rc, Matrix Dc, Vector X,
        Vector Y, Vector Xd, Vector Yd) {

    int n = X.size();

    //Convert Initial Data to Decimal Values
    Vector R_decimal = S2D(R,'r','r');
    Vector D_decimal = S2D(D,'d','r');

    Vector Rc_decimal = S2D(Rc,'r','r');
    Vector Dc_decimal = S2D(Dc,'d','r');

    //Perform Trig Calculations
    Vector s_RRc, c_RRc, t_D;

    double s_Dc = sin(Dc_decimal[0]);
    double c_Dc = cos(Dc_decimal[0]);
    double t_Dc = tan(Dc_decimal[0]);

    for (int i=0; i < n; i++ ){
        s_RRc[i] = sin(R_decimal[i]-Rc_decimal[0]);
        c_RRc[i] = cos(R_decimal[i]-Rc_decimal[0]);
        t_D[i] = tan(D_decimal[i]);
    }


    //Calculate Standard Coordinates
    Vector Xi;
    Vector Eta;
    for (int i=0; i<n; i++){
        Xi.push_back(-1 * (s_RRc[i] / (s_Dc*t_D[i] + c_Dc*c_RRc[i])));
        Eta.push_back(-1 * ((t_D[i] - t_Dc*c_RRc[i]) / (t_Dc*t_D[i] + c_RRc[i])));
    }

    //Method of Least Square to Determine the Plate Constants
    Vector ones(n,1);
    Vector zeros(n,0);

    Matrix A_Mat = {
        { X },
        { Y },
        { ones },
        { Xi },
        { zeros }
    };

    Matrix B_Mat = {
        { X },
        { Y },
        { ones },
        { Eta },
        { zeros }
    };

    Vector ab = LeastSquare(A_Mat);
    Vector de = LeastSquare(B_Mat);

    ab[0] -= 1;
    de[1] -= 1;

    int numDebris = Xd.size();

    Vector Xi_d(numDebris);
    Vector Eta_d(numDebris);

    for (int i=0;i<numDebris;i++){
        Xi_d[i] = (ab[0]+1)*Xd[i]+ab[1]*Yd[i]+ab[2];
        Eta_d[i] = de[0]*Xd[i]+(de[1]+1)*Yd[i]+de[2];
    }

    //Determine the Right Ascension and Declination of the Debris
    Vector t_RdRc, Rd1, t_Dd, Dd1;
    Matrix Rd, Dd;

    for(int i=0;i<numDebris;i++){
        t_RdRc.push_back(Xi_d[i]/(cos(Dc_decimal[i]) - Eta_d[i]*sin(Dc_decimal[i])));
        Rd1.push_back(atan(t_RdRc[i])+Rc_decimal[i]);
        t_Dd.push_back(((Eta_d[i]*cos(Dc_decimal[i])+sin(Dc_decimal[i]))*(sin(Rd1[i]-Rc_decimal[i])))/Xi_d[i]);
        Dd1.push_back(atan(t_Dd[i]));
    }

    Rd = D2S(Rd1, 'r','r');
    Dd =D2S(Dd1,'d','r');

    return make_pair(Rd,Dd);
}