# An Enhanced Non-Coherent Pre-Filter Design for Tracking Error Estimation in GNSS Receivers
## 5 Conclusions and Future Work  
This paper presents an enhanced non-coherent pre-filter design. Firstly, the observation noise variance of non-coherent pre-filter is analyzed through Monte Carlo Simulation. The LUTs are subsequently created to store the relationship among \(T_{\text{coh}}\), \(C/N_{0}\), and the estimation noise variances of the ATAN/ATAN2/NC-EMLE discriminator. The LUTs provide a method to set the observation noise variance matrix of non-coherent pre-filter correctly according to estimated \(C/N_{0}\). Secondly, a simple FDE structure is introduced to overcome the inherent deficiency of the ATAN discriminator, whose outputs are observations of the non-coherent pre-filter. Through the FDE structure, the effective estimation range of the non-coherent pre-filter for carrier phase error extends from \((-0.25\text{ cycle},0.25\text{ cycle})\) to \((-0.5\text{ cycle},0.5\text{ cycle})\). This is a significant improvement that makes the non-coherent pre-filter outperform the coherent pre-filter in highly dynamic scenes. The performance of the proposed enhanced non-coherent pre-filter is compared with traditional ATAN/ATAN2/NC-EMLE discriminators and the coherent pre-filter in carefully designed scenarios. The estimation accuracy and robustness of the enhanced non-coherent pre-filter outperform the traditional discriminator and coherent pre-filter in weak signal condition and high tracking error dynamic scene. Additionally, the estimation accuracy of the enhanced non-coherent pre-filter for carrier phase error outperforms the coherent pre-filter in strong signal scenes. The best operating conditions of the coherent/non-coherent pre-filter for tracking error estimation are discussed in detail in the performance evaluation section. This can be the basis of hybrid pre-filter design, where tracking error would be estimated by coherent and non-coherent pre-filter simultaneously. The accuracy evaluation of discriminator and pre-filter algorithms is based on the simulated I/Q correlation signal in this paper. It is also necessary to evaluate the accuracy improvements which can be obtained by using the enhanced non-coherent pre-filter in the aspect of position fixing and velocity determination. Besides, the tracking error estimated by pre-filter is less noisy than that of the ATAN/ATAN2/NC-EMLE discriminator. If the state variables of the pre-filter, instead of discriminator outputs, are used to generate carrier/code NCO feedback command, the tracking loop is able to track  
Figure 16: The STD values of estimation error of code phase error in different \(C/N_{0}\). weaker signal or higher signal dynamic, or both. However, it is still a question how to generate NCO command according to state variables of pre-filter. The performance of the pre-filter can be further improved by adjusting the system noise co-variance matrix, which is not discussed in this paper. These three aspects can be the future research orientations. This work is funded by the National Natural Science Foundation of China under grant No.61633008, No. 61304234, No. 61773132 and No. 61374007. The authors would like to thank all the editors and anonymous reviewers for improving this article. This paper is the achievement of joint efforts of all the authors. [PERSON] was in charge of paper writing. [PERSON] was responsible for experimental design and paper revision. [PERSON] took charge of performing the experiments and data analysis. [PERSON] contributed the ideas of open loop evaluation method for pre-filters, and Monte Carlo simulation. The authors declare no conflict of interest.