static void Main0(string[] args)
{
// Ground station
const int N_obs = 6;
const double Step = 1200.0;
Vector Null3D = new Vector(0.0, 0.0, 0.0);
const double sigma_range = 10.0; // [m]
const double sigma_angle = 0.01 * OrbitConsts.RadPerDeg; // [rad] (=36")
string[] Label = { "x [m] ", "y [m] ", "z [m] ",
"vx [m/s]", "vy [m/s]", "vz [m/s]" };
// Variables
int i, iterat;
double Mjd0, t, MjdUTC, Theta;
double Azim = 0, Elev = 0, Dist = 0;
Vector Y0_ref = new Vector(6), Y0_apr = new Vector(6), Y0 = new Vector(6), Y = new Vector(6), r = new Vector(3), R = new Vector(3), s = new Vector(3);
Vector dAds = new Vector(3), dEds = new Vector(3), dDds = new Vector(3);
Vector dAdY0 = new Vector(6), dEdY0 = new Vector(6), dDdY0 = new Vector(6);
Matrix dYdY0 = new Matrix(6, 6), U = new Matrix(3, 3), E = new Matrix(3, 3);
LsqEstimater OrbEst = new LsqEstimater(6);
Vector dY0 = new Vector(6), SigY0 = new Vector(6);
ObsType[] Obs = new ObsType[N_obs];
// Ground station
R = new Vector(+1344.0e3, +6069.0e3, 1429.0e3); // [m]
E = CoordTransformer.XyzToGeoCoord(new XYZ(R.OneDimArray)).ToLocalNez_Matrix();
// Header
var endl = "\r\n";
var info = "Exercise 8-2: Least-squares orbit determination" + endl + endl;
Console.Write(info);
// Generation of artificial observations from given epoch state
Mjd0 = DateUtil.DateToMjd(1995, 03, 30, 00, 00, 00.0); // Epoch (UTC)
Y0_ref = new Vector(-6345.000e3, -3723.000e3, -580.000e3, // [m]
+2.169000e3, -9.266000e3, -1.079000e3); // [m/s]
Y0 = Y0_ref;
info = "Measurements" + endl + endl
+ " Date UTC Az[deg] El[deg] Range[km]" + endl;
Console.Write(info);
for (i = 0; i < N_obs; i++)
{
// Time increment and propagation
t = (i + 1) * Step; // Time since epoch [s]
MjdUTC = Mjd0 + t / 86400.0; // Modified Julian Date
Kepler.TwoBody(OrbitConsts.GM_Earth, Y0_ref, t, ref Y, ref dYdY0); // State vector
// Topocentric coordinates
Theta = IERS.GetGmstRad(MjdUTC); // Earth rotation
U = Matrix.RotateZ3D(Theta);
r = Y.Slice(0, 2);
s = E * (U * r - R); // Topocentric position [m]
GeoCoord.LocalEnzToPolar(s, out Azim, out Elev, out Dist); // Azimuth, Elevation, Range
// Observation record
Obs[i].Mjd_UTC = MjdUTC;
Obs[i].Azim = Azim;
Obs[i].Elev = Elev;
Obs[i].Dist = Dist;
// Output
info = " " + DateUtil.MjdToDateTimeString(MjdUTC) + String.Format("{0, 10:F3}{1, 10:F3}{2, 12:F3}", +OrbitConsts.DegPerRad * Azim, OrbitConsts.DegPerRad * Elev, Dist / 1000.0) + endl;
Console.Write(info);
}
;
Console.WriteLine();
//
// Orbit determination
//
Mjd0 = DateUtil.DateToMjd(1995, 03, 30, 00, 00, 00.0); // Epoch (UTC)
Y0_apr = Y0_ref + new Vector(+10.0e3, -5.0e3, +1.0e3, -1.0, +3.0, -0.5);
Y0 = Y0_apr;
// Iteration
for (iterat = 1; iterat <= 3; iterat++)
{
OrbEst.Init();
info = "Iteration Nr. " + iterat + endl + endl
+ " Residuals:" + endl + endl
+ " Date UTC Az[deg] El[deg] Range[m]" + endl;
Console.Write(info);
for (i = 0; i < N_obs; i++)
{
// Time increment and propagation
MjdUTC = Obs[i].Mjd_UTC; // Modified Julian Date
t = (MjdUTC - Mjd0) * 86400.0; // Time since epoch [s]
Kepler.TwoBody(OrbitConsts.GM_Earth, Y0, t, ref Y, ref dYdY0); // State vector
