A valid comparison of vector and scalar tracking loops

Abstract

This paper analyzes the benefits offered by vector tracking loops relative to scalar tracking loops. A method for designing equivalent scalar and vector tracking loops is first introduced. The benefits of vector tracking are then determined by comparing the two equivalent algorithms. The improvements in signal tracking afforded by vector tracking are quantified in different scenarios using covariance analysis and Monte Carlo simulations. The vector tracking algorithms show a maximum improvement in tracking threshold of 6.2 dB with an eleven satellite constellation and a minimum improvement of 2.4 dB with a five satellite constellation. The results presented in this paper demonstrate the amount of improvement vector tracking can provide in different situations. Furthermore, the analysis technique used to design the equivalent tracking loops provides a simple way to compare other attributes of the algorithms, such as their multipath immunity and robustness.

Deep fusion of vector tracking GNSS receivers and a 3D city model for robust positioning in urban canyons with NLOS signals

“…After averaging L output of discriminator over LT a ms, they are used by the non-linear discriminator to estimate the code phase and frequency shift errors. At each time epoch, the earlyminus-late power discriminator output of each satellite number i = 1, ..., N is given by [10],…”

“…where F is the transition matrix corresponding to a constant velocity motion model [10]. In the non-coherent VDLL, the used measurements in the EKF are the averaged outputs of the code phase and carrier frequency discriminators.…”

“…where H k+1 is the geometric matrix composed of zeros and LOS vectors [10]. The estimation of position, velocity, and clock parameters via the VDLL EKF are given by the correction step of the Kalman filter as follows,…”

“…where K k+1 is the Kalman gain matrix and e k+1 is the vector of measurements residuals obtained from equation (9). The required noise statistics R and Q for tuning the EKF of the VDLL is adopted from existing references [10], [8], [18].…”

Position domain joint tracking

“…In [5] it's shown that the robustness of a VDLL receiver is increased compared to the traditional setup. As a drawback, the VDLL only processes the noisy code-phase and carrier-frequency measurements.…”