# Standalone GPS L1 C/A Receiver for Lunar Missions
## 2 The _WeakHEO_ Receiver Architecture
### GPS Tracking
#### 2.6.2 Weak Signal Tracking  
The _WeakHEO_ receiver is assumed to be a stand-alone receiver with a low rate communication interface to the spacecraft platform. Therefore, knowledge of the full navigational data sequence is not assumed and data wipe-off is not used. Data wipe-off allows the use of pure (non-squaring) PLL discriminators to be used in tracking for lower jitter and a larger pull-in range compared to Costas-type discriminators. Typical expressions for the jitter of conventional GNSS tracking loop can be found in [23; 32]. Figure 13a shows the expected PLL jitter and a conservative loss of lock threshold for a third order Costas PLL, assuming thermal and oscillator noise (based on the _WeakHEO_ OCXO) are the only error sources and an integration time of 20 ms. This indicates that in the presence of navigation data flips we need to use bandwidth as low as 1 Hz to operate at 15 dB-Hz. The code tracking loop of the receiver is a first order loop aided by the carrier loop and uses a bandwidth of 0.1 Hz. Figure 13b shows the PLL jitter for the dot-product power discriminator with a 0.1 Hz, a 20 ms integration time and different early-to-late correlator spacing \(d\). Correlator spacings of 0.25 chip or greater are required to maintain code tracking at 15 dB-Hz. If an adaptive spacing is used, smaller correlator spacings can be used at higher signal levels to reduce the pseudorange jitter. It should be noted that using such low bandwidths to improve the performance in weak signal environments lengthens the time between statistically independent measurements from the code and carrier loops [32]. This is not critical for this application. These low bandwidths are suitable for operation at altitudes significantly above the GNSS constellation; however, during the first part of the MTO the line-of-sight jerk can be as high as 6 ms\({}^{-3}\). The received signal strength is far greater at this point but still requires a carrier loop PLL bandwidth  
Figure 12: Success rate of acquisition stages with varying signal levels. of around 5 Hz to tolerate this jerk [32]. Therefore, when conventional approaches to GNSS tracking are used for this application the carrier loop bandwidth will need to be adjusted during the MTO. Conventional tracking models the incoming system as having deterministic dynamics by typically using fixed tracking loop bandwidths. An alternative method, which provides more flexibility is based on Kalman filter theory. Rather than assuming deterministic dynamics, the Extended Kalman Filter (EKF) assumes that the signal dynamics follow a linear stochastic model. This allows an adaptive scheme where the response to dynamics is adjusted based on the signal conditions. Therefore, the ranging processor is designed to adapt the tracking loop bandwidths as a function of the measured \(C/N_{0}\), to maintain the optimum trade-off between noise resistance and dynamics response. It should be noted that this is not exclusively possible with the EKF based tracking and can be applied to conventional tracking. However, this is performed implicitly when using the EKF approach as part of its dynamic model. A number of variations on EKF tracking have been developed for both code and carrier tracking [29; 33; 34; 35]. Comparing EKF tracking to conventional architectures is troublesome as the non-linear models used in the EKF implementation are effectively constantly adapting its tracking bandwidth. Generally, jitter comparisons are made with conventional architecture under different dynamic conditions. However, this does provide to opportunity to choose scenarios and tracking loop settings to exaggerate the benefits of one technique over another. An attempt to compare the techniques by experimentally determining the steady-state bandwidth of the EKF and finding the equivalent performing PLL is found in [36]. Here, the EKF is demonstrated to be able to track the carrier phase down to 10 dB-Hz, around a 7 dB improvement under equivalent conditions.