## 2 Materials and Methods
### Experimental Works
#### 2.4.2 Sequential Online Adjustments of Total Station Positions  
At the first total station position over the point 1 (see Figures 2 and 3), the observational-mixed model is given by the equation  
\[\varepsilon\text{=X}\beta\ -\mathbf{y} \tag{41}\]\[\left[ \begin{array}{c}\varepsilon_{\mathbf{TS1}}\\ \varepsilon_{\mathbf{TS2}}\\ \varepsilon_{\mathbf{TS3}}\\ \varepsilon_{\mathbf{TS4}}\\ \varepsilon_{\mathbf{TS5}}\\ \varepsilon_{\mathbf{GPS1}}\\ \varepsilon_{\mathbf{GPS2}}\\ \varepsilon_{\mathbf{GPS3}}\\ \varepsilon_{\mathbf{GPS4}}\\ \varepsilon_{\mathbf{EGM1}}\end{array} \right]=\mathbf{X}\left[ \begin{array} []{c}\mathbf{d}_{1}\\ \mathbf{d}_{2}\\ \mathbf{d}_{3}\\ \mathbf{d}_{4}\\ \mathbf{d}_{\mathbf{A}}\\ \mathbf{d}_{\mathbf{B}}\end{array} \right]-\mathbf{y} \tag{42}\]  
where  
* \(\beta=\left[ \begin{array}{cccccc}\mathbf{d}_{1}^{T}&\mathbf{d}_{2}^{T}& \mathbf{d}_{3}^{T}&\mathbf{d}_{4}^{T}&\mathbf{d}_{\mathbf{A}}^{T}&\mathbf{d}_ {\mathbf{B}}^{T}&|&d_{5}&d_{\eta_{1}}&d\Sigma_{1}\end{array} \right]^{T}\) is the vector of corrections to the approximate geocentric coordinates \(X,Y,Z\) of the points 1, 2, 3, 4, A, B (e.g., \(\mathbf{d}_{1}^{T}=\left[ \begin{array}{cc}dX_{1}&dY_{1}&dZ_{1}\end{array} \right]\)) and corrections \(d\xi_{1},d\eta_{1},d\Sigma_{1}\) to the approximate orientation angles of the total station \(\xi_{1},\eta_{1},\ \Sigma_{1}\),
* \(\varepsilon=\left[ \begin{array}{cccccc}\varepsilon_{TS1}^{T}&\varepsilon_{ TS2}^{T}&\varepsilon_{TS3}^{T}&\varepsilon_{TS4}^{T}&\varepsilon_{TS5}^{T}&|& \varepsilon_{GPS1}^{T}&\varepsilon_{GPS2}^{T}&\varepsilon_{GPS3}^{T}& \varepsilon_{GPS4}^{T}&|&\varepsilon_{EGM1}^{T}\end{array} \right]^{T}\) is the vector of total station measurement random errors \(\varepsilon_{x},\varepsilon_{y},\ \varepsilon_{z}\) of the \(x,y,z\) coordinates of the points 2, 3, 4, B, A, respectively (e.g., \(\varepsilon_{TS1}^{T}=\left[ \begin{array}{cc}\varepsilon_{x_{1}}&\varepsilon_ {y_{1}}&\varepsilon_{z_{1}}\end{array} \right]\)); the GNSS measurements' random errors \(\varepsilon_{X},\varepsilon_{Y},\ \varepsilon_{Z}\) of the \(X,Y,Z\) coordinates of the points 1, 2, 3, 4, respectively (e.g., \(\varepsilon_{GPS1}^{T}=\left[ \begin{array}{cc}\varepsilon_{X_{1}}&\varepsilon _{Y_{1}}&\varepsilon_{Z_{1}}\end{array} \right]\)); and the random errors \(\varepsilon_{\hat{\varepsilon}},\varepsilon_{\hat{\eta}}\) of the deflection of the vertical components \(\xi_{1},\eta_{1}\) at the first total station position (at point 1): \(\varepsilon_{EGM1}^{T}=\left[ \begin{array}{cc}\varepsilon_{\xi_{1}}& \varepsilon_{\eta_{1}}\end{array} \right]\). * **X, y** is the known design matrix and free terms' vector. The solution \(\hat{\mathbf{\theta}}\), \(\Sigma_{\hat{\beta}}\) of the observational model \(\varepsilon=\mathbf{X}\beta-\mathbf{y}\) is given by Equations (33)-(40). In the next total station standpoint 2 (see Figures 2 and 4), the observational-mixed model \(\varepsilon=\mathbf{X}\beta+\mathbf{U}\mathbf{y}-\mathbf{y}\) is given by  
Figure 3: Surveying geometry at the total station position 1. The numbered points marked TS relate to total station surveys; GPS are measured using GNSS (GPS) technology, whereas EGM stands for the Earth Gravitational Model. \[\left[ \begin{array}{c}\varepsilon_{\mathbf{TS}6}\\ \varepsilon_{\mathbf{TS}7}\\ \varepsilon_{\mathbf{TS}8}\\ \varepsilon_{\mathbf{TS}9}\\ \varepsilon_{\mathbf{TS}10}\\ \varepsilon_{\mathbf{TS}11}\\ \varepsilon_{\mathbf{TS}12}\\ \varepsilon_{\mathbf{TS}13}\\ \varepsilon_{\mathbf{G}\mathbf{P}55}\\ \varepsilon_{\mathbf{G}\mathbf{P}56}\\ \varepsilon_{\mathbf{G}\mathbf{P}57}\\ \varepsilon_{\mathbf{G}\mathbf{P}57}\\ \varepsilon_{\mathbf{E}\mathbf{G}\mathbf{G}\mathbf{Z}}\end{array} \right]= \mathbf{X}\left[ \begin{array}{c}\mathbf{d}_{5}\\ \mathbf{d}_{6}\\ \mathbf{d}_{7}\\ \mathbf{d}_{\mathbf{C}}\\ \mathbf{d}_{\mathbf{D}}\\ \mathbf{d}_{\mathbf{A}}\\ \mathbf{d}_{\mathbf{B}}\end{array} \right]+\mathbf{U}\left[