# Fault-Free Protection Level Equation for CLAS PPP-RTK and Experimental Evaluations
###### Abstract
Unfortunately, the protection level equations of GBAS or SBAS cannot be directly applied to the CLAS PPP-RTK position solutions, because GBAS or SBAS do not use the carrier phase as ranging sources. Previous studies have proposed protection-level equations for PPP and RTK that use the carrier phase as ranging sources [14; 15; 16; 17; 18; 19]. These studies were based on receiver autonomous integrity monitoring (RAIM) [20], and their protection levels were derived to protect against the hard-to-detect faults in ranging measurements and cycle slips. [PERSON] proposed a Kalman filter-based RAIM for the carrier phase [14]. In this approach, the de-correlated innovations of the Kalman filter were used to detect faults. Protection levels were computed either from the covariance matrix of the Kalman filter or from using the geometry of the satellite whose faults would be most difficult to detect. References [15; 16] proposed isotropy-based protection levels (IBPL), particularly designed for the PPP position solutions. Assumptions regarding the behavior of ranging errors in terms of their size, direction, and protection levels as derived from a multivariate t-distribution of measurement errors were not made in IBPL. [PERSON] et al. proposed protection levels for RTK, which were modelled in a modified form from the solution-separation RAIM methods [17; 18]. An integrity risk in this approach considers the mutually exclusive events of correct and incorrect ambiguity resolutions in the least-squares ambiguity decorrelation adjustment (LAMBDA) method, which was introduced in [19]. Although these studies can be applied to derive protection levels for the CLAS PPP-RTK position solutions, their protection levels would be relatively larger because they do not use the CLAS integrity messages or the fault monitoring capability of the CLAS network. This paper proposes a protection-level equation for the PPP-RTK services broadcasting quality messages. Because both PPP-RTK and SBAS broadcast state space representation (SSR) of the correction messages, our proposed protection level equations are based on the SBAS protection level equations and are extended to reflect virtual reference station (VRS)-RTK positioning scheme, which is a method of processing the PPP-RTK correction messages on the user side. Additionally, the integrity messages of the CLAS service are assumed to have a standard deviation of a Gaussian distribution, similar to the SBAS. This study compared the protection levels computed using the CLAS integrity messages with the VRS-RTK position errors. For the VRS-RTK process, we used CLAS L6 messages and GNSS observation measurements from the GNSS Earth Observation Network (GEONET) station in Japan. The L6 integrity messages were only used to compute the protection levels, because they were significantly inflated from the actual error distribution of the correction messages; however, the VRS-RTK process used the correction error distributions used in practice, whose standard deviation was significantly smaller than that of the integrity messages. This paper provides an overview of the architecture of CLAS and broadcasting messages in Section 2. Section 3 discusses the proposed protection-level equations for PPP-RTK. Section 4 presents examples of broadcast integrity indices and computed horizontal and vertical protection levels with the dataset. Finally, the discussion and conclusions are presented.