# A Review of High-Sensitivity Tracking Techniques for Satellite Navigation Signals
## 2 Methods
### Conventional Approach
#### 2.4.1 Improving Discriminator Estimation Precision  
The open-loop tracking method was first proposed by [PERSON] [42], who discussed the advantages and disadvantages of open-loop and closed-loop tracking in detail. He emphasized how open-loop tracking can utilize FFT to generate a three-dimensional image of the current signal stack, allowing for satellite signal tracking by identifying its maximum value. [PERSON] further proposed a zoomed FFT technique to reduce the computational complexity of FFT. She evaluated open-loop tracking performance by adjusting the scaling window size and cyclic update rates [43].  
Building on this, [PERSON] reduced the computational burden of FFT by suggesting it be applied to process I/Q coherent integration results rather than intermediate frequency (IF) data. He proposed that all channels could share a single FFT module and perform a complex squaring operation to mitigate the effect of data bit values. Additionally, a performance comparison between FFT and SEFT (Scaled FFT) was conducted [11].  
The study of discriminators has advanced beyond just FFT to explore more accurate estimation methods. For instance, [PERSON] proposed improvements to [PERSON]'s method beyond FFT-based discriminators, offering two enhancements to improve performance in low-SNR scenarios [44].  
Additionally, [PERSON] used the UKF for open-loop carrier tracking, with the structure shown in Figure 10. He designed a four-dimensional UKF phase estimator with the state vector \(\left[\begin{array}{cccc}\hat{\theta}_{k}&\hat{w}_{d,k}&\hat{w}_{d,k}^{1}&\hat{w }_{d,k}^{2}\end{array}\right]\), where \(\hat{\theta}_{k}\) represents the carrier phase, \(\hat{w}_{d,k}\) is the Doppler shift, and \(\hat{w}_{d,k}^{1}\) and \(\hat{w}_{d,k}^{2}\) are the first- and second-order Doppler shift change rates. [PERSON] introduced a compensator after the UKF estimator to adaptively adjust the estimated four-dimensional state vectors [138].  
Figure 10: Methods of a four-dimensional unscented KF for open-loop carrier tracking.  
Figure 9: Three-dimensional signal image of the traditional open-loop tracking method.  
[PERSON] proposed an open-loop tracking algorithm based on the dual Kalman Filter (DKF), which uses carrier frequency and pseudo-code phase differences from different channels as observation vectors and the receiver's position and velocity as state vectors. This approach improves tracking accuracy [45]. [PERSON] proposed a two-stage frequency estimation method combining coarse frequency estimation using discrete Fourier transform (DFT) and fine frequency estimation based on ML estimation (MLE) [46].  
As open-loop tracking discriminators have evolved, various solutions have emerged. Initially, FFT was applied directly to IF data processing, which later evolved into basic coherent integral signal processing. These advances have gradually alleviated the high computational requirements of traditional open-loop tracking. Future research should focus on further improving the accuracy of discriminators based on coherent integral signal processing.  
Table 8 provides a summary of the major discriminator optimization techniques developed for open-loop tracking, highlighting their respective advantages, challenges, and representative references.