1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
|
/***********************************************/
/**
* @file observationPodEnergy.cpp
*
* @brief Precise Orbit Data (POD) observations (Energy integral).
*
* @author Torsten Mayer-Guerr
* @date 2006-02-02
*
*/
/***********************************************/
#include "base/import.h"
#include "parallel/parallel.h"
#include "files/fileInstrument.h"
#include "files/fileSatelliteModel.h"
#include "classes/earthRotation/earthRotation.h"
#include "classes/parametrizationGravity/parametrizationGravity.h"
#include "classes/observation/observation.h"
#include "misc/observation/observationMisc.h"
#include "misc/observation/covariancePod.h"
#include "classes/observation/observationPodEnergy.h"
/***********************************************/
ObservationPodEnergy::ObservationPodEnergy(Config &config)
{
try
{
FileName fileNameSatellite;
FileName orbitName, starCameraName;
renameDeprecatedConfig(config, "satelliteModel", "inputfileSatelliteModel", date2time(2020, 8, 19));
renameDeprecatedConfig(config, "representation", "parametrizationGravity", date2time(2020, 6, 3));
readConfig(config, "inputfileSatelliteModel", fileNameSatellite, Config::OPTIONAL, "{groopsDataDir}/satelliteModel/", "satellite macro model");
readConfig(config, "rightHandSide", rhs, Config::MUSTSET, "", "input for the reduced observation vector");
readConfig(config, "inputfileOrbit", orbitName, Config::MUSTSET, "", "used to evaluate the observation equations, not used as observations");
readConfig(config, "inputfileStarCamera", starCameraName, Config::MUSTSET, "", "");
readConfig(config, "earthRotation", earthRotation, Config::MUSTSET, "", "");
readConfig(config, "ephemerides", ephemerides, Config::OPTIONAL, "jpl", "");
readConfig(config, "parametrizationGravity", parametrization, Config::MUSTSET, "", "gravity field parametrization (potential)");
readConfig(config, "parametrizationBias", bias, Config::MUSTSET, "", "unknown total energy per arc");
readConfig(config, "interpolationDegree", interpolationDegree, Config::DEFAULT, "8", "orbit differentation by polynomial approximation of degree n");
readConfig(config, "integrationDegree", integrationDegree, Config::DEFAULT, "7", "integration of forces by polynomial approximation of degree n");
readConfig(config, "covariancePod", covPod, Config::OPTIONAL, "", "covariance matrix of kinematic orbits");
if(isCreateSchema(config)) return;
if(interpolationDegree%2 != 0)
throw(Exception("polnomial degree for interpolation must be even."));
if(!fileNameSatellite.empty())
readFileSatelliteModel(fileNameSatellite, satellite);
// test instrument files
// ---------------------
orbitFile.open(orbitName);
starCameraFile.open(starCameraName);
InstrumentFile::checkArcCount({orbitFile, starCameraFile});
for(UInt j=0; j<rhs.size(); j++)
InstrumentFile::checkArcCount({orbitFile, *rhs.at(j)->orbitFile, *rhs.at(j)->accelerometerFile});
// orbit differentation coefficients (position -> velocity)
Matrix P(interpolationDegree+1, interpolationDegree+1);
for(UInt i=0; i<=interpolationDegree; i++)
for(UInt n=0; n<=interpolationDegree; n++)
P(n,i) = ((n==0) ? 1.0 : std::pow((static_cast<Double>(i)-interpolationDegree/2), n));
coeff = Vector(interpolationDegree+1);
coeff(1) = 1.0;
solveInPlace(P, coeff);
// polynomial integration matrix
integrationMatrix = Matrix(integrationDegree+1, integrationDegree+1);
for(UInt i=0; i<integrationMatrix.rows(); i++)
{
integrationMatrix(0,i) = 1.0;
for(UInt n=1; n<integrationMatrix.columns(); n++)
integrationMatrix(n,i) = (i-integrationDegree/2.) * integrationMatrix(n-1,i);
}
inverse(integrationMatrix);
}
catch(std::exception &e)
{
GROOPS_RETHROW(e)
}
}
/***********************************************/
void ObservationPodEnergy::observation(UInt arcNo, Matrix &l, Matrix &A, Matrix &B)
{
try
{
OrbitArc orbit = orbitFile.readArc(arcNo);
StarCameraArc starCamera = starCameraFile.readArc(arcNo);
UInt rhsCount = rhs.size();
UInt posCount = orbit.size();
UInt obsCount = posCount-interpolationDegree;
UInt half = interpolationDegree/2;
Double dt = (orbit.at(half+1).time - orbit.at(half).time).seconds();
Arc::checkSynchronized({orbit, starCamera});
// calculate earthrotation
// -----------------------
std::vector<Rotary3d> rotEarth(obsCount);
std::vector<Vector3d> rotAxis(obsCount);
std::vector<Vector3d> rotAxisDot(obsCount);