// Topocentric coordinates
Theta = IERS.GetGmstRad(MjdUTC); // Earth rotation
U = Matrix.RotateZ3D(Theta);
r = Y.Slice(0, 2);
s = E * (U * r - R); // Topocentric position [m]
// Observations and partials
GeoCoord.LocalEnzToPolar(s, out Azim, out Elev, out dAds, out dEds); // Azimuth, Elevation
Dist = s.Norm(); dDds = s / Dist; // Range
dAdY0 = (dAds * E * U).Stack(Null3D) * dYdY0;
dEdY0 = (dEds * E * U).Stack(Null3D) * dYdY0;
dDdY0 = (dDds * E * U).Stack(Null3D) * dYdY0;
// Accumulate least-squares system
OrbEst.Accumulate(dAdY0, (Obs[i].Azim - Azim), sigma_angle / Math.Cos(Elev));
OrbEst.Accumulate(dEdY0, (Obs[i].Elev - Elev), sigma_angle);
OrbEst.Accumulate(dDdY0, (Obs[i].Dist - Dist), sigma_range);
// Output
info = " " + DateUtil.MjdToDateTimeString(MjdUTC) + String.Format("{0, 10:F3}{1, 10:F3}{2, 10:F3}", OrbitConsts.DegPerRad * (Obs[i].Azim - Azim), OrbitConsts.DegPerRad * (Obs[i].Elev - Elev)
, Obs[i].Dist - Dist) + endl;
Console.Write(info);
}
;
// Solve least-squares system
OrbEst.Solve(dY0);
SigY0 = OrbEst.StdDev();
info = endl + " Correction:" + endl + endl
+ " Pos" + dY0.Slice(0, 2)
+ " m " + endl
+ " Vel" + dY0.Slice(3, 5)
+ " m/s" + endl + endl;
Console.Write(info);
// Correct epoch state
Y0 = Y0 + dY0;
}
;
// Summary
info = "Summary:" + endl
+ " a priori correction final sigma"
+ endl;
Console.Write(info);
for (i = 0; i < 6; i++)
{
info = " " + String.Format("{0, 10:S}", Label[i])
+ String.Format("{0, 12:F3}{1, 11:F3}{2, 14:F3}{3, 11:F3}", Y0_apr[i], Y0[i] - Y0_apr[i], Y0[i], SigY0[i])
+ endl;
Console.Write(info);
}
Console.ReadKey();
}
static void Main0(string[] args)
{
// Constants
double[] t = { 0.04, 0.32, 0.51, 0.73, 1.03, 1.42, 1.60 };
double[] z = { 2.63, 1.18, 1.16, 1.54, 2.65, 5.41, 7.67 };
// Variables
int i;
double b;
Geo.Algorithm.Vector a = new Geo.Algorithm.Vector(3), c = new Geo.Algorithm.Vector(3), d = new Geo.Algorithm.Vector(3);
Matrix R = new Matrix(3, 3);
LsqEstimater PolyFit = new LsqEstimater(3);
// Header
var endl = "\r\n";
var info = "Exercise 8-1: Least-squares fit using Givens rotation"
+ endl + endl;
Console.Write(info);
// Accumulation of satData equations
for (i = 0; i < 7; i++)
{
// Data equation
a[0] = 1.0;
a[1] = t[i];
a[2] = t[i] * t[i];
b = z[i];
info = "Observation " + i + endl + endl
+ String.Format(" a = {0, 8:F4}", a) + " "
+ String.Format(" b = {0, 8:F4}", b) + endl + endl;
Console.Write(info);
// Process satData equation
PolyFit.Accumulate(a, b);
// Square-root information matrix and transformed satData
R = PolyFit.SRIM();
d = PolyFit.Data();
info = " " + R.Row(0) + " "
+ " " + String.Format("{0, 8:F3}", d[0]) + endl;
Console.Write(info);
info = " R = " + R.Row(1) + " "
+ " d = " + String.Format("{0, 8:F3}", d[1]) + endl;
Console.Write(info);
info = " " + R.Row(2) + " "
+ " " + String.Format("{0, 8:F3}", d[2]) + endl + endl;
Console.Write(info);
}
// Solution of least squares system
PolyFit.Solve(c);
info = endl + "Adjusted polynomial coefficients" + endl + endl;
for (i = 0; i < 3; i++)
{
info += " c(" + i + ") = "
+ String.Format("{0, 8:F3}", c[i]) + endl;
}
Console.WriteLine(info);
Console.ReadKey();
}
