The use of consider covariance analysis in choosing data weights to reduce the effect of errors in model parameters on satellite orbit determination accuracy
Abstract
Choosing data weights to reduce the effect of errors in model parameters on satellite orbit determination accuracy is studied. The effect of these errors is evaluated using consider covariance analysis. A derivation of consider covariance analysis is given. In consider covariance analysis, errors are modeled as random variables. Three weighted least squares (WLS) filters are investigated. The first filter uses a scalar weight for each batch of data. Values of the weights are found that reduce the trace of the consider covariance, tr(P(sub c)). This filter is the Reduced Consider Covariance (RCC) filter. The weights are determined in a numerical minimization. The RCC filter is able to minimize tr(P(sub c)) with respect to the scalar data weights at the batch epoch. When the accuracy of the mapped estimate is examined, it is found that, for some cases, the RCC filter is among the poorest performers. In general, the RCC filter is not useful for mapping problems because it is not possible to predict how suitable a weight is for a mapping interval based on epoch results. The next filter investigated is the SRCC filter. This filter is similar to the RCC filter, except that each scalar data point is assigned a scalar weight. The data are processed one scalar data point at a time, and the weights are solved for analytically. The SRCC filter is found to be unpredictable and unreliable. The final filter investigated is the minimum consider covariance (MCC) filter. The MCC filter uses a weight matrix that is a full matrix in order to obtain the absolute minimum tr(P(sub c)) at epoch. <In mapping, the MCC filter performs poorly. &This is due to the MCC filter being equivalent to estimating the consider parameters. The MCC filter should not be used to obtain mapped estimates. The MCC filter could be used in nonmapping problems. *However, this would be equivalent to estimating all of the consider parameters. There could be two unwanted effects. First, the covariance could be optimistic. Second, information that should go to the estimate could be absorbed by the estimation of the consider parameters.
 Publication:

Ph.D. Thesis
 Pub Date:
 August 1991
 Bibcode:
 1991PhDT........37P
 Keywords:

 Covariance;
 Errors;
 Orbit Calculation;
 Parameter Identification;
 Random Variables;
 Satellite Orbits;
 Least Squares Method;
 Mathematical Models;
 Optimization;
 Scalars;
 Astrodynamics