# Adjustment Algorithm for Free Station Control Network of Ultra-Large Deepwater Jacket
## 1 Introduction  
A jacket platform is one of the main engineering facilities for offshore oil development [1], and the accuracy of its construction will directly affect the safety of operators and the economic benefits of the whole project. Due to the numerous components of the conductor frame and its complex spatial structure, the construction site observation conditions are exceptionally complicated, posing significant challenges in terms of precise measurement [2]. The line of sight between the control points will be blocked during construction (as shown in Figure 1), so it is necessary to lay a high-precision free station control network around the assembly site. However, as the jacket is assembled, its great weight will gradually deform the surrounding ground surface, and each control point may be affected to different degrees, resulting in non-uniform changes to the whole network [3]. The control network is the datum for subsequent construction, so judging the stability ofthe control network [4] and analyzing the deformation of each control point become the primary problems of data processing. Selecting two or more control points to be constrained in adjustment is usually necessary [5], and this is called parameter adjustment with redundant known equations. Still, if the constrained points have undergone a large deformation, this forcible constraint will cause whole-network scale change and azimuthal distortion. The classical free network adjustment only constrains the necessary starting data, such as a point's coordinates and a side's azimuth. However, the problem of how to select reliable starting data remains. The rank loss of free network adjustment [6] (also known as the rank-deficient problem of least squares adjustment models [7]) considers all points as deformation points. It solves the rank loss problem by attaching the center-of-gravity data of all points as constraints, which is a feature that makes it widely used in the deformation monitoring of high-speed rail [8], embankment dams [9], and subways [10], and so forth. However, station location is also a pending parameter in a free station control network, which is inconsistent in each phase. Therefore, the assumption that the center-of-gravity datum remains unchanged is no longer tenable. In addition, if some relatively stable control points exist, disregarding such information will affect the accuracy of the deformation amount sought [11]. Quasi-stable free network adjustment (hereinafter referred to as \"quasi-stable adjustment\") divides the control points into two categories, stable points and unstable points [12], and fits unknowns by attaching the center-of-gravity data of all stable points; that is, minimizing the sum of squares of parameter corrections and observation residuals [13]. Theory and practice have proved the necessity and superiority of the quasi-stable adjustment in the monitoring network [14]. However, selecting the stable points that meet reality is still a challenging problem [15]. A weighted quasi-stable adjustment method is proposed that uses posterior variance to determine the weight of the datum [16]. This method requires high-order control points, but jacket control networks often only have a primary control network. In engineering practice, the commonly used methods for stability analysis include the t-test method [17], the average gap method [18], the block gap method [19], the weighted iteration method [20], the distance and azimuthal difference method [21], the supervised clustering method [22], etc. However, most of these methods involve complicated calculation steps and mathematical statistics, which are not easy to use in engineering practice; in addition, in the free station control network [23], there is usually no direct observation between the control points, and the location of the stations varies from phase to phase,  
Figure 1: Typical scenarios for complicated line-of-sight conditions during the construction of a jacket. (**a**) The inside of the jacket, (**b**) the outside of the jacket.