# A Review of High-Sensitivity Tracking Techniques for Satellite Navigation Signals
## 2 Methods
### Scalar Tracking
#### 2.2.2 Optimizing the Discriminator  
In the pursuit of improving GNSS receiver discriminator sensitivity, past research has predominantly focused on Frequency-Locked Loop (FLL) discriminators, which include ML frequency estimation, differential amplitude (DA) discriminators, and FFT-based discriminators. [PERSON] was the first to propose the use of ML estimation for frequency estimation of coherent integration signals. This approach, based on the Discrete-Time Fourier Transform (DTFT), enables effective frequency estimation using ML principles [78]. The DA discriminator was first introduced by [PERSON], who used multiple Numerically Controlled Oscillators (NCOs) to replicate the same structure as the early delay, enabling frequency discrimination [25]. Building on this, [PERSON] proposed a memory discriminator that combines the DA discriminator with a moving window function. This modification improves Doppler estimation quality by reducing measurement variance, minimizing noise effects, and enhancing tracking performance [27]. FFT operations provide a more efficient way to obtain linear measurements and offer lower tracking SNR thresholds compared to conventional discriminators [79]. As a result, FFT-based frequency tracking has become an increasingly powerful solution [15; 78; 80; 81; 82]. However, due to the high computational complexity of FFT, most studies have focused on its use in open-loop tracking, with fewer applications in scalar tracking. The use of FFT in closed-loop tracking was first introduced by [PERSON], who proposed using FFT to process the in-phase and quadrature (I/Q) coherent integration results in closed-loop tracking, reducing computational complexity and marking its application in scalar tracking [11]. This approach was further extended by incorporating INS to improve tracking sensitivity [83]. Additionally, [PERSON] introduced an FFT-based tracking method for GPS code phase and carrier frequency [80], and [PERSON] implemented an FFT-based dynamic segmentation tracking loop [84]. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Technique** & **Advantages** & **Challenges** & **Representative References** \\ \hline Maximum Likelihood & Extends coherent integration by performing data erasure after bit synchronization. & Navigation bit flips; computational complexity. & [PERSON] (2012) [22] \\ \hline Non-Coherent Integration & Combines multiple 20 ms coherent integrations using a memory discriminator. & Computational complexity; synchronization between different channels. & [PERSON] (2009) [59], [PERSON] (2009) [60] \\ \hline Assisted GNSS & Eliminates the effects of data bit flipping using reference base stations. & Requires a reference station; limited by signal availability. & [PERSON] (2009) [18] \\ \hline Deep Combining with INS & Enhances GNSS tracking by combining with inertial navigation systems to mitigate receiver dynamics. & High cost of INS; requires sophisticated integration. & [PERSON] (2005) [20], [PERSON] (2009) [64] \\ \hline Wiener Filtering & Robustly tracks the carrier phase by modeling oscillator noise. & Complexity of filter design; requires high-quality oscillators. & [PERSON] (2012) [23] \\ \hline Kalman Filtering & Uses Kalman filters to track oscillator noise and improve carrier phase tracking accuracy. & High computational load; needs accurate noise models. [PERSON] [PERSON] (2017) [26], [PERSON] (1998) [19] \\ \hline Quartz Phase-Locked Loop & Optimizes tracking loops into a common loop and multiple individual loops to improve stability. & Receiver vibration can still impact performance; requires strong signals. & [PERSON] (2020) [77] \\ \hline Long Coherent Integration & Uses multi-channel cooperative loops to track oscillator error for ultra-long coherent integration cycles. & Requires strong satellite signals; high complexity. [PERSON] [PERSON] (2023) [12] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of techniques for extending coherent integration time.