# Weak and Dynamic GNSS Signal Tracking Strategies for Flight Missions in the Space Service Volume
## 4 INS-Assisted Open Loop Tracking Strategy
### Structure of INS-Assisted Tracking Strategy  
It must be admitted that OL batch processing is less favorable than the CL sequential method with respect to computation efficiency, resulting from the complicated FFT calculation. Additionally, the OL batch scheme does not improve the measurement accuracy as compared to the CL sequential architecture. Instead, the OL scheme mainly promotes the robustness and reliability of the tracking loop, especially in challenging environment, such as SSV applications. Thus, it is necessary to put forward a new OL structure to ease the computation burden. In Figure 4, a suggested OL architecture is proposed with this purpose. Figure 4: Suggested architecture of INS-assisted open loop tracking. The proposed architecture is built on the basis of Doppler prediction utilizing inertial measurement unit (IMU) and GNSS ephemeris. IMU is a cluster of sensors, including accelerometers and gyros, which is responsible for obtaining the motion and attitude of the SSV user receiver, whereas the GNSS satellite ephemeris is used to calculate the position and velocity of the satellite by accurate orbit propagation models. Referring to [21], the Doppler frequency shift caused by the motion of the SSV user receiver relative to the GNSS satellite can be easily determined. The estimation of the Doppler frequency is used to reduce the local frequency search space, and the estimation accuracy depends on the quality of IMU. If the space vehicles are equipped with high quality IMUs, the expected Doppler frequency error accumulates slowly over time, which is adequate for SSV navigation. The ephemeris is obtained during visible intervals and saved into onboard registers for orbital propagation. It has been proved that the outage time when no satellite is in view does not exceed 108 min for SSV flight missions [1], and the length of the orbit propagation is relatively short so that the dynamic aiding is accurate enough. After A/D (Analog-to-Digital) conversion, the digitized incoming IF signal is generally expressed as:  
\[s(k)=AC(k-\tau)D(k)\text{cos}[2\pi kT(f_{IF}+f_{d})+\varphi]+n(k) \tag{25}\]  
where \(k\) is the time index of each sampling time interval, and \(T\) is the sampling time interval; \(A\) is the signal amplitude, \(C(\cdot)\) is the spreading code sequence and \(D(\cdot)\) is the navigation data bit; the three parameters to be estimated are code delay \(\tau\), Doppler frequency shift \(f_{d}\), and carrier phase \(\varphi\); \(f_{IF}\) is IF in Hz, and \(n(k)\) is additive band-limited white Gaussian noise (AWGN). Using the dynamic aiding with IMU and ephemeris described in Figure 4, we get the estimated Doppler frequency \(\hat{f}_{d}\). If the estimated initial phase is \(\hat{\phi}_{0}\), the two orthogonal carriers representing the outputs of carrier NCO are:  
\[\left\{ \begin{array}{l}i_{LO}(k)=\text{cos}[2\pi(f_{IF}+\hat{f}_{d})kT+\hat{ \phi}_{0}]\\ q_{LO}(k)=\text{sin}[2\pi(f_{IF}+\hat{f}_{d})kT+\hat{\phi}_{0}]\end{array} \right. \tag{26}\]  
The received signals in Equation (25) are correlated with the local replica signals in Equation (26) to generate the correlated results as:  
\[\left\{ \begin{array}{l}I(k)=AR(\delta\tau)D(k)\text{cos}(2\pi kT\cdot\delta f +\delta\phi_{0})+n_{i}(kT)\\ Q(k)=AR(\delta\tau)D(k)\text{sin}(2\pi kT\cdot\delta f+\delta\phi_{0})+n_{q}( kT)\end{array} \right. \tag{27}\]  
where \(\delta f\) is the Doppler frequency estimation error, \(\delta\phi_{0}\) is the initial phase estimation error, \(\delta\tau\) is the code delay error, \(R(\cdot)\) is the autocorrelation function (ACF) of C/A code, \(n_{i}\) is the in-phase noise and \(n_{q}\) is the quadrature noise. After coherent integration, we get the integration results of \(I_{P}\) and \(Q_{P}\)[22]:  
\[\left\{ \begin{array}{l}I_{P}(k)=AR(\delta\tau)D(k)\text{sinc}(kT\cdot\delta f )\text{cos}[2\pi\delta f(kT+\frac{T_{coh}}{2})+\delta\phi_{0}]\\ Q_{P}(k)=AR(\delta\tau)D(k)\text{sinc}(kT\cdot\delta f)\text{sin}[2\pi\delta f (kT+\frac{T_{coh}}{2})+\delta\phi_{0}]\end{array} \right.