# An Improved RAIM Availability Assessment Method Based on the Characteristic Slope
###### Abstract  
The availability assessment is an important step for onboard application in Receiver Autonomous Integrity Monitoring (RAIM)s. It is commonly implemented using the protection level (PL)-based method. This paper analyzes the deficiencies of three kinds of PL-based methods: RAIM availability might be optimistically or conservatively assessed using the classic-PL-base method; might be conservatively assessed using the enhanced-PL-based method, and neither be optimistically nor conservatively assessed using the ideal-PL-based method with the cost of large calculation amount on-board. An improved slope-based RAIM availability assessment method is proposed, in which the characteristic slope is designed as the assessment basis, and its threshold that can exactly match the integrity risk requirement is derived. The slope-based method has the same RAIM availability assessment result as the ideal-PL-based method. Moreover, because the slope threshold can be calculated offline and searched online, the on-board calculation burden can be reduced using the slope-based method. Simulation is presented to verify the theoretical analysis of the RAIM availability assessment performances for the three PL-based and the slope-based methods. RAIM; availability; characteristic slope; protection level +
Footnote †: journal: _Sensors_  
0000-0  
increase in nominal position error. In addition, some studies have committed to accurately modeling the stochastic measurement noise, such as the discrete error-distribution (NavDEN) model proposed by [PERSON] and [PERSON] [6] and the distribution model considering both elevation angle and orbit type proposed by [PERSON] [7]. These measurement noise models are all helpful for obtaining a tight PL. However, in the process of pursuing a lower PL, i.e., higher availability of RAIM, there is a key issue that is ignored by most researchers: whether the PL can accurately assess RAIM availability. [PERSON] and [PERSON] noted this issue [3]. They qualitatively described that the classic PL, the product of the characteristic slope and the Minimum Detection Bias (MDB) proposed by [PERSON] and [PERSON] [8], was too optimistic for RAIM availability assessment. The slope is a geometric feature-related parameter that qualitatively describes the relationship between positioning error and pseudo-range residual [9]. The reason is \"PL < AL\" might not mean that the integrity risk satisfies the requirement for the measurement bias less than MDB. Meanwhile, its enhancement, abbreviated as the enhanced PL in the following, which provides an additional term to protect against the variation in position error proposed by [PERSON] [10], is too conservative. The reason is \"PL \(\geq\) AL\" might not mean that the integrity risk exceeds the requirement. Here, measurement bias means the measurement error caused by the satellite fault, which is different from the measurement noise in the nominal mode. Furthermore, they proposed the ideal PL. It is the minimum PL value that guarantees the integrity risk, satisfying its requirement for arbitrary measurement bias. The ideal PL can prevent RAIM availability assessment from being optimistic or conservative. However, it cannot be solved analytically. A numerical search for the ideal PL begins with an improbably large value [3], which leads to a large amount of calculation, increasing the computational burden of a GNSS receiver or an onboard computer. In recent years, most researchers have focused on Advanced RAIM (ARAIM), in which PL is calculated after fault detection [11]. ARAIM supports multi-constellation dual-frequency GNSS integrity monitoring. Multiple hypothesis solution separation (MHSS) algorithm is used in ARAIM. How to solve the accurate PL for MHSS is a research hotspot, including the PL calculation method for each fault mode and the optimization strategy for the ultimate PL [12; 13; 14; 15; 16]. [PERSON] and [PERSON] adopted the ideal PL [3] in ARAIM and verified it was more accurate than other PLs for the ARAIM availability assessment [17; 18].