for(UInt k=0; k<obsCount; k++)
{
const Time time = orbit.at(k+half).time;
rotEarth.at(k) = earthRotation->rotaryMatrix(time);
rotAxis.at(k) = earthRotation->rotaryAxis(time);
rotAxisDot.at(k) = earthRotation->rotaryAxisDerivate(time);
}
// position + velocity
// -------------------
std::vector<std::vector<Vector3d>> position(rhsCount);
std::vector<std::vector<Vector3d>> velocity(rhsCount);
std::vector<std::vector<Vector3d>> velocityEarth(rhsCount);
for(UInt j=0; j<rhsCount; j++)
{
OrbitArc orbit = rhs.at(j)->orbitFile->readArc(arcNo);
position.at(j).resize(obsCount);
velocity.at(j).resize(obsCount);
velocityEarth.at(j).resize(obsCount);
for(UInt k=0; k<obsCount; k++)
{
position.at(j).at(k) = orbit.at(k+half).position;
for(UInt i=0; i<coeff.rows(); i++)
velocity.at(j).at(k) += (coeff(i)/dt) * orbit.at(k+i).position;
// Earth fixed velocity in spaced fixed coordinates
velocityEarth.at(j).at(k) = velocity.at(j).at(k) - crossProduct(rotAxis.at(k), position.at(j).at(k));
}
}
// reference acceleration
// ----------------------
Matrix integrand(obsCount, rhsCount);
for(UInt j=0; j<rhsCount; j++)
{
AccelerometerArc accl = rhs.at(j)->accelerometerFile->readArc(arcNo);
for(UInt k=0; k<obsCount; k++)
{
Vector3d g = rhs.at(j)->forces->acceleration(satellite, orbit.at(k+half).time, orbit.at(k+half).position, orbit.at(k+half).velocity,
starCamera.at(k+half).rotary, rotEarth.at(k), earthRotation, ephemerides);
g = rotEarth.at(k).inverseRotate(g); // rotation into CRF
if(accl.size()!=0)
g += starCamera.at(k+half).rotary.rotate(accl.at(k+half).acceleration); // accelerometer
integrand(k,j) = inner(g, velocityEarth.at(j).at(k))
- inner(crossProduct(rotAxisDot.at(k), position.at(j).at(k)), velocity.at(j).at(k));
}
}
// reduced observations
// --------------------
l = Matrix(obsCount, rhsCount);
for(UInt j=0; j<rhsCount; j++)
{
const Double l0 = 0.5 * velocity.at(j).at(0).quadsum() - inner(velocity.at(j).at(0), crossProduct(rotAxis.at(0), position.at(j).at(0)));
for(UInt k=1; k<obsCount; k++)
l(k,j) = 0.5 * velocity.at(j).at(k).quadsum() - inner(velocity.at(j).at(k), crossProduct(rotAxis.at(k), position.at(j).at(k))) - l0;
}
// reduce integral
// ---------------
Matrix integral(integrand.rows(), integrand.columns());
Vector integralFactors;
for(UInt i=1; i<integrand.rows(); i++)
{
const UInt idx = std::min(std::max(i, integrationDegree/2)-integrationDegree/2, integrand.rows()-integrationDegree-1);
if((i<=integrationDegree/2) || (i>=integrand.rows()-(integrationDegree+1)/2))
{
integralFactors = Vector(integrationDegree+1);
const Double tau1 = i-idx-integrationDegree/2.-1;
const Double tau2 = i-idx-integrationDegree/2.;
for(UInt n=0; n<integralFactors.rows(); n++)
axpy(dt/(n+1)*(std::pow(tau2, n+1)-std::pow(tau1, n+1)), integrationMatrix.column(n), integralFactors);
}
integral.row(i) += integral.row(i-1);
matMult(-1., integralFactors.trans(), integrand.row(idx, integralFactors.rows()), integral.row(i));
}
l -= integral;
// arc related parameters (energy constant)
// ----------------------------------------
B = Matrix();
const std::vector<Time> times = orbit.times();
bias->setInterval(times.front(), times.back()+medianSampling(times), TRUE);
if(bias->parameterCount())
{
B = Matrix(obsCount, bias->parameterCount());
for(UInt i=0; i<obsCount; i++)
copy(bias->factors(orbit.at(i+half).time).trans(), B.row(i));
}
// Design matrix A (gravitational potential)
// -----------------------------------------
A = Matrix(obsCount, parametrization->parameterCount());
for(UInt k=0; k<obsCount; k++)
parametrization->potential(orbit.at(k+half).time, rotEarth.at(k).rotate(orbit.at(k+half).position), A.row(k));
// decorrelation
// -------------
if(covPod)
{
// linearized variance propagation
Matrix D(obsCount, 3*posCount);
for(UInt k=0; k<obsCount; k++)
for(UInt i=0; i<coeff.rows(); i++)
{
D(k,3*(i+k)+0) = (coeff(i)/dt) * velocity.at(0).at(k).x();
D(k,3*(i+k)+1) = (coeff(i)/dt) * velocity.at(0).at(k).y();
D(k,3*(i+k)+2) = (coeff(i)/dt) * velocity.at(0).at(k).z();
}
Matrix C = covPod->covariance(arcNo, orbit);
Matrix DCD = D * C * D.trans();
DCD.setType(Matrix::SYMMETRIC);
cholesky(DCD);
// apply Cholesky matrix
triangularSolve(1., DCD.trans(), A);
triangularSolve(1., DCD.trans(), l);
if(B.size()!=0)
triangularSolve(1., DCD.trans(), B);
}
}
catch(std::exception &e)
{
GROOPS_RETHROW(e)
}
}
/***********************************************/
|
