## 1 Introduction  
Global navigation satellite system (GNSS) receivers use tracking loops to synchronize replicated signals with received signals to maintain a continuous lock on the received signals. Traditional GNSS receivers use scalar-tracking loops (STLs). Vector-tracking loops (VTLs) are a new type of tracking loop. The basic strategy of VTLs is to combine signal tracking and navigation state (position and velocity) estimation into a single algorithm. Compared to STLs, VTLs improve the receiver tracking sensitivity and dynamic adaptability, increase the resistance to interference, and have the ability to bridge short-term interrupt signals [1]. In GNSS receivers, the carrier-to-noise ratio (_C/N\({}_{0}\)_), which is the ratio of the signal power to the noise power density, is an important parameter for measuring the quality of the received signal. In the acquisition phase, _C/N\({}_{0}\)_ provides a priori information that is used to determine the optimal detection threshold. In the tracking phase, _C/N\({}_{0}\)_ information facilitates the suppression of near-far interference and the avoidance of loss of lock. In particular, various positioning algorithms also use _C/N\({}_{0}\)_ to calculate the navigation solutions, such as the weighted least squares method [2]. _C/N\({}_{0}\)_ can also be used to facilitate the determination of the current working environment (indoor or outdoor) of the receiver and the construction of an environmentally adaptive navigation system [3]. In a vector receiver, _C/N\({}_{0}\)_ is an important basis for determining the validity of the measurements and for estimating the measurement noise [4]. In summary, based on the _C/N\({}_{0}\)_, GNSS receivers can implement a variety of functions to improve performance. The accurate estimation of the \(C\)/\(N_{0}\) is vital to developing advanced signal-processing algorithms. In the GNSS context, various \(C\)/\(N_{0}\) estimators have been intensively investigated by a broad range of literature. The main strategy of \(C\)/\(N_{0}\) estimation is to construct a statistic that contains the \(C\)/\(N_{0}\) information by using the sampled values of the correlator outputs or to directly estimate the signal and noise powers. Commonly used algorithms for \(C\)/\(N_{0}\) estimation include the narrow-to-wideband power ratio method (NWPR) [5], the correlator comparison method [5] (the additional noise channel method [6], ANCM), and the variance summing method (VSM) [7]. NWPR is a classic measurement method, which is also known as the standard estimator [8] and is used as a benchmark for algorithm comparison [9]. These estimation algorithms exhibit satisfactory estimation performance in a benign signal environment. However, under weak signal conditions, to obtain an accurate \(C\)/\(N_{0}\) measurement, a relatively long averaging time is required, thereby resulting in a significant time lag in the \(C\)/\(N_{0}\) estimation [5]. In challenging environments such as dense foliage and urban canyons, the signal power and \(C\)/\(N_{0}\) change rapidly if satellite signals are blocked. If the \(C\)/\(N_{0}\) shows a large change, the traditional estimation methods must adjust the averaging time, which causes the \(C\)/\(N_{0}\) estimation to be delayed, and cannot accurately reflect the change of the real signal. A fatal drawback of the vector receiver is that a faulty tracking channel can contaminate all of the remaining tracking channels [1; 10]. \(C\)/\(N_{0}\) is typically an important parameter for the identification of fault-tracking channels [4]. Therefore, timely and accurate estimation of the signal \(C\)/\(N_{0}\) is crucial for the vector receiver. The delay in the \(C\)/\(N_{0}\) estimation process may cause erroneous measurements to be passed to the navigation Kalman filter (KF), which would severely degrade the navigation performance. For these reasons, the conventional \(C\)/\(N_{0}\) estimation algorithms that are discussed above can impair the performance of vector-tracking loops in harsh environments.