# Modeling DGNSS Pseudo-Range Correction Messages by Utilizing Satellite Repeat Time
## 1 Introduction  
Global Navigation Satellite System (GNSS) users can select an optimal data processing technique according to the required positioning accuracy, data processing time, etc. Among many techniques, the Differential GNSS (DGNSS) technique using pseudo-range correction (PRC) has been widely used in a number of fields because it can improve positioning accuracy in real time using a low-cost receiver. Recently, DGNSS positioning algorithms are considered as a critical component of sensor fusion for autonomous vehicle navigation [1; 2; 3]. To improve positioning accuracies, quite many studies of coupled GNSS and multi-sensors integration [3; 4] and reduction of the multipath error [1; 5] have been published. GLONASS, BeiDou, and Galileo signals in addition to GPS are used in multi-GNSS positioning to improve accuracy, reliability, and availability of DGNSS positioning [6; 7; 8]. DGNSS is a code-based relative positioning technique that employs two or more receivers simultaneously tracking the same satellites. PRC values are generated at a reference station whose precise coordinates are known beforehand, and then transmitted in real time to the user's receiver through a choice of transmission media. Positioning accuracy ranges from less than a meter up to a couple of meters, depending on the performance of the receiver, the baseline length between the base and rover sites, and the transmission rate for PRC [9; 10]. Thus, DGNSS has been widely used in various fields, such as car navigation and location-based services as well as surveying, aviation, logistics, etc. It basically assumes that GNSS errors at the base station and the rover are highly correlated. However, range corrections to the satellite can be spatially de-correlated with separation of the user from the reference station, and temporally de-correlated with the latency of PRC [11; 12]. The PRC information created at the reference station is provided via communications links, such as a radio beacon, Networked Transport of RTCM via Internet Protocol (NTRIP), Digital MultimediaBroadcasting (DMB), Radio Data System (RDS), FM Data Radio Channel (DARC), etc. DGNSS users obtain higher accuracy using PRC data continuously received through the transmission media. However, positioning accuracy can be significantly degraded if PRC data cannot be transmitted due to radio interference or loss of correction signals. The expected accuracy with DGNSS is typically 1-3 m, whereas it can degrade to as much as 10 m without PRC [13; 14; 15]. In this regard, continuous reception of PRC is essential to acquiring the expected DGNSS performance. A number of studies have been conducted to model and generate PRC values, even in situations where corrections cannot be received. Two of the most notable schemes are based on neural networks and the Kalman filter. Neural networks can predict future data using an optimized modeling system by repeated training based on past values. Therefore, this system needs time for training in order to have an effective prediction time. Case studies using an autoregressive moving average [16; 17] and recurrent neural networks [18; 19] showed that the predicted PRC had a range error of about 1.0 m. The Kalman filter is a method to recursively update estimates of the system parameters by processing successive measurements. It uses a series of measurements observed over time, and produces estimates of unknown variables. [PERSON] [18] used the Kalman filter method in Differential Global Positioning System (DGPS), and showed that RMS errors of predicted values were less than 0.4 m.  
Even though a neural network algorithm and a Kalman filter showed a prediction error of less than \(\sim\)1.0 m, those two methods require PRC observations collected right before modelling starts, and thus work only for a relatively short period of time after data loss. For this reason, we devised an algorithm with which one can obtain PRC estimates at any desired epoch through a simple mathematical formula.