# A Review of High-Sensitivity Tracking Techniques for Satellite Navigation Signals
## 2 Methods
### Scalar Tracking  
Scalar tracking is the most traditional method of closed-loop tracking, and its block diagram is shown in Figure 2. This tracking loop consists of four main components: a correlation module, a discriminator module, a loop filter, and a voltage-controlled oscillator.  
\begin{table}
\begin{tabular}{c l l l l} \hline
**Tracking Method** & **Core Concept** & **Advantages** & **Limitations** & **Representative References** \\ \hline \multirow{4}{*}{Scalar Tracking} & Each satellite channel is tracked & \multirow{4}{*}{Sample structure; low computational cost.} & \multirow{4}{*}{Poor performance in dynamic or degraded environments; no channel cooperation.} & \multirow{4}{*}{[PERSON] (1998) [19], [PERSON] (1996) [13],} \\  & independently without & & & \\  & exploiting inter-satellite & & & \\  & geometry. & & & \\  & & & & \\  & & & & \\  & & & & \\  & Navigation solution derived & & & & \\  & from all channels jointly feeds & & & & \\  & & & & \\  & back into all loops, utilizing & & & & \\  & back into all loops, utilizing & & & \\  & inter-channel geometric & & accuracy. & & \\  & relationships. & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline \multirow{4}{*}{Vector Tracking} & Signal parameters are estimated & High observability; robust re-acquisition in fading. & High computational complexity; less suitable for real-time use. & & \\  & & & & \\  & & & & \\ \hline \multirow{4}{*}{Direct Position Estimation} & Jointly estimates position & High positioning & \multirow{4}{*}{Computionally expensive; limited practical deployment.} & \multirow{4}{*}{[PERSON] (2005) [54], [PERSON] (2016) [56], [PERSON]. (2019) [57]} \\  & directly from raw signals & accuracy; bypasses & & & \\  & without intermediate & code/carrier & & \\  & synchronization steps. & synchronization. & & \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of major GNSS signal tracking methods.  
The open-loop transfer function is defined as  
\[G_{OL}(s)=\frac{K_{d}K_{o}F(s)}{s} \tag{1}\]  
The closed-loop transfer function is  
\[H_{CL}(s)=\frac{G_{OL}(s)}{1+G_{OL}(s)}=\frac{K_{d}K_{o}F(s)}{s+K_{d}K_{o}F(s)} \tag{2}\]  
The error transfer function is  
\[E(s)=\frac{1}{1+G_{OL}(s)}=\frac{s}{s+K_{d}K_{o}F(s)} \tag{3}\]  
where \(K_{d}\) is the phase discriminator gain, \(K_{o}\) is the voltage-controlled oscillator gain, and \(F(s)\) is the loop filter transfer function.  
For a second-order tracking system, the loop filter \(F(s)\) can be explicitly expressed as  
\[F(s)=\frac{\tau_{2}s+1}{\tau_{1}s} \tag{4}\]  
where \(\tau_{1}\) is the integrator time constant of the filter, and \(\tau_{2}\) is the zero time constant of the filter.  
For commonly used parameters in satellite signal tracking, the inherent frequency \(\omega_{n}\) and damping factor \(\zeta\) of this are  
\[\omega_{n}=\sqrt{\frac{K_{d}K_{o}}{\tau_{1}}}=\sqrt{K_{d}K_{o}K_{2}} \tag{5}\]  
\[\zeta=\frac{\tau_{2}}{2}\sqrt{\frac{K_{d}K_{o}}{\tau_{1}}}=\frac{\tau_{2} \omega_{n}}{2}=\frac{K_{1}}{2}\sqrt{\frac{K_{d}K_{o}}{K_{2}}} \tag{6}\]  
Substituting these parameters into the closed-loop transfer function expression, the second-order tracking system transfer function can be simplified as:  
\[H(s)=\frac{2\zeta\omega_{n}s+\omega_{n}^{2}}{s^{2}+2\zeta\omega_{n}s+\omega_{ n}^{2}} \tag{7}\]  
Figure 1: Overview of satellite signal tracking techniques in GNSS receivers.  
To enhance the tracking sensitivity of the scalar tracking loop, researchers have proposed three primary approaches: (1) improving the SNR by extending the coherent integration time, (2) enhancing the discriminator's estimation accuracy to more precisely capture signal features, and (3) optimizing the loop filter to improve overall signal processing performance.  
As Assisted GNSS (A-GNSS) has already been integrated into some of these innovations, the combination of scalar tracking with A-GNSS is not discussed separately in this section.