# A Novel Carrier Tracking Approach for GPS Signals Based on Gauss-Hermite Kalman Filter
###### Abstract  
In a conventional GPS receiver, the carrier tracking system is the key stage that keeps the receiver locked to the radio navigation parameters (RNPs) of the received signal. The most commonly used approaches to the tracking system are phase lock loop (PLL), frequency lock loop (FLL), and FLL-assisted PLL. The main limitation of the above approaches is that their performance deteriorates when working with weak signals and in harsh environments. In recent years, Kalman filter (KF)-based tracking loop architectures have gained increased attention due to their robust and better performance compared with conventional architectures. In this paper, a novel Gauss-Hermite Kalman filtering-based carrier tracking algorithm is proposed for static and moving receivers with weak GPS signals. The performance of the proposed algorithm is compared with two other approaches: extended Kalman filter (EKF) and unscented Kalman filter (UKF). Simulations were conducted using a software-defined GPS simulator and software device radio (SDR) modules. A comparative analysis of the tracking methods demonstrated that the proposed tracking method shows a better performance and improves the tracking sensitivity and capability under weak signal conditions as compared with EKF- and UKF-based tracking methods. In addition, the results show that the proposed approach improves the Doppler frequency measurement accuracy under dynamic operation conditions. G 2022 11 2022 11 2022 11 2022  
validation of a full KF-based tracking loop in GNSS receivers. In [8], a multifrequency carrier tracking architecture based on the LKF was proposed to improve the robustness and accuracy of carrier tracking loop in frequency-selective fading environments. This architecture combines a traditional single frequency-independent tracking mode, which only uses measurements from a single carrier, a multifrequency joint tracking mode, which linearly combines measurements from multiple carriers, and a multifrequency optimal tracking mode, which incorporates signal strength in multicarrier combinations via a generalized LKF. In ref. [9], an approach was introduced for designing a system of automated positioning of the engineer reconnaissance devices under high-dynamic-reception conditions with a weak GPS signal. Accordingly, a two-stage carrier tracking system was proposed, which involved both coarse and fine tracking. The first stage was implemented through the use of a conventional scheme, where the PLL and FLL were combined to provide a rough estimate of both the carrier phase and the Doppler frequencies of the received signal. The fine tracking was implemented using LKF, starting after successful bit synchronization. It was demonstrated that the proposed method improved the tracking performance and prevented the bit synchronization loss while simultaneously improving the Doppler frequency measurement accuracy under highly dynamic conditions. However, the LKF approach assumes that the posteriori probability density at the outputs of discriminators is Gaussian. One disadvantage of this design is that the measurement noise at the discriminator output is not always white Gaussian. This follows from the fact that the use of nonlinear discriminators leads to loss of the white Gaussian property at low values of signal-to-noise ratio [10]. In other words, in the LKF algorithm, the phase estimated accuracy is limited by the nonlinearity of the phase discriminator. This reduces the performance of the LKF when receiving weak signals. In this case, other approaches have been considered that use several different strategies for approaching the optimal solution. These approaches are suboptimal and include the extended Kalman filter (EKF) and unscented Kalman filter (UKF) [11; 12; 13; 14; 15; 16; 17; 18; 19]. In this variant, a suboptimal nonlinear tracking filter (EKF or UKF) replaces both the discriminator and the tracking loop filter. In this case, the measurements are the quadrature components of the signals at the outputs of the nonlinear correlators.