# An Algorithm to Assist the Robust Filter for Tightly Coupled RTK/INS Navigation System
## 1 Introduction  
Global Navigation Satellite Systems (GNSS) have developed rapidly in recent decades. The introduction of new satellites, new signals, and multiple positioning algorithms is constantly driving the development of precise navigation [1; 2]. The Real-Time Kinematic (RTK) technique is a representative positioning solution that is widely used to meet the requirement for high positioning precision [3]. RTK utilizes a reference station to obtain the Double-Differenced (DD) GNSS measurements, which significantly mitigate common errors between the reference station and the movable receiver [4]. Furthermore, RTK uses both the pseudo-range and carrier phase measurements to provide centimeter-level precision [5]. The carrier phase is much more precise than the pseudo range. However, the carrier phases are ambiguous by an unknown integer number of wavelengths, as the phase tracking loop can only match the phase of the local and received signals within one cycle [6]. As a result, the Ambiguity Resolution (AR) procedure plays an important role in RTK. Only when the ambiguities in the phase are accurately resolved can RTK provide centimeter-level precision [7]. Dual-frequency RTK and triple-frequency RTK benefit from the combination of different signals. The wide-lane and extra-wide lane combinations with longer wavelengths make AR more efficient [8]. Studies have proven that dual-frequency short-baseline RTK can finish fast AR while triple-frequency signals significantly contribute to the long-baseline RTK [9; 10]. In contrast, it is difficult for single-frequencyRTK to achieve a high correct ambiguity fixed rate, especially in dynamic conditions, which means its performance is restricted, as the wavelength of a single signal is not long enough [11; 12]. Notably, the expansion of GNSS constellations brings more visible satellites and better spatial geometric distribution, which greatly improves the performance of single-frequency RTK and other GNSS positioning algorithms. The main GNSS systems include the Global Positioning System (GPS), the China-developed Beidou Navigation Satellite System (BDS), the European Galileo system, the Russian GLObal Navigation Satellite System (GLONASS), and the Japanese Quasi-Zenith Satellite System (QZSS) [13]. Many studies have proven the benefit generated by the multi constellations on the performance of RTK, including GPS/BDS [14], GPS/Galileo [15], GPS/Galileo/BDS/QZSS [16], and GPS/BDS/GLONASS [12]. We implement our code to process single-frequency GPS/BDS measurements in our work. The GPS signal is L1 C/A at 1575.42 MHz whereas the BDS signal is BII at 1561.098 MHz. It is stringent for the receiver to simultaneously track dual frequency or triple frequency, which leads to the high cost of the geodetic-grade multifrequency receivers. In comparison, single-frequency consumer-grade receivers offer a more comprehensive range of applications. Receivers used in urban areas are often confronted with GNSS-hostile or even GNSS-denied environments. The surrounding buildings, bridges, trees, and tunnels can reflect and block the GNSS signals, causing multiple errors like the multipath effect on the measurements and obstructing GNSS receivers' ability to maintain signal tracking [17]. The errors in the measurements can degenerate the positioning accuracy. RTK or other GNSS methods cannot provide positioning results when the number of satellites is insufficient. Other sensors should be introduced to overcome the issues to provide continuous and accurate positioning results in harsh urban environments. The Inertial Navigation System (INS) is a common auxiliary solution [18]. INS is based on an Inertial Measurement Unit (IMU) consisting of gyroscopes and accelerometers. INS is a self-contained system to track the position, velocity, and attitude of an object, which means INS is immune to environmental disturbances [19]. However, INS can only output a relative solution from a starting point that must be provided by other absolute positioning systems, such as GNSS.