# A Review of High-Sensitivity Tracking Techniques for Satellite Navigation Signals
## 2 Methods
### Conventional Approach
#### Direct Position Estimation  
The concept of DPE, initially proposed by [PERSON], deviates from the traditional receiver approach that relies on Time Difference of Arrival (TDOA) estimation, instead estimating the position directly from the received data. The block diagram for the DPE flow is shown in Figure 12. This method combines the data from all visible satellites to jointly perform position estimation, overcoming biases caused by multipath effects or transient satellite link blockage. Based on the invariance principle of position estimation, [PERSON] derives the ML estimate for the position from the ML estimate of the synchronization parameters [48]. \[\hat{\chi}_{n+1}=\underset{\chi}{\operatorname{argmax}}\left\{\sum_{i=1}^{M} \Lambda_{i}\big{(}\tau_{i}(\chi),f_{d_{i}}(\chi)\big{)}\right\}=\hat{\chi}_{n} \tag{24}\]  
Here, \(M\) represents the number of visible satellites, and \(\Lambda_{i}(\tau_{i}(\chi),f_{d_{i}}(\chi))\) represents the correlation value between the local signal of the \(i\)-th visible satellite at the selected position \(\chi\) and the received signal. The magnitude of the correlation value is determined by the code phase and Doppler frequency of the local signal. The innovation of the DPE method lies in its ability to naturally incorporate prior information, which traditional synchronization-based methods struggle to achieve due to difficulties in modeling the evolution of these parameters. The user's coordinate information can be obtained from motion models, tightly integrated IMU, or other potential sources of user motion data, thus enhancing the sensitivity of satellite signal tracking [48]. Despite the inherently high sensitivity of the DPE algorithm, the main challenge lies in its high implementation complexity. Subsequent research has focused on optimizing the  
Figure 11: Hybrid open-loop and closed-loop tracking methods. algorithm, integrating sensor fusion, and combining various filtering methods to improve stability, ease of implementation, and performance in complex environments. [PERSON] et al. [53; 54; 139] conducted a detailed comparison between the DPE method and traditional synchronization techniques, demonstrating that both approaches exhibit consistent asymptotic unbiasedness and efficient estimation performance. Their study also validated the robustness of DPE under various challenging conditions, including multipath, fading, and dynamic user scenarios. Building on this, [PERSON] derived the Cramer-Rao lower bounds (CRLB) for both conventional and DPE-based positioning methods and provided the corresponding root mean square error (RMSE) performance analysis [51]. [PERSON] et al. [140] evaluated DPE performance in high-dynamic environments, such as scenarios with high-speed motion and rapid acceleration changes, and confirmed that DPE maintains superior positioning accuracy even when GPS signal quality is degraded. In the context of urban canyon environments, [PERSON] et al. [141] investigated DPE's resilience against multipath interference. Their results indicated that, by improving the signal modeling to better account for multipath and Non-Line-of-Sight (NLOS) effects, DPE significantly outperforms conventional receivers in complex urban environments. [PERSON] et al. [142] further validated these findings through field tests in various urban settings, showing that DPE outperforms conventional scalar tracking methods in lightly obstructed environments, although its performance degrades under severe multipath conditions. In terms of methodological innovation, [PERSON] extended DPE into a Bayesian framework by proposing a Bayesian DPE algorithm, exploring multiple possible state space formulations, and validating the feasibility of the approach through simulations [50]. He also integrated DPE with inertial measurement unit (IMU) data and compared the performance of different fusion filtering approaches [52].