# Improved 2D Ground Target Tracking in GPS-Based Passive Radar Scenarios
## 2 System Operation Principle
### GPS Passive Radar Signal Processing  
In each GPS transmitter, the navigation message of the signal civil part, \(N_{M}(t)\), is encoded by a unique Pseudo-Random Noise (PRN) code with a repetition cycle of 1 ms, \(CA(t)\), to generate a spread spectrum signal, and placed in a common carrier frequency, \(f_{c}\), which depends on the GPS band.  
The civilian signal transmitted in the L1 band is described by (4), where i is the satellite PRN index, and Ap is the amplitude factor. Since the carrier frequency is shared by all GPS satellites, the PR acquired signal is composed of signals from multiple illumination sources. This problem and the low received power in reference and surveillance channels, make the use of a traditional PR processing schema in which the acquired reference signal is directly employed in the coherent processing stage impossible. To solve both problems, a PR processing scheme based on the use of reconstructed reference GPS signals was selected. The GPS based processing chain employed in this paper is depicted in Figure 2. Firstly, the reference channel is used to find, track and regenerate the available GPS signals, providing signal source differentiation.  
\[SAT_{i}(t)=Ap_{i}\cdot N_{Mi}(t)\cdot CA_{i}(t)\cdot cos(2\pi f_{c}t) \tag{4}\]  
The acquired direct path signal, \(s_{i}\), after quadrature demodulation, excluding constant amplitude and phase terms, can be modelled as (5), where the sub-index \(i\) represents the PRN associated with the GPS satellites in line of sight from PR location. Each individual GPS signal will be delayed in time, \(\tau_{i}(t)\), and shifted in frequency, \(f_{D,i}(t)\), due to the space-platform distance and movement, respectively. Due to the orbital movement, the delay and Doppler shift are time dependent, so a signal tracking process is required.  
\[s_{i}(t)=N_{Mi}(t-\tau_{i}(t))\cdot CA_{i}(t-\tau_{i}(t))\cdot exp(j2\pi f_{D,i} (t)t) \tag{5}\]  
The GPS receiver software available in the literature allows the GPS signal search and tracking process necessary for signal reconstruction [18]. In this work, the satellite presence and the first time delay and Doppler frequency estimations were carried out using a circular correlation method. In the signal tracking stage, a combination of a digital second order Phase Locked Loop (PLL), and a Delay Locked Loop (DLL), is implemented in intervals of 1 ms to provide the Doppler frequency and time delay tracking of the GPS signals. Once the Doppler frequency and time delay are estimated, the navigation message is extracted and the whole reference signal can be reconstructed.  
Before CAF generation, direct path interference components from all available satellites are filtered in the surveillance signals acquired by the different single radiating elements of the surveillance antenna array, using ECA filters [19].  
The search stage ideally finds all GPS signals that are acquired on the reference channel. However, very low power echoes are expected from targets, and signals with low  
Figure 2: Signal processing schema based on GPS signal regeneration, adaptive filtering and CAF.  
correlation levels compromise the performance of the PR. In this work, the target location will be obtained using a single satellite signal. Therefore, the coherent radar processing stage to generate the Range Doppler Maps (RDMs) is performed with the CAF taking as input the reconstructed reference signal associated with the most powerful received satellite, and the filtered surveillance signal.