## 1 Introduction
The most mature indoor pseudolite system is produced by LOCATA [8]. ProprietaryTimeLoc technology is utilized for tight time synchronization, allowing the clock difference in the carrier phase measurement equation to be ignored. The horizontal error of the non-differential positioning is less than 6 cm, and the precision of the altitude direction is about 15 cm [9]. The frequency stability and accuracy of the PL clock are much inferior to the GPS, and PL clock errors are difficult to obtain accurately [2]. Although LOCATA can ensure PL clock synchronization, many pseudolite systems lack this costly technology at present. Reference [10] achieved centimeter-level PPP (Precise point positioning) results with a new prototype pseudolitesystem without relying on accurate time synchronization. It is believed that PL would be more extensively applicable for integration with GNSS and INS (Inertial Navigation System). Reference [11] proposed a new concept of pseudolite-based navigation to overcome the receiver modification problem of systems. However, only meter-level positioning precision could be achieved in poor geometry tests. References [10; 11] did not consider quality control under severe conditions as well. In reference [12], [PERSON] et al. built a new pseudolite-based indoor positioning system and the clock could be synchronized with each other. Nevertheless, only simulated data wereused to obtain high-precision positioning results. References [13; 14] believed that the convergence precision of initial coordinate values was important for positioning, but how to ensure centimeter-level positioning precision has not been considered with bad initial coordinate value. Reference [15] used carrier interferometry to conduct analyses on indoor pseudolite positioning. However, this method has great limitations in applications. Reference [16] proposed a new method for indoor pseudolite positioning based on AFM and DD pseudorange observations with good data. However, it is generally known that data quality has a great influence on the AFM. Current high-precision PL positioning algorithms mainly are applied based on carrier phase observations. However, the indoor environment is more severe than outdoors. Whether the carrier phase observations or the positioning results are reliable remains to be discussed. To the authors' knowledge, there are few methods to guarantee the reliability of the results for indoor pseudolite positioning and no effective strategy to ensure the positioning accuracy when fault happens. Therefore, the application of receiver autonomous integrity monitoring (RAIM) for pseudolite system is of great significance in practical positioning. There are two types of RAIM algorithm, snapshot RAIM, and sequential RAIM. The snapshot RAIM includes the parity vector method, the least-square residual method [17; 18; 19], weighted RAIM algorithm, etc. Sequential RAIM is almost based on the Kalman filter which is an indispensable component of many navigation systems [20]. In view of the above, the carrier phase-based RAIM (CRAIM) algorithm [21] proposed by [PERSON] applied tothe high-precision positioning of the indoor pseudolite system. Reference [22] proposed an INS-assisted RAIM algorithm to increase the level of reliability and integrity for an integrated navigation system. Reference [23] explored the application of the snapshot RAIM method for GNSS vessel receivers when space segment geometry was poor. However, the proposed algorithm did not discuss how to determine the protection level with a given probability of missed detection (MD) and false alarm (FA). Reference [24] showed a correlation between traditional Shapiro-Wilk test statistics when multiple faults occur. The paper proposed a criterion to overcome the correlation based on the reliability principle and designed a multi-fault processing method based on an extended Shapiro-Wilk test. [PERSON] et al. proposed a complete algorithm to ensure reliability in attitude measurement [25].