# Performance and Evaluation of GNSS Receiver Vector Tracking Loop Based on Adaptive Cascade Filter
## 1 Introduction
However, in many harsh scenarios, such as high dynamics, low C/N\({}_{0}\) ratio, intermittent signal interruption, multipath interference, non-line-of-sight reception, etc., in order to improve the usability of GNSS receivers in modern navigation applications, the vector tracking-based architecture has aroused widespread attention and discussion in the challenging environment of GNSS. Vector tracking makes full use of the internal relationship between the tracking channels to convert the discriminator output into a pseudo-range error and a pseudo-range rate error. When the navigation solution and satellite ephemeris are known, the code phase error and frequency error of the next epoch are predicted to update the NCO [13]. Many scholars have elaborated on the characteristics of vector tracking algorithms. [PERSON] [14; 15] compares the performance of three adaptive estimation methods in the vector tracking process. Under high dynamic conditions, they all show the same level of error. The performance of the algorithm depends on the specific implementation and debugging, as well as the amount of calculation. As discussed in [16; 17], a scalar-vector FLL is proposed in scenarios, such as lack of signal interruption and high dynamics. Under the equivalent noise bandwidth, the performances of the FLL of scalar, least square method, and EKF are analyzed. The KF depends on the appropriate system noise covariance matrix. When the signal is interrupted for a long time, a frequency error lock may occur. Vector tracking can provide more accurate frequency and code phase estimation, but it needs navigation solution information. As presented in [18; 19; 20; 21; 22], different forms of robust Vector Phase Lock Loop (VPLL) methods are proposed for the carrier phase joint tracking when GNSS signals suffer from ionospheric scintillation, or for the fast-maneuvering situation, the relationship between filter gain and noise covariance is analyzed. [PERSON] [23] proposed a joint vector carrier tracking scheme to achieve high sensitivity and flexible parameter selection. It mainly includes a separate loop for each channel to track the specific dynamics of the satellite and the total channel based on the EKF to track the common dynamics of different channels. The structure of EKF-based software receivers is analyzed in [24], including special modules for tracking loop initialization and maintenance, and NCOupdate rules. As far as the final positioning accuracy is concerned, the advantages and disadvantages of the EKF and traditional FLL/PLL+DLL are compared. As described in [25], a simple classification of existing vector tracking methods is carried out. Under noisy or high dynamic environments, the performances of vector receiver and traditional receiver are compared. The advantages of vector tracking are: (1) the best user state estimation is obtained by combining different measurement noises; (2) the weak signal is assisted by a strong signal; (3) after the satellite signal is lost, it is reacquired. Combining the main points of the above paper, the improvement of the accuracy and robustness of GNSS signals in challenging environments, such as dense forests, urban canyons, satellite occlusion, and signal attenuation are topics worthy of discussion. We present an adaptive cascaded vector tracking loop frame design. In the signal tracking loop, the KF is used to accurately estimate the code phase error, carrier phase error, and carrier frequency error, which are converted into pseudo-range and pseudo-range rate errors, and applied to the navigation solution module based on the EKF. Because the output of the nonlinear discriminator is non-Gaussian, it results in inaccurate and even divergent filtering effects. The process noise variance matrix and the measurement noise variance matrix are adjusted by the innovation orthogonality and C/N\({}_{0}\) estimation method. The advantages of the proposed method in positioning accuracy, tracking loop stability, and C/N\({}_{0}\) estimation are presented through the vehicle test.