# An Enhanced Non-Coherent Pre-Filter Design for Tracking Error Estimation in GNSS Receivers
In terms of discriminator, there are a variety of discriminator algorithms that can be used for tracking error estimation, for example the two-quadrant arctangent (ATAN) discriminator for carrier phase error estimation, the four-quadrant arctangent (ATAN2) discriminator for carrier frequency error estimation, and non-coherent early minus late envelope (NC-EMLE) discriminator for code phase error estimation [9]. These discriminator algorithms are all implemented by the linear or nonlinear combination of coherent or non-coherent integration results. Unfortunately, there are some flaws for traditional discriminator. Firstly, the outputs of the traditional discriminator are often very noisy. That is, real tracking error is buried in noise. This situation becomes even worse in weak signal condition. Secondly, their effective working ranges are limited. For example, the most popular ATAN discriminator would only work properly when the input carrier phase error belongs to (\(-0.25\) cycle, \(0.25\) cycle). If the carrier phase tracking error exceeds the scope of (\(-0.25\) cycle, \(0.25\) cycle) (which may be caused by high dynamic motion), the ATAN discriminator would output the wrong carrier phase error estimation. Thirdly, not only the internal relationship among tracking error, but also the statistic characteristic of estimation noise of discriminator is totally ignored. Accurate tracking error estimation cannot be done by traditional discriminator. Using KF-based pre-filter to estimate tracking error has recently received considerable attention in the design of GNSS scalar tracking loop, vector tracking loop, and GNSS/INS (i.e., Inertial Navigation System) deep integration navigation system that is of federated structure [12; 13; 14; 15; 16]. Compared with the traditional discriminator, the pre-filter would provide more accurate tracking error estimation because it fully utilizes the smoothing effect of the system model and the statistical characteristics of observation noise. The pre-filter in GNSS receivers can be classified into two categories: coherent pre-filter and non-coherent pre-filter [17]. The coherent pre-filter chooses coherent integration outputted by correlators as observations. For coherent pre-filter design, the observation vector is often a nonlinear function of state variables (i.e., tracking error), and hence it is often implemented by extended Kalman filter (EKF), which results in heavy computation burden. Many theoretical analyses have demonstrated that the coherent pre-filter can achieve high estimation accuracy in strong signal condition, but cannot perform well in weak signal condition [13]. However, there is no comprehensive performance evaluation of their performance in weak signal or high dynamic condition. The non-coherent pre-filter chooses discriminator outputs as observations. The system model and observation model of non-coherent pre-filter are all linear, thus a linear Kalman filter is enough for its implementation. It performs well in both strong signal and weak signal conditions. However, since it takes the discriminator outputs as observations, the performance of the non-coherent pre-filter is affected by drawbacks of the traditional discriminator. These drawbacks include the limited effective working region and unknown observation noise variance. The coherent pre-filter and non-coherent pre-filter have complementary characteristics, which can be used to design a hybrid pre-filter structure [18]. An adaptive hybrid coherent/non-coherent GNSS vector tracking loop has been proposed to adaptively switch the pre-filter type that is working in tracking channel according to the signal strength [19]. The coherent pre-filter works in strong signal condition, while the non-coherent pre-filter works in weak signal condition. However, the switching threshold (24 dB-Hz) is determined by the designer's experience, instead of comprehensive study.