# A Novel Carrier Tracking Approach for GPS Signals Based on Gauss-Hermite Kalman Filter
## 5 Simulation Setup and Experiment Results  
### Test Setup  
To evaluate the proposed algorithm, the tracking algorithm described above was implemented on a software-defined GPS receiver, implemented in Matlab. The receiver directly processes the IF signal, which is read from a data file. The datasets (50 s) were generated using a software-defined GPS simulator, which was implemented using a SDR device, ADALM-PLUTO SDR. The simulator generates GPS baseband signal data streams, which can be converted to RF using the ADALM-PLUTO SDR platform. This simulator is programmed as a 12-channel GPS signal simulator in the L1 (1575, 420 MHz) band. This makes it possible to determine motion patterns of the receiver, taking into account the power of the transmitted signal from each satellite [27]. The RF signal was received by another SDR device, SDRplay RSPdx, and recorded to a data file using a 3 MHz sampling frequency and a 16 bit signal resolution. The experiment setup is shown in Figure 2.  
This test was investigated for the evaluation of EKF-, UKF-, and GHKF-based tracking algorithms. Sensitivity of the receiver is an important parameter when comparing the mentioned tracking system algorithms. Tracking sensitivity was evaluated using the carrier-to-noise ratio (\(C/N_{0}\)) estimates. \(C/N_{0}\) represents the ratio of the received signal power to the spectral power of the receiver thermal noise in a 1 Hz bandwidth (measured in dB-Hz) and can be written as follows [11; 12]:  
\[C/N_{0}=10\log_{10}(\frac{\hat{A}^{2}}{2 To_{IQ}^{2}}). \tag{29}\]  
The tracking threshold of the parameter \(C/N_{0}\) was assumed to be 4 dB-Hz, i.e., the error of \(C/N_{0}\) estimates had to be lower than 4 dB-Hz [12; 13]. Similarly, the tracking threshold of the Doppler frequency was assumed to be 25 Hz [12; 13]. In this simulation, the coherent integration time was equal to one period of the C/A code, i.e., \(T=1\) ms. For simplicity, only the performance of PRN 27 satellite is illustrated here. Table 1 shows the initial parameters of the three nonlinear algorithms.  
In this simulation, the degree of the proposed GHKF was set to 3. At the same time, the UKF scale parameters were empirically chosen as follows: (\(\alpha=0.7\), \(\beta=2\), and \(\kappa=0\)).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(Q\)} & \multicolumn{5}{c}{**Square Roots from Diagonal Elements \(P_{0}\)**} \\ \hline \(q_{A}\) & \(q_{\varphi}(\frac{\mathrm{Hz}}{\mathrm{Hz}})\) & \(q_{f}(\frac{1}{\mathrm{Hz}})\) & \(q_{f^{\prime}}(\frac{\mathrm{m}/s^{3}}{\mathrm{Hz}})\) & \(\sigma_{A_{0}}\) & \(\sigma_{\phi_{0}}\) (rad) & \(\sigma_{f_{\mu\mu}}\) (Hz) & \(\sigma_{\hat{f}_{\mu\mu}}\) (\(\frac{\mathrm{Hz}}{\mathrm{s}}\)) \\ \hline \(10^{-3}\) & \(10^{-19}\) & \(8\,\times\,10^{-19}\) & \(5\) & \(1\) & \(2\pi\) & \(10\) & \(20\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Initial parameters of the proposed tracking system.  
Figure 2: The SDR devices used in the experiment.  
Two scenarios of the signal environment were simulated: static and dynamic weak signals. For each scenario, a comparative analysis of the tracking methods was carried out.