# Performance Analyses of a RAIM Algorithm for Kalman Filter with GPS and NavIC Constellations
## 1 Introduction  
Since its inception, satellite navigation has become a critical infrastructure that supports a significant part of everyday life today. Its diverse array of applications includes power grid synchronization, precision farming, and emergency services, to name a few [1]. Although the system keeps the modern world running, it is vulnerable to numerous sources of signal degradation, anomalies, and intentional or unintentional interference. It is estimated that a failure of the global navigation satellite systems (GNSS)--a collective term for different satellite navigation systems--could cost modern economies billions of dollars [2]. Furthermore, growing reliance on GNSS for safety- and liability-critical applications, such as civil aviation and autonomous navigation, requires adherence to stringent performance standards for continuity and reliability of services. Faults or anomalies without timely detection can lead to hazardous consequences in such operations. Potential failure modes of GNSS for precise positioning are discussed in detail in [3]. While the performance of the global positioning system (GPS) has improved since 2012 with a lower number of fault counts [4], continuous monitoring is required by the constellation service provider as well as at the user level for high-reliability applications. Newer constellations (e.g., navigation with Indian constellation (NavIC) of India [5]) would possibly need several years to reach a state with few observed faults, thus requiring constantmonitoring. Integrity is considered an important performance metric for operations that demand high reliability. It quantifies the level of trust placed in GNSS positioning. Receiver autonomous integrity monitoring (RAIM) is a GNSS receiver-based algorithm implemented in the user equipment to monitor integrity. It carries out consistency checks to detect faults and outputs position error bounds or protection levels (PL) when no anomaly is found. If an anomalous behavior is detected, the system needs to issue an alert to the user within a pre-determined time called the time to alert to avoid misleading information. RAIM can be broadly classified into two categories depending on the standard implementations of the navigation processor of the receiver--weighted least squares (WLS) RAIM and Kalman filter (KF) RAIM. There exists a substantial amount of research on WLS RAIM [6; 7; 8]. In contrast, KF RAIM is much less explored [9]. KF is considered an integral component of advanced navigation algorithms. Examples are precise point positioning with GNSS [10], vector receiver architecture [11], and multi-sensor integration [12]. KF is a preferred choice in these systems for its ability to combine dynamics or a priori information with measurements and to estimate residual sensor errors [13]. The aforementioned advanced methods are shown to enhance performance by either improving accuracy, tracking high dynamics, or bridging GNSS outages in challenging environments. In order to ensure reliability along with these desirable features, integrity monitoring is an essential step. As a result, developing KF RAIM algorithms has received significant attention in recent years. A literature survey of contemporary work on KF-based integrity monitoring is provided next. Reference [9] reviews different sensor integration architectures for intelligent transportation systems and state-of-the-art methods for fault detection and exclusion (FDE) and PL calculations. In this context, all KF-based methods up to the time of writing are also discussed. In [14], an FDE method is developed for the tight coupling of GNSS and inertial navigation system (INS) to detect multiple GNSS as well as GNSS and INS faults. It uses two detectors to separate GNSS and INS faults and a two-step fault exclusion process. A no subset advanced RAIM (ARAIM) algorithm is derived in [15] for the tight integration of GNSS and INS under some assumptions. It is shown to reduce the computational load to a great extent and provide global coverage for CAT I precision approaches.