Safety assured navigation in polar regions: Kalman filter-based integrity monitoring methods considering fault duration

Abstract

The inaccuracy of the magnetometer and the satellite navigation system is typical limitation in Polar navigation. To overcome the constraint, we proposes a GNSS/inertial integrated navigation system that uses GNSS-based heading estimates as an alternative to the magnetometer and the GLONASS constellation suitable for the high latitudes. This thesis presents Kalman filter-based integrity monitoring methods considering fault duration to ensure the safety of heading and position solutions. First, an integrity monitoring method ensuring a heading integrity is presented. The GNSS-based heading determination is performed by estimating a baseline vector between two antennas mounted on a vehicle. The known baseline distance of two antennas is exploited to enhance success rate of ambiguity resolution. If the unknown integer ambiguities are incorrectly fixed due to GNSS noises, an unexpectedly large error in heading estimate can be derived. In particular, Kalman filter heading estimates can be corrupted by consecutive measurement faults occurring over a period of time, which is the worst integrity threat considered in the Kalman filter-based integrity monitoring. This thesis introduces a new Kalman-filter-based integrity monitoring algorithm considering the fault duration length as a variable. In conventional Kalman-filter-based integrity monitoring methods, a rigorous evaluation is conducted by determining the worst-case fault that maximizes the integrity risk

however, these methods overestimate the integrity risk by assuming a single fault duration and the constant prior probability regardless of the fault duration. In this study, the existing integrity monitoring algorithms are extended to account for the multiple hypotheses of the fault duration. Mutually exclusive and collectively exhaustive hypotheses are defined to cover a wide range of potential fault modes with respect to the fault duration. The methods for integrity risk computations are presented for the case of both single and multiple cumulative innovation monitors. A performance analysis of the proposed method is carried out by applying it to an unmanned aerial vehicle flight simulation where the GNSS is used for heading determination. In this process, the prior probabilities of the fault hypotheses are modeled through Monte Carlo simulations. Subsequently, the heading integrity risk is evaluated using three different methods: the existing approach based on a single hypothesis and two multi-hypothesis approaches newly proposed in this research, one with a single monitor and another with multiple monitors. The results demonstrate that tighter integrity risk bound can be achieved when using the multiple monitors considering the multiple fault hypotheses. Next, a study is conducted on how to guarantee the positioning integrity according to the two scenarios: stand-alone GNSS or local-area differential GNSS using a ground system. As GLONASS constellation is additionally utilized, the average number of visible satellites increases. When the ground system is not in use, the probability of simultaneous multiple satellite faults increases to the level of integrity risk requirements. However, the existing method of the protection level calculation only assumes the single satellite fault, which may leads to hazardous events that the protection level cannot bound errors with a guaranteed probability due to the multiple satellite faults. Thus, we derive a new method of protection level calculation considering multiple satellite faults. Furthermore, we confirm the benefits of using a ground station in the protection level derivation. In this regard, the conventional monitoring algorithms of the ground station that were designed for the GPS constellation are modified in order to reflect the different characteristics of the GLONASS constellation. Finally, we analyze the impact of ionospheric spatial gradients on the positioning integrity when using the local-area differential GNSS architecture.