Varince component estimation in geodetic networks

Sammanfattning: A summary of some of the existing variance component estimators are given, namely the MINQE, the IMINQ, the general case of BQUNE (best Quardratic Unbiased Non negative Estimator), the Helmert estimators, the Förstner estimator and the Kubik estimator. A derivation of a special case of the BQUNE is made. The MINQE is always unbiased, while the others are not necessarily unbiased and the Kubik estimator is always biased. The MINQE and the IMINQE does not require that the observation is block structured while the other does. The MINQE, the IMINQE, and the Helmert estimator can give negative variance components are given for the IMINQE.Some numerical investigations are performed for the application of minor direction distance measured geodetic networks. The first test is a comparison of different variance component models. An estimation with the IMINQE for a three component model with two components for the distance, one for the constant and one for the distance dependent part, showed that there is a strong correlation between the two parts. Therefore, a separation of the two components seems difficult.The effects on the iteration process for some of the estimators and for different apriority values are studied. The start values did hardly effect the number of iterations for the IMINQE and the Helmert estimator. A mean number in the performed networks is about three iterations. Already after one iteration the estimates were closed to the final values. Some differences appeared for the Förstner and the Kubik estimators. The bias for the Kubik estimator is usually large in the studied application and that makes this estimator useless in practice.An estimation of the mean square errors of some of the estimated variance components is carried out. The mean square errors for the MINQU, the IMINQE and the Förstner estimator were of similar magnitude.A parameter estimation of the geodetic networks is done, both with assumed standard and rather arbitrarily chosen weights and with weights from the variance component estimation did not improve the parameter estimation.