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The article describes selected case studies of the trilateration network design. The analyzed case studies may be of interest to the geodetic community but may also be potentially interesti...

Optimization of a geodetic network is a process in which a specific stage (or stages) is designed in such a way that the obtained result meets the assumed (optimum) design requirements. The...

The design of surveying networks inside tunnels is of crucial importance because an optimal design enables the network to fulfill its required quality parameters, for instance, precision an...

The article presents an original approach to the design of geodetic networks, taking into account quality criteria. This approach is based on the geodetic network design using the methods o...

In this paper, the use of the parameter estimation method in a split functional model in the analysis of geodetic network deformation is presented. Special attention is drawn to the situati...

This paper presents an estimation method allowing direct and robust outlier assessment of parameter shifts in functional models of geodetic observations. The systems adopted in the discussion refer to functional models used in geodetic network deformation analysis. The proposed method is a robustness-oriented development of Shift-Msplit estimation. The problem of robustness is solved using an additional random variable with realizations that are outliers. The paper shows that the application of this variable also facilitates the selection of the appropriate number of competitive models in Msplit(q) estimation. Two numerical examples explain the manner of Shift-Msplit∗ estimation performance and indicate the basic properties of the determined estimates.

In the computation of a geodetic network, it is well known that the least-squares adjustment may not be the ideal solution when gross errors appear. In general there are two fundamental approaches to determining gross errors: the application of the detection tests (Baarda’s data snooping, Pope’s τ test, etc.) over the least-squares solution, and the use of robust estimation methods. It has been shown that in the case of more than one gross error, these detection tests become inefficient. Moreover, even for the case of single error detection, these tests may be questionable. Hence, data snooping relies on a good a priori precision estimation, and, regarding Pope’s τ test, it is the purpose of this paper to analyze the limitations in its use with correlated observations, even for a single gross error detection. Conclusions will be drawn by means of a generalization of a result mentioned in Pope’s work (originally restricted to the case of uncorrelated data) and then applied in an example.

The main design criteria in a geodetic network are precision, reliability and strength, and economy. The proper design of geodetic networks is an integral part of the geodesist's task. The main goal of this paper is to suggest a strategy for designing a geodetic network to meet high reliability and geometrical strength criteria. In this context, a real 2D deformation monitoring scheme has been selected to evaluate its design criteria. The results indicate that the perimeter of a geodetic network is relatively weaker than the middle. This means that the perimeter observations are usually weaker than those in the middle, the maximum distortions are usually located on the edge netpoints, and the maximum robustness parameters belong to the perimeter of the network. A strategy has been recommended to counter this problem. The results also showed that the robustness parameters in rotation, shear, and scale are affected by redundancy numbers. Actually, the largest robustness parameters are due to the weak observ...

The vertical motions of 11 control points in the Northern part of Israel (Haifa North‐East) are studied seasonally for a period of one full year (October 1988 to September 1989). The purpose of this paper is to compare the mathematical equivalence between various leveling‐adjustment techniques, namely, the classical minimum variance estimate, free net method, and the least‐squares collocation method, by using, as an example, a number of leveling loops in Northern Israel. A comparison of results showed that there were no significant differences between the free net and the least‐squares collocation methods (LSC). The elevation differences between the bench marks for the free net and condition equations method were the same, but the estimated heights were different. Even though the LSC technique is much more complicated and time consuming, it confirms the stability of points on the bedrock and the vertical movement of points on the high‐tension poles. It is, therefore, convenient to use either the free net ...

In 1987 the Orange County Surveyor initiated the conversion of its horizontal control system to the North American Datum of 1983 (NAD 83). The decision to make the transition was precipitated by the need to establish a stable geodetic network for major federal, state, and county engineering projects currently impacting transportation, flood control, and land development in Orange County. A comprehensive geodetic survey was completed using 21 primary control stations. Upon the completion of field procedures, nine control stations were held fixed, and the network was adjusted using a three‐dimensional least‐square program. Global positioning survey (GPS) technology (satellite surveying) was used to complete the geodetic network. No county general funding was used to support the conversion. The county's successful transition to NAD 83 has established a geodetic network available for county wide mapping, providing accessible control for present and future development projects, and ensuring survey monument pre...

The mathematical model of the adjustment of a geodetic network is generally supplemented by restrictions concerning the unknown parameters. This can occur with datum problems or by constraints resulting from the formulation of the problem. A method is presented that, at a large number of restrictions, works more economically than the commonly used way of adding the restrictions to the normal equations. This is demonstrated by an example from engineering surveying. Thus, the required CPU time and size of memory for making up and inverting the matrix of normal equations is reduced

Statistically rigorous densification of horizontal geodetic networks must consist of a simultaneous adjustment of both the densification and the densified networks. Equivalently, the effect of the already adjusted (existing) network to be densified may be rigorously propagated into the densification network, through an appropriately derived weight matrix of the common station positions. The nonrigorous schemes utilize information available on the existing network in a statistically nonrigorous way. In this paper, two main statistically nonrigorous schemes used in practice are recognized. Their results, both mathematical and numerical, are compared to results obtained rigorously. A way to convert the nonrigorous results into rigorous ones practically and economically is also shown.

Inertial Surveying Systems are a very recent advance in surveying technology; they are the single most comprehensive geodetic positioning tool available today. Their historical development is brief...

Small space trilateration nets in which distances are measured between points can be likened to structural space frameworks in which elastic members are manufactured and joined together by pins. Accordingly, structural programs used for structural analysis can be used to adjust trilateration nets. Program STRUDL is used to illustrate the procedure. The preparation of data as input is discussed in detail. The output directly yields the distance corrections and the variation of coordinates of the new points. Two numerical examples are given.