# RTK with the Assistance of an IMU-Based Pedestrian Navigation Algorithm for Smartphones
## 1 Introduction  
Over the past two decades, GNSS has been evolving rapidly [1]. The U.S. government has promoted the Global Positioning System (GPS) modernization program, adding the second civil signal on L2 frequency (L2C) and the third civilian signal on L5 frequency (L5). As of 24 April 2019, there were a total of 31 operational satellites in the GPS constellation, not including the decommissioned, on-orbit spares [2]. Europe is developing the Galileo system to provide global services. Up to 12 February 2019, there were a total of 22 satellites in operation [3]. Galileo navigation signals are transmitted in the following four frequency bands: E1, E5a, E5b, and E6 bands. The frequency of E1 is equal to that of L1 of GPS (1575.42 MHz), while the frequency of E5a is equal to that of L5 of GPS (1176.45 MHz) [4]. RTK was first proposed as a differential positioning technology that processes both the pseudorange and carrier phase measurements of GPS to provide cm-level accuracy in real time [5]. RTK involves at least one stationary receiver and at least one movable receiver. The stationary receiver, which is called the base station, plays the role of the reference to calculate the position of the movable receiver, which is called the rover [6]. Solving the ambiguity of the carrier phase is one of the most important procedures of RTK. The revolution of GNSS improves the performance of RTK thanks to the increasing number of visible satellites and civilian signals. Utilizing other constellations in addition to GPS improves spatial distribution and reduces problems caused by obstructions, which improves the accuracy and availability of RTK, as shown for GPS/Galileo [7],GPS/GLONASS [8], GPS/BDS [9], and GPS/BDS/Galileo/QZSS [10]. RTK also benefits from the dual frequency, as the accuracy and ambiguity resolution performance are improved [11; 12]. Compared with geodetic-grade dual-frequency and multi-frequency receivers, consumer-grade receivers are more widely used due to their low costs. However, low-cost commercial receivers often use inexpensive hardware, especially antennas with poor performance, which leads to the lower carrier-to-noise ratio (CNR), worse resistance to multipath, and poorer ambiguity resolution performance [13]. However, smartphones are often equipped with low-cost receivers. The antennas on smartphones are often linearly polarized (LP) [14], while circular polarization (CP) is generally adopted in satellites to avoid Faraday rotation problems [15]. As a result, the smartphone's antenna has a loss in the power of signals received, which leads to lower CNR. Before 2016, Raw GNSS measurements collected by a smartphone were not available to users. Most users only had access to the position computed by the GNSS chipsets. A software-defined receiver called GRIDwas adopted to generate measurements from signals collected by smartphone antennas. The test showed that poor multipath suppression of these antennas did harm to the integer ambiguity resolution [16]. Conditions had changed as Google introduced the Android 7.0 operating system in 2016, indicating that users could get raw GNSS measurements including pseudorange, Doppler, and carrier phase through some APIs. Raw measurements collected by a Samsung Galaxy S7 with the BCM4774 GNSS chipset were analyzed in November 2016. Results confirmed that the quality of carrier-phase measurements could potentially allow for a centimeter-level positioning. However, not only the poor quality of the antenna, but also the duty cycling prevent smartphones from being used as practical RTK units [17]. Duty cycling is a technique to prolong battery life. The duty cycling switches on the navigation chip for a fixed period before switching it off. This fixed period is called the burst period. The burst period can last for 200 milliseconds in one second. What happens in the remaining 800 milliseconds is not known [18; 19]. The duty cycling prevents the smartphone from tracking the carrier phase continuously.