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  • 1.
    Eshagh, Mehdi
    et al.
    University West, Department of Engineering Science, Division of Computer, Electrical and Surveying Engineering. Royal Institute of Technology, Division of Geodesy, Stockholm, Sweden .
    Lars E:, Sjöberg
    Royal Institute of Technology, Division of Geodesy, Stockholm, Sweden .
    The modified best quadratic unbiased non-negative estimator (MBQUNE) of variance components2008In: Studia Geophysica et Geodaetica, ISSN 0039-3169, E-ISSN 1573-1626, Vol. 52, no 3, p. 305-320Article in journal (Refereed)
    Abstract [en]

    Estimated variance components may come out as negative numbers without physical meaning. One way out of this problem is to use non-negative methods. Different approaches have been presented for the solution. Sjöberg presented a method of Best Quadratic Unbiased Non-Negative Estimator (BQUNE) in the Gauss-Helmert model. This estimator does not exist in the general case. Here we present the Modified BQUNE (MBQUNE) obtained by a simple transformation from the misclosures used in the BQUE to residuals. In the Gauss-Markov adjustment model the BQUNE and MBQUNE are identical, and they differ in condition and Gauss-Helmert models only by a simple transformation. If the observations are composed of independent/disjunctive groups the MBQUNE exists in any adjustment model and it carries all the properties of the BQUNE (when it exists). The presented variance component models are tested numerically in some simple examples. It is shown that the MBQUNE works well for disjunctive groups of observations.

  • 2.
    Eshagh, Mehdi
    et al.
    Department of Geodesy, K.N.Toosi University of Technology, Tehran, Iran.
    Romeshkani, Mohsen
    Department of Geodesy, K.N.Toosi University of Technology, Tehran, Iran.
    Quality assessment of terrestrial gravity anomalies from GOCE gradiometric data and Earth's gravity models using variance component estimation2013In: Studia Geophysica et Geodaetica, ISSN 0039-3169, E-ISSN 1573-1626, Vol. 57, no 1, p. 67-83Article in journal (Refereed)
    Abstract [en]

     The satellite gravity gradiometry (SGG) data of the recent European satellite mission, the Gravity field and steady-state Ocean Circulation Explorer (GOCE), can be used as an external source for quality description of terrestrial gravity anomalies and the Earth's gravity models (EGMs). In this study integral estimators are provided and modified in a least-squares sense to regenerate the SGG data of GOCE from terrestrial gravity anomalies and an existing EGM. Based on the differences between the generated and real GOCE SGG data, condition adjustment models are constructed and variance component estimation (VCE) is applied for balancing the a priori errors of data with these differences. Here, a 1-month orbit of GOCE is considered over Iran and the condition adjustment models and VCE process are used to calibrate the errors of the GOCE data, terrestrial gravity anomalies of the area and the EGM. Numerical studies over Iran show that the a priori errors of the GOCE data and the EGM were properly presented. Also the average error of the terrestrial gravity anomalies, with a resolution of 0.5° × 0.5°, after condition adjustment and VCE process using Tzz, Tx, Tyz and −Txx −Tyy is about 30 mGal.

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