## 1 Introduction  
While personal navigation devices, including GNSS receivers and other self-contained sensors, are capable of providing highly reliable and accurate navigation solution in open sky environments, their performance still remains limited when it comes to navigating in GNSS-challenged environments such as natural and urban canyons. In such areas, GNSS signals, when available, are significantly affected by multipath effects and if used contribute to significant errors in the navigation solution while, if not used, result in lower solution availability. Moreover, GNSS suffers from other challenges, such as limited availability leading to poor geometry, high noise due to signal attenuation, non-normality of the measurement errors. For personal navigation systems that are implemented as an integrated Global Navigation Satellite System/Inertial Navigation System (GNSS/INS), especially those using relatively low cost micro electromechanical systems (MEMS) inertial measurement units (IMUs), the quality of GNSS signals plays a significant role in the navigation solution. The absence of GNSS or the presence of biased GNSS measurements can thus result in significant errors, depending upon the quality of the IMUs and the mechanization algorithm used. The most common approach to address these challenges is to use a suitable fault detection and exclusion (FDE) scheme to identify and reject aberrant measurements. Receiver autonomous integrity monitoring (RAIM) is the most popular technique used for that purpose. There are numerous types of RAIM methods, based on implementation particularities. Nonetheless, all of these schemes are based on some kind of self-consistency checks among the available measurements. However, in harsh GNSS signal conditions such as in urban canyons, the FDE schemes are overwhelmed with various challenges like lack of sufficient measurement redundancy and simultaneous multiple faults. As GNSS measurements are already depleted in such environments, further rejection is not desirable since it limits the overall redundancy of the estimation and solution availability. Moreover, the measurement error distribution in those environments can no longer be assumed normal nor are the measurements uncorrelated in time, thus negating fundamental requirements of the standard Kalman filter. Improper handling of faulty measurements can result in an unreliable navigation solution. Reliability is the level of trust that can be placed on the navigation solution provided by a personal navigation device. For example, if a navigation system estimates a position with accuracy (1\(\sigma\)) of 2 m along a particular axis, then it means that the error along that axis is expected to be less than 6 m with a confidence of 99.7% (_i.e._, 3\(\sigma\) along that axis). However, if the true position along that axis is 10 m away from the estimated position, then the navigation solution is considered unreliable. Hence, a reliable navigation solution should have good consistency between the navigation solution and the estimated accuracy. Thus, in the context of this paper, reliability is defined as the capability of the navigation system to give a solution with proper accuracy and is formulated as the percentage of errors bounded by \(\pm\)3\(\sigma\) or 99.7% (three times the estimated standard deviation of the position solution along a particular axis envelope). In this regard, the main objective of this paper is to develop and analyze a new filtering algorithm for personal navigation systems that is more robust against outliers and optimizes the use of available GNSS measurements in harsh environments in order to obtain greater reliability. The paper identifies the significance of assumed GNSS measurement error distributions when determining the reliability of a navigation solution and proposes a method that assumes an adaptive error distribution which is moreconsistent with the true one. The method initially presented in [1] is further developed, tested and analysed in greater detail herein.