Abstract
To adjust the survey results of multi‐row networks the Gauss–Markov model can be used, including accuracy weight matrix for the values observed, as well as in‐ cluding the apparent observational equations for the coordinates of tie points. To the apparent observational equations the relevant accuracy weights are assigned for the analysed coordinate points or their covariance matrices. Many authors of scientific papers use for that purpose the sequential adjustment of measurement results, i.e. the adjustment carried out in a few stages. By foreign authors, there are the works of Baardy [2], Teunissen [14] and Rao [13]. By domestic authors, there are the pa‐ pers of Adamczewski [1], Baran [3], Gaździcki [7], Kadaj [8], Wiśniewski [15] and Kaminski [9]. Many computer programmes, e.g. GOENET [8], use this procedure to adjust measurement results of the multirow control networks. The issue of the estimation of the horizontal and vertical control point coordi‐ nates in tying to national geodetic control networks is similar to multirow networks adjustment but specific allocation of these networks set down different conditions of tying them to national geodetic control networks. This problem, in relation to determination of point displacement, was worked on in Canada by Chrzanowski [4] and in Germany by Pelzer [10]. Similar deliberations were made nationally by Cza‐ ja [6] and Proszynski and Kwaśniak [12]. The deliberations included in this pub‐ lication will only be referred to three thematically nearest positions, i.e. Czaja [5], Proszynski [11] and Wiśniewski [16]. In paper [5] the author proposes to include the observations of connecting national geodetic control network points to the adjuste‐ ment of horizontal and vertical control network. For the coordinates of national ge‐ odetic control points the author proposes to juxtapose the pseudo‐observation equa‐ tions including their ccovariance matrices. Proszynski [11] in his paper presents the method of tying the horizontal and vertical control networks to the national geodetic
Highlights
To adjust the survey results of multi‐row networks the Gauss–Markov model can be used, including accuracy weight matrix for the values observed, as well as in‐ cluding the apparent observational equations for the coordinates of tie points
In which n states for the number of observed geodetic elements in the tie construc‐ tion, and k is a number of estimated coordinates of horizontal and vertical control network points, which are included in the tie construction
Tional geodetic control networks the following estimates determined from model (2) will be used: covariance matrix cov(X 2 ) for the coordinates of horizontal and vertical control points established according to the formula (17), and variance coefficient σ 02 for the values observed in the tie construction specified with relation (19)
Summary
To adjust the survey results of multi‐row networks the Gauss–Markov model can be used, including accuracy weight matrix for the values observed, as well as in‐ cluding the apparent observational equations for the coordinates of tie points. The adjustment of measurement results in tie construction leads to determina‐ tion of coordinate estimates of the selected horizontal and vertical control points and the national geodetic control points as well as their covariance matrices. To formulate the accuracy criteria for tying horizontal and vertical control net‐ work it is necessary, for tie construction, to introduce separate formulas for estima‐ tion of point coordinates and their covariance matrices of the horizontal and verti‐ cal control network and the national geodetic control network The introduction of these formulas is done by way of solving the system of four matrix equations, which result from the reciprocal of properly defined block matrix. Value of the standard deviation is deter‐ mined on the basis of the variance coefficient obtained from the estimation of points coordinates in tie construction and the variance included in the weight matrix for Accuracy Standards of Tying the Horizontal and Vertical Control Network. In which n states for the number of observed geodetic elements in the tie construc‐ tion, and k is a number of estimated coordinates of horizontal and vertical control network points, which are included in the tie construction
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