Estimating variance components of ellipsoidal, orthometric and geoidal


The Best Quadratic Unbiased Estimation (BQUE) of variance components in the Gauss-Helmert model is used to combine adjustment of GPS/levelling and geoid to determine the individual variance components for each of the three height types. Through the research, different reasons for achievement of the negative variance components were discussed and a new modified version of the Best Quadratic Unbiased Non-negative Estimator (MBQUNE) was successfully developed and applied. This estimation could be useful for estimating the absolute accuracy level which can be achieved using the GPS/levelling method. A general MATLAB function is presented for numerical estimation of variance components by using the different parametric models. The modified BQUNE and developed software was successfully applied for estimating the variance components through the sample GPS/levelling network in Iran. In the following research, we used the 75 outlier free and well distributed GPS/levelling data. Three corrective surface models based on the 4, 5 and 7 parameter models were used through the combined adjustment of the GPS/levelling and geoidal heights. Using the 7-parameter model, the standard deviation indexes of the geoidal, geodetic and orthometric heights in Iran were estimated to be about 27, 39 and 35 cm, respectively.