## 1 Introduction  
Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), have severe inaccuracies in urban environments due to multipath interference and non-line of sight (NLOS) reception [1, 2]. Multipath interferences are common in urban, forested, and terrain with significant valleys or mountains. For instance, a narrow downtown street with tall buildings on either side has poor GPS reception. Furthermore, when a signal's direct line of sight (LOS) is obstructed, it can only be received via reflection, known as NLOS reception. In extreme multipath conditions, the LOS signal may be blocked entirely, leaving only the reflected signals. The code correlation peak is distorted by the reflected signals, making it difficult to detect the precise code phase of the direct LOS signal. Multipath errors as shown in Figure 1 are spatially uncorrelated errors that cannot be eliminated by observational differential processing, in contrast to some other correlated types of errors, such as the ionospheric and tropospheric errors. Observations that deviate significantly from most of the observation sample are known as outliers. One of the primary sources of inaccuracy for high-accuracy positioning systems is the irrelevancy between different instants and the appearance of uncertainty during the observation period. Despite the precautions taken throughout the observation period and the enhanced models used to eliminate systematic errors, observations may still be tainted by outliers, which frequently lower the quality of the estimated states and make them unreliable for any significant interference. Smoothing the ranging results can increase accuracy by reducing NLOS propagation's effects. A well-known estimator based on minimal mean square error (MMSE) is the Kalman filter (KF) [3]. It is generally accepted that, in linear systems with white Gaussian noise, KF uses MMSE as the best criterion. However, non-Gaussian sounds are frequently present in many real-world settings and can cause a significant decline in performance. Furthermore, the extended Kalman filter (EKF), an extension of the linear Kalman filter for handling nonlinear systems, will degrade if non-Gaussian noise disturbs the system. The process and measurement noises' high-order information is not utilized by the EKF when the noise exhibits non-Gaussianity. Numerous severe flaws in the EKF and unscented Kalman filter (UKF) techniques prevent widespread use. The non-Gaussian process and observation noises of the models and the unknowable noise covariance matrices are unique issues they cannot be managed. Additionally, because the estimated results are susceptible to significant outliers and non-Gaussian noise, the EKF struggles when the systems are combined with colored noise, which occurs in many real-world application settings. Despite being capable of handling non-Gaussian, nonlinear systems, the particle filter (PF) requires a significant investment in computing power for online implementation. The extent to which the EKF's performance depends on a predefined dynamic model is one major inconvenience. The designers must know the dynamic process and measurement models beforehand and assume that a zero-mean Gaussian white noise corrupts both models to provide accurate estimation results. The state vector has been estimated using the innovation-based adaptive Kalman filter (AKF) [4; 5] technique to avoid divergence brought on by incorrect modeling. Additionally, a process that is adaptable can be used to identify modeling flaws or system model uncertainty dynamically. The model-matched state estimation filters that are running concurrently in the interacting multiple model (IMM) algorithm [6; 7; 8; 9; 10; 11; 12] exchange information (interact) at each sampling period. Target-tracking applications were the first to use the IMM method, followed by navigation applications. A model probability evaluator first determines the likelihood that the receiver dynamic is currently in each potential mode.