# A Review of High-Sensitivity Tracking Techniques for Satellite Navigation Signals
## 2 Methods
### Scalar Tracking
#### 2.2.1 Extending Coherent Integration Time  
In GNSS receivers, extending the coherent integration time is a key strategy for improving tracking sensitivity. It also helps mitigate undesirable effects such as multipath and Non-Line-of-Sight (NLOS) propagation. However, extending the coherent integration time introduces three major challenges: navigation bit flips, receiver dynamics, and oscillator instability [58]. For standalone GNSS receivers, [PERSON] first proposed using Maximum-Likelihood (ML) algorithms to extend coherent integration by performing data erasure after bit synchronization [22]. [PERSON] later achieved the integration of multiple 20 ms coherent integrations using non-coherent integration combined with a memory discriminator, which effectively mitigates the effects of data bit flipping [59; 60]. When a reference base station is available, A-GNSS can be used to eliminate the effects of data bit flipping [18]. Furthermore, for modern signal regimes such as B1c and L5, tracking these signals is not impacted by navigation data bit flipping, as the guiding frequency signals are modulated into known secondary codes [61; 62]. To address the effects of receiver dynamics, inertial navigation systems (INSs) are commonly used to assist GNSS receivers [20]. The concept of deep combining was first introduced by [PERSON] at Draper Laboratories in 1996, describing a combinatorial navigation method for extended code tracking loops. Following this, Draper Laboratories conducted extensive research on ultra-tight combining in a collaborative military project [63]. This led  
Figure 2: Methods of the scalar tracking loop. to the development of the theoretical foundation for ultra-tight combining, which involves assisting the scalar tracking loop of the GNSS receiver with INS data. The architecture of a scalar ultra-tight combined tracking loop assisted by INS is shown in Figure 3.  
Since the beginning of the 21 st century, ultra-tight integration navigation technology has developed rapidly. Researchers have demonstrated that GNSS carrier loops can operate effectively under quasi-static conditions with the assistance of INS [64; 65; 66]. [PERSON] quantitatively assessed the negative impact of inertial assistance for different types of INS by modeling phase-locked loop (PLL) in a deeply integrated Global Positioning System(GPS)/INS system using scalar tracking. Their results show that the carrier phase tracking errors are below 1.2 degrees for Micro-Electro-Mechanical System (MEMS) IMUs and below 0.8 degrees for tactical IMUs, which are much smaller than the inherent receiver errors. This indicates that even low-cost MEMS IMUs can assist in signal tracking, while tactical-grade IMUs provide higher-quality auxiliary information [67]. [PERSON] et al. demonstrated through real-world, highly dynamic field tests that the carrier phase error of a MEMS IMU-assisted PLL is nearly identical to that under static conditions [66]. Ultra-tight GNSS/INS integration has been validated as an effective method for mitigating receiver dynamics during long coherent integrations [64; 66; 68]. Oscillator phase noise can be categorized into long-term and short-term effects. Long-term effects include deterministic phase and frequency trends, such as frequency bias and linear frequency drift, while short-term effects involve random phase and frequency fluctuations [23]. The process of oscillator phase noise can be described as follows [23; 69]:  
\[\Psi_{n+1}(t)=2\pi f_{0}t+\sum_{i=2}^{N}\frac{2\pi\delta f_{i-1}}{i!}t^{i}+ \psi(t)=\Psi_{n}(t) \tag{8}\]  
where \(f_{0}\) and \(\delta f_{i}\) represent the constant average frequency and the \(i\)-th order frequency drift of the oscillator, respectively [69]. The short-term effect, \(\psi(t)\), is modeled as a zero-mean stochastic process. Any non-zero average phase noise can be absorbed into the system  
Figure 3: Methods of the INS-assisted scalar ultra-tight combined tracking loop. drift.