PreprocessingPod

This program estimates empirical covariance functions of the instrument noise and determine arc wise variances to downweight arc with outliers.

A complete least squares adjustment for gravity field determination is performed by computing the observation equations, see observation:podIntegral or observation:podVariational for details. The normal equations are accumulated and solved to outputfileSolution together with the estimated accuracies outputfileSigmax. The estimated residuals $\hat{\M e}=\M l-\M A\hat{\M x}$ can be computed with computeResiduals.

For each component (along, cross, radial) of the kinematic orbit positions a noise covariance function is estimated \[ \text{cov}(\Delta t_i) = \sum_{n=0}^{N-1} a_n^2 \cos\left(\frac{\pi}{T} n\Delta t_i\right). \]The covariance matrix is composed of the sum of matrices $F_n$ and unknown variance factors \[ \M\Sigma = a_1^2\M F_1 + a_2^2 \M F_2 + \cdots + a_N^2\M F_N, \]with the cosine transformation matrices \[ \M F_n = \left(\cos\left(\frac{\pi}{T} n(t_i-t_k)\right)\right)_{ik}. \] An additional variance factor can be computed (estimateArcSigmas) for each arc $k$ according to \[ \hat{\sigma}_k^2 = \frac{\hat{\M e}_k^T\M\Sigma^{-1}\hat{\M e}_k}{r_k}, \]where $r_k$ is the redundancy. This variance factor should be around one for normal behaving arcs as the noise characteristics is already considered by the covariance matrix but bad arcs get a much larger variance. By appling this factor bad arcs or arcs with large outliers are downweighted.

Name	Type	Annotation
outputfileSolution	filename	estimated parameter vector (static part only)
outputfileSigmax	filename	standard deviations of the parameters (sqrt of the diagonal of the inverse normal equation)
outputfileParameterName	filename	names of estimated parameters (static part only)
estimateArcSigmas	sequence
outputfileSigmasPerArcPod	filename	accuracies of each arc (POD2)
estimateCovarianceFunctions	sequence
outputfileCovarianceFunctionPod	filename	covariance functions for along, cross, radial direction
computeResiduals	sequence
outputfilePodResiduals	filename
observation	choice	obervation equations (POD)
podIntegral	sequence	precise orbit data (integral approach)
inputfileSatelliteModel	filename	satellite macro model
rightHandSide	podRightSide	input for the reduced observation vector
inputfileOrbit	filename	used to evaluate the observation equations, not used as observations
inputfileStarCamera	filename
earthRotation	earthRotation
ephemerides	ephemerides
gradientfield	gravityfield	low order field to estimate the change of the gravity by position adjustement
parametrizationGravity	parametrizationGravity	gravity field parametrization
parametrizationAcceleration	parametrizationAcceleration	orbit force parameters
keepSatelliteStates	boolean	set boundary values of each arc global
integrationDegree	uint	integration of forces by polynomial approximation of degree n
interpolationDegree	uint	orbit interpolation by polynomial approximation of degree n
accelerateComputation	boolean	acceleration of computation by transforming the observations
podVariational	sequence	precise orbit data (variational equations)
rightHandSide	sequence	input for observation vectors
inputfileOrbit	filename	kinematic positions as observations
inputfileVariational	filename	approximate position and integrated state matrix
ephemerides	ephemerides
parametrizationGravity	parametrizationGravity	gravity field parametrization
parametrizationAcceleration	parametrizationAcceleration	orbit force parameters
integrationDegree	uint	integration of forces by polynomial approximation of degree n
interpolationDegree	uint	orbit interpolation by polynomial approximation of degree n
accelerateComputation	boolean	acceleration of computation by transforming the observations
covariancePod	sequence
sigma	double	apriori factor of covariance function
inputfileSigmasPerArc	filename	apriori different accuaries for each arc (multiplicated with sigma)
inputfileCovarianceFunction	filename	approximate covariances in time
inputfileCovariancePodEpoch	filename	3x3 epoch covariances
sampling	double	[seconds] sampling of the covariance function
inputfileArcList	filename	list to correspond points of time to arc numbers
adjustmentThreshold	double	Adjustment factor threshold: Iteration will be stopped once both SST and POD adjustment factors are under this threshold
iterationCount	uint	(maximum) number of iterations for the estimation of calibration parameter and error PSD

This program is parallelized.