###### Abstract  
Kalman filtering (KF)-based tracking has been commonly employed in global navigation satellite system (GNSS) receivers to achieve robust tracking. However, under more serious conditions, such as severe strength attenuation and abrupt dynamic coexisting environments, it is difficult for KF-based tracking to keep tracking well due to the fixed noise statistics. To further enhance the carrier tracking performance, this paper proposes an adaptive KF carrier tracking method for resisting signal strength fading and high dynamic environments. The proposed method introduces the adaptive factor to adjust the process noise covariance to accommodate the noise statistics in actual variable situations. Moreover, we apply the chi-square hypothesis test to detect system stability. The adaptive factor is only applied when the system is not stable, which can enhance computational efficiency. The proposed method is conducted in the GPS L1 software receivers. According to the results, the proposed algorithm can improve the robustness in tracking performance compared with other tracking methods under signal serious fading and high dynamic conditions. Using the proposed method, GNSS receivers' navigation performance can be improved under complex conditions. GNSS receivers; tracking loop; adaptive Kalman filter; weak and high dynamic signals; robust carrier tracking +
Footnote †: journal: _electronics_  
0000-0001-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-50000-5000-5000-5000-50000-50000-5000  
tracking sensitivity and can obtain more accurate state estimations than the conventional tracking loop under weak signal conditions. Nevertheless, the KF estimation performance is determined by accurate dynamic and stochastic models. The process noise covariance matrix (\(\mathbf{Q}_{k}\)) can influence Kalman gains during the whole filtering process. If there are errors in the noise covariances, the filtering estimations may be suboptimal or even divergent. However, accurate noise covariances are usually difficult to determine due to complex environments. Moreover, in variable situations, the actual noise covariances are changeable and cannot be obtained precisely. In fact, the noise covariance matrices in KF are predefined before the filtering process, which will not be changed anymore in the system. The predetermined noise covariances are typically obtained from the empirical analysis, which is not suitable for the actual noise stochastic properties under time-varying environments [15]. To enhance the KF performance's robustness, many adaptive Kalman filter (AKF) algorithms have been proposed. [PERSON] et al. [16] and [PERSON] et al. [17] have employed different AKF algorithms in integrated navigation systems and localization systems to improve estimation performance. Apart from linear KF systems, non-linear functions also need to adjust the covariance matrices to improve the filtering adaptivity [18; 19]. In addition, there are also several AKF algorithms applied in the carrier tracking system. [PERSON] et al. [20] proposed a novel adaptive two-stage KF for tracking loops in high dynamic conditions. [PERSON] et al. [21] proposed a novel adaptive joint Kalman filter algorithm for the vector PLL, but this is not suitable for the scalar tracking loop. [PERSON] et al. [22] and [PERSON] et al. [23] proposed the adaptive EKF (extended Kalman filter) method for carrier tracking, which is only fit for ionospheric scintillation conditions. [PERSON] et al. [24] proposed the variational Bayesian adaptive cubature Kalman filter algorithm for high dynamic signal conditions. However, there is not enough research on weak and high dynamic signal conditions. In signal fading and high dynamic environments, the signal strength and the Doppler frequency are both variable and sometimes change rapidly. The KF carrier tracking with unchanged noise covariance matrices cannot obtain optimal estimations in this situation, or they even lose lock.