## 1 Introduction  
Since the development of a centimeter-level accuracy positioning techniques in real-time, based on the integer ambiguity resolution of the Global Navigation Satellite System (GNSS) measurements, there have been great advances in real-time kinematic (RTK) applications. Under the conventional RTK, raw measurements for the reference station are transmitted to the rover for the integer ambiguity resolution and final coordinate estimation [1]. Therefore, most common errors can be cancelled out by differential techniques. However, single-base RTK baseline length should not exceed 20 km in practice [2] due to distance-dependent biases, such as ionospheric and tropospheric delays. New approaches, such as Virtual Reference Stations (VRS), Flachen Korrektur Parameter (FKP), and/or Master-Auxiliary corrections (MAX) were introduced in mid-1990s. These new approaches are known as network RTK (NRTK or RTN), and were successfully used for more than a decade in many applications, especially navigation and surveying. The aim of RTN is to minimize the influence of the distance-dependent errors from a network of permanent GNSS receivers [3] on estimated coordinates at the rover. Precise models of the error sources derived from the whole reference network are interpolated at the rover's position [4]. The typical RTN procedure consists of (1) network ambiguity resolution at the master control, based on the known coordinates of the reference stations; (2) estimation of distance-dependent correction model coefficients; and (3) transmission of the coefficients to the user (or rover). Real-time modeling of a reference network and reliable instantaneous ambiguity resolution are required in a short period of time [5; 6; 7; 8]. Due to the different temporal variations of the dispersive and non-dispersive errors, the update rate of the coefficients should be adequately selected (for example, every 10 s for ionospheric delay and 60 s for orbit and tropospheric errors). Several interpolation methods, such as linear interpolation and least-squares collocation (LSC), have been analyzed in detail [3; 9]. All methods can significantly reduce the distance-dependent biases in the measurements with a similar performance or comparable accuracy levels. The state-space modeling to better represent the error characteristics (or physical error sources) was suggested by [10], where all error components can be consistently modeled with high accuracy. The performance analysis, including quality assurance, of RTN was evaluated by many researchers, mostly focusing on the accuracy of the interpolated corrections, positioning accuracy, and initialization time required for precise positioning [11]. Most RTN methods currently used in the industry, such as VRS, FKP, and MAX, provide comparable performance in terms of accuracy and precision of the final solution [3; 12], while some differences exist with regards to the processing load, the application of the interpolation algorithm, and the bandwidth of the correction information [13]. It is worthy of notice that the addition of GLONASS observables does not necessarily mean a significant improvement in the RTN results [14]. It is also known that the Radio Technical Commission for Maritime Services(RTCM) version (2 or 3) and/or new proprietary format for the transmission of the corrections have no immediate relationship with the accuracy of the real-time solutions [9; 15]. National Geodetic Survey (NGS) guidelines for establishing GNSS-derived ellipsoidal (NGS-58) and orthometric (NGS-59) heights were published in 1997 and 2008, respectively [16; 17]. Since then, there have been tremendous advancements in GNSS, particularly in receiver/antenna technology, as well as data processing algorithms and software. In addition, GNSS modernization, including new signals, is underway, and new constellations of GNSS with better satellite orbits are also available.