# Performance and Evaluation of GNSS Receiver Vector Tracking Loop Based on Adaptive Cascade Filter
## 1 Introduction  
With the upgrading of satellite navigation systems, such as the GPS in the United States, Beilou in China, Galileo in Europe, and Quasi-Zenith in Japan, the Global Navigation Satellite System (GNSS) receiver technology is also stimulating new vitality. Its main function is to use the local replica signal to synchronize with the input signal, and decode the ephemeris to obtain the position, velocity, and time (PVT) information. Software receivers are favored by the majority of scholars because of more potential advantages of algorithm scalability, flexibility, and high module repeatability [1]. Reliable GNSS data can provide auxiliary information for aerial photography, geodetic surveying, and other remote sensing fields to improve the measurement accuracy of the target area. As a special scenario of remote sensing, Intelligent Transportation has attracted more attention in the Internet of Things (IoT). When vehicles or unmanned autonomous vehicles are driving in the urban environment and encounter tall buildings or dense trees, the proposed method can still maintain high navigation and positioning information. According to the multi-sensor data provided by the vehicle, they bring a reliable source of information for road monitoring of the entire city. The traffic flow can be adjusted to the best condition to ensure that vehicles can travel freely on the road. Managers can make roads and vehicles more scientific and rigorous for intelligent management and intelligent decision-making. In the scalar tracking loop, the discriminator output is directly fed back to the Numerically Controlled Oscillator (NCO), which works well in the case of high carrier-to-noise ratio and low dynamics. However, the fixed bandwidth and gain make it easier for the loop to lose lock at a lower Carrier-to-Noise ratio (C/N\({}_{0}\)). In an ideal situation, the phase error measurement of strong satellite signals should be given more weight than weak signals. Because the different channels of the traditional tracking loop of the GNSS receiver work independently, there is no information sharing between the channels, and it is impossible to excavate all the information of the satellite constellation and the user's location. According to different filter schemes, the methods adopted mainly include the Phase Lock Loop (PLL)/Delay Lock Loop (DLL), or Frequency Lock Loop (FLL) nonlinear discriminator output as the measurement of the Kalman Filter (KF) [2; 3]. They are directly used as baseband I phase and Q phase correlators output inside the tracking loop as measurement of the Extended Kalman Filter (EKF) [4; 5; 6] and so on. Among them, the nonlinear discriminator output of I and Q signals is used to estimate the signal parameter error, and the matrix design is simple. However, it will cause the measurement noise covariance matrix to lose the Gaussian white noise characteristics. According to the KF theory, the optimal estimation is based on an accurate noise statistical model, otherwise the filtering result will be inaccurate or divergent. Therefore, an adaptive strategy is needed to adjust measurement noise covariance R and process noise covariance matrix Q to improve the robustness and accuracy of the filter. The parameter setting criteria and the influencing factors of the tracking loop are described in detail in [7; 8]. According to the selection of different measurement residuals and the establishment of the state matrix, many researchers have also studied the implementation of the KF in different forms to evaluate the performance of different loop tracking methods [9; 10; 11; 12]. By comparing the noise bandwidth, open and closed loop transfer functions, in addition to the use of time-varying gains, these KF methods are mathematically equivalent to traditional methods, and provide a reference for how to adjust the Kalman parameters according to the expected performance.