## 2 DGPS and FKP
### Network RTK and FKP  
The positioning method based on the carrier-phase measurement is quite difficult because of the process of determining the integer ambiguity [14]. The spatial decorrelation affects the resolution of the integer ambiguity. Hence, many studies have been conducted on the spatial decorrelation and several network-RTK methods have been developed such as the VRS, master-auxiliary concept (MAC), and FKP. The VRS is the most widely used augmentation system worldwide. It provides an accurate, stable, and suitable service for static users. It can be used in all receivers wherein the RTCM message is employed. Moreover, the VRS has better performance than the other methods. However, a bidirectional communication is required because the corrections are transmitted only after receiving the position of the user [15]. Therefore, there is a privacy problem and it is unsuitable for dynamic users who are moving continuously and can go anywhere. In case of a system used in a local area such as precise farming, the correction received from the starting point may be continuously valid [16]. However, the performance deterioration due to the spatial decorrelation is inevitable for the user moving away from the starting point, and the correction from a new VRS point for the current user position should be updated to compensate for the decorrelation error, thereby leading to a VRS hand-over problem. The MAC has been developed to supplement the previously developed VRS and compensate for the drawbacks of the FKP with more accurate and stable positioning compared to the VRS and FKP. The MAC comprises a master RS and several auxiliary RSs. Each auxiliary RS sends its own measurements to the master, and the inter-station difference in the correction is used to estimate the required correction. This correction can be divided into dispersive (ionospheric) and non-dispersive (geometric) corrections for broadcast efficiency, and it can be modified for the low-cost GPS receivers. In addition, this solution can be applied with a one-way communication; thus, a user of a kinematic application can determine the position regardless of any interruption or discontinuity. However, the amount of data is somewhat high, and the method applied by the user is somewhat complicated [15]. The FKP is an \"area-correction parameter\" and it is one of the first methods that was developed to implement a network RTK. The FKP is used to calculate the coefficients of a polynomial surface, which models the correction difference referenced to the master station. These coefficients are horizontal gradients for the dispersive and non-dispersive errors, and are used to evaluate the error polynomial at the desired location. The user interpolates the corrections and applies them with the master station observations or corrections [15; 17]. It helps broadcast coefficients that can express the error plane efficiently in a way described in Figure 2. Thus, it is suitable for broadcasting corrections. Like the MAC, this solution can be applied with a one-way communication; thus, a user of a kinematic application can determine the position regardless of any interruption or discontinuity. Although the decision made by the provider regarding the complexity of the model can influence the performance of the user, and the accuracy of the FKP is less than that of other methods, the amount of data is small; moreover, the method applied by the user is simple [15; 18]. Hence, in this study, we propose a new augmentation method to improve the accuracy of the current DGPS using practical and suitable FKP corrections for all the users described above. The range errors due to the spatial decorrelation in the space between the two RSs can be estimated, as shown in Figure 3. In other words, the FKP RS is used to calculate the distance-dependent range errors in close proximity to itself by comparing the range errors of nearby RSs. Subsequently, it helps convert them into error surfaces and broadcast their first-order linear approximated gradients as FKP corrections.