## 9. The adjustmentThe set of coefficients that define the model were found through least squares adjustment (Arley 1950, Bevington 1968). Each of the data points provides us with two equations of condition; namely, the and components of the spherical vector equation (15). The design matrix can be constructed straightforwardly, although its huge size (Mb for and simple precision) made necessary a careful programming of the least squares routine. The existence of large systematic errors in the SAO catalogue for
polar stars suggested the introduction of a weighting scheme. For each
difference in each observation
and the weight factors were introduced as: where the normalization factor is: To simplify the construction of the weighted normal equations, each of the conditional equations was multiplied by the square root of the effective weight (19). Another important parameter to adjust is the maximum degree of the Fourier series . This was done by a simple examination of the RMS of the adjustment: which is related to the statistic through the equation: and to the Birge ratio used in the least squares process as a scale factor of the uncertainties (Cohen & Taylor 1987). For each of the groups of stars, several least squares adjustments were carried out varying the degree of the Fourier series from 1 to 20. It is found that the RMS stabilizes around mas for in the case of positional parameters. On the other hand, was enough to find stable values of the proper motion parameters. As a final process, outliers were eliminated using the
© European Southern Observatory (ESO) 2000 Online publication: July 13, 2000 |