# Fault-Free Protection Level Equation for CLAS PPP-RTK and Experimental Evaluations
###### Abstract  
Centimeter level augmentation system (CLAS) of the quasi-zenith satellite system (QZSS) is the first precise point positioning-real time kinematic (PPP-RTK) augmentation system of the global navigation satellite system (GNSS), which is currently providing services for Japan. CLAS broadcasts the state-space representation of correction messages along with integrity messages regarding satellite faults and the quality index of each correction. In other GNSS augmentation systems, such as the space-based augmentation system (SBAS) of GNSS, the quality indices of correction messages are used to generate fault-free protection levels that represent a position bound containing a true user position with a probability of missed detections. Although the protection level equations are well defined for the SBAS, a protection level equation for the CLAS PPP-RTK service has not been rigorously discussed in the literature. This paper proposes a fault-free protection level equation for the PPP-RTK methods that considers the probability of correct integer ambiguity fixes in the GNSS carrier phase measurements as well as the CLAS correction quality messages. The computed protection levels with position errors were experimentally compared by processing the GNSS measurements from the GNSS Earth Observation Network (GEONET) stations in Japan and the L6 messages from the CLAS broadcast using the virtual reference station-real time kinematic (VRS-RTK) techniques. Our results, based on the GEONET dataset spanning 7 days, showed that the computed protection levels using the proposed equations were larger than the position errors for all epochs. In the dataset, the RMS errors of the CLAS VRS-RTK position were 4.6 and 14 cm in the horizontal and vertical directions, respectively, whereas the horizontal protection levels ranged from 25 cm to 2.3 m and the vertical protection levels ranged from 50 cm to 5.2 m based on fault-free integrity risk of \(10^{-7}\). GNSS precise positioning; protection levels; integrity; PPP-RTK +
Footnote †: journal: _Sensors_  
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Gaussian error distributions of each visible satellite to the position-domain Gaussian error distributions via a user-to-satellite geometry. The range-domain error distributions used in the protection level equations are determined by the GBAS and SBAS service providers and are broadcast to users as quality indicators associated with each correction message. An important characteristic of the range domain error distribution is to overbound the actual error distribution of the correction messages in order for the protection levels, computed using the quality indicators, to overbound the actual user position errors with a missed-detection probability. Consequently, studies have been conducted on various overbounding techniques based on probability density function (PDF), cumulative distribution function (CDF), and paired overbounding [5; 6; 7; 8]. Centimeter level augmentation system (CLAS) of the quasi-zenith satellite system (QZSS) is a very recent GNSS augmentation system of Japan [9; 10; 11]. Unlike the GBAS and SBAS, which primarily use the GNSS code phase measurements as ranging sources, CLAS is a precise point positioning-real-time kinematic (PPP-RTK) augmentation system that allows users to resolve integer ambiguities in carrier phase measurements within several minutes by using the CLAS correction messages. Therefore, the CLAS users can use the carrier phase as a ranging source and achieve precise positioning similar to that of RTK. CLAS also provides quality indicators (also called integrity messages) for each correction message so that the users can compute the protection levels. However, the CLAS protocol currently does not specify any forms of protection-level equations, and quality message generation schemes are not well known [12; 13]. Owing to lack of information, the CLAS users are not encouraged to rely on the quality messages for safe navigation.