# Performance Evaluation of GPS Auto-Surveying Techniques
## 1 Introduction  
The Global Navigation Satellite System (GNSS) has, since its introduction in 1978, revolutionized several industries, such as aviation, transportation and agriculture, with a continued increase in the number of GNSS-enabled devices for the foreseeable future. Most of these devices make use of the positioning capabilities provided by GNSS and show that there is a strong and dynamic market for precise positioning capabilities [1]. A single-frequency GNSS receiver can estimate its position with an accuracy of less than 10 m. To improve these results, high-quality dual-frequency GNSS receivers can attain position solutions with an error below 1 or 2 m [2]. These receivers are usually very expensive, on the order of thousands of euros, although newer low-cost receivers have recently appeared on the market [3]. While these receivers can be enough for many applications, others require an accuracy down to the decimeter or centimeter level [3, 4]. To solve this problem, a GNSS receiver can employ differential methods such as Differential GNSS (DGNSS) and Real-Time Kinematics (RTK), which, for absolute positioning, make use of a static reference receiver, a base station, with a known position. DGNSS positioning, in its more usual form, is based on comparing the pseudorange obtained by the reference station to a given satellite with the expected pseudorange given the same satellite and the previously surveyed reference station position. Given the spatial correlation of the GNSS signals, the pseudorange error of the reference station to a given satellite will be similar to that of another receiver nearby, and as such a correction factor can be obtained and applied to the received pseudoranges of the rover receiver. In RTK, the process is similar, but instead of using only pseudoranges, the positioning is based on the measurement of both the pseudorange and carrier phase of the received signals. A reference station with a known position creates a set of carrierphase measurements that can then be transmitted to a rover receiver, which in turn will create a Double Difference solution and solve the the integer ambiguity problem of the carrier phase observable, allowing for much more precise results than those possible with simply pseudoranges [2]. It should be noted, however, that this only applies to RTK usage for absolute positioning. In the case of relative positioning using RTK, as with attitude estimation, the position estimate of the base station is unnecessary; however, that application is outside of the scope of the present paper. The problem this paper intends to tackle is how to obtain a precise estimate for the position of a base station, a so-called auto-survey, which then can be used to obtain the necessary corrections for a differential positioning system. This problem is part of the \"Survey Phase\" illustrated in Figures 1 and 2 and a critical part of the entire differential positioning system. Current research trends in the GNSS precise static positioning area are focused on the application of Precise Point Positioning (PPP) [5; 6; 7] for the problem of static receiver positioning. If a base station already exists, both RTK [3; 8; 9] and DGPS [10] can also be used for determining the position of a new base station. However, these methods require external communications, usually in the form of internet access or radio links as well as at least one already existing base station, making them unsuitable for remote applications and/or for deployment in developing countries. In an attempt to solve this problem, this paper aims to characterize position estimation methods that require no external connectivity and can be used in low-cost setups, with regards to both the precision and time of convergence of the position solution. While high-end receivers can output not only pseudorange and carrier phases but also Doppler and signal-to-noise ratios, for example, the research presented in this paper was restricted to those observables that are guaranteed to be present in low-end receivers.