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The estimation of the zero-height geopotential level of a local vertical datum (LVD) is a key task towards the connection of isolated physical height frames and their unification into a common vertical reference system. Such an estimate resolves, in principle, the 'ambiguity' of a traditional crust-fixed LVD by linking it with a particular equipotential surface of Earth's gravity field under the presence of an external geopotential model. The aim of this paper is to study the estimation scheme that can be followed for solving the aforementioned problem based on the joint inversion of co-located GPS and leveling heights in conjunction with a fixed Earth gravity field model. Several case studies with real data are also presented that provide, for the first time, precise estimates of the LVD offsets for a number of Hellenic islands across the Aegean and Ionian Sea.

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The aim of this study is to present the results of several 'external' quality tests for the most recent (at the time of writing this paper) global geopotential models (GGMs) using precise GPS and leveled orthometric heights over the area of Greece. The tested GGMs include the GRACE-based combined model GGM03C, the latest EIGEN-type combined models EIGEN-GL04C and EIGEN-GL05C, the ultra-high resolution model EGM08 that was released last year by the US National GeospatialIntelligence Agency, and also the older NASA/NIMA/OSU's EGM96 model. The evaluation tests are based on comparisons of absolute and relative geoid undulations that are computed from the selected GGMs and the external GPS/levelling data. The test network covers the entire part of the Hellenic mainland and it consists of more than 1500 benchmarks which belong to the Hellenic national triangulation network, with direct levelling ties to the Hellenic vertical reference frame. The spatial positions of these benchmarks have been recently re-determined at cm-level accuracy (with respect to ITRF00) through a nation-wide GPS campaign that was organized in the frame of the HEPOS project. Our results show that the EGM08 model offers a remarkable improvement for the agreement among geoidal, ellipsoidal and orthometric heights in the mainland part of Greece, compared to the performance of other combined GGMs over the same area. Finally, our study gives a preliminary (yet realistic) accuracy assessment for GGM/GPS-aided orthometric height determination, over different baseline lengths, throughout the Hellenic mainland.

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SUMMARY The optimal inversion of a linear model under the presence of additive random noise in the input data is a typical problem in many geodetic and geophysical applications. Various methods have been developed and applied for the solution of this problem, ranging from the classic principle of least‐squares (LS) estimation to other more complex inversion techniques such as the Tikhonov–Philips regularization, truncated singular value decomposition, generalized ridge regression, numerical iterative methods (Landweber, conjugate gradient) and others. In this paper, a new type of optimal parameter estimator for the inversion of a linear model is presented. The proposed methodology is based on a linear transformation of the classic LS estimator and it satisfies two basic criteria. First, it provides a solution for the model parameters that is optimally fitted (in an average quadratic sense) to the classic LS parameter solution. Second, it complies with an external user‐dependent constraint that specifies a priori the error covariance (CV) matrix of the estimated model parameters. The formulation of this constrained estimator offers a unified framework for the description of many regularization techniques that are systematically used in geodetic inverse problems, particularly for those methods that correspond to an eigenvalue filtering of the ill‐conditioned normal matrix in the underlying linear model. Our study lies on the fact that it adds an alternative perspective on the statistical properties and the regularization mechanism of many inversion techniques commonly used in geodesy and geophysics, by interpreting them as a family of ‘CV‐adaptive’ parameter estimators that obey a common optimal criterion and differ only on the pre‐selected form of their error CV matrix under a fixed model design.