# Vector Tracking Loops (RWTH/EECS)

The Chair of Electrical Engineering and Computer Systems contributes to the project with the development of vector tracking loops.

# Vector Tracking Loops for a robust satellite tracking

Motivation: In current GNSS receivers, the calculation of position, velocity, and time (PVT) is performed as a standalone algorithm, which is for example based on the least-mean-squares method or an extended Kalman filter (EKF). The PVT calculation uses the signal parameters (code phase and carrier frequency) obtained by the tracking only as an input variable and has no feedback to the tracking. However, current research focuses on filter approaches that combine the PVT calculation and the tracking of all satellite signals into one general algorithm. The so-called vector tracking loops (VTL) consider the satellite positions extracted from the navigation message and the receiver position calculated by the PVT algorithm during tracking. Thus, they gain the advantage of utilizing relations between the signal parameters resulting from the spatial arrangement of satellites and the receiver. This advantage mainly shows up when it comes to shadowing effects where, for example, buildings disturb direct line of sight between receiver and satellite. Therefore, the objective in Galileo Online: GO! is to study methods and optimization approaches in order to enable an efficient realization of the VTL in mobile GNSS Receivers.

Functionality: The code delays and the Doppler frequencies of the satellite signals are directly related to the distances and relative velocities between the satellites and the receiver. However, the standard loops (STL) consider these signal parameters separated from the spatial arrangement and the movements of the satellites and the receiver. Additionally they control each satellite signal in an individual loop which is completely independent of the others. In contrast, the VTL combines all the observed signal parameters with the positions and velocities of the satellites and the receiver into an integrated system model. They regulate the signal parameters and estimate the PVT of the receiver in a common algorithm. Figure 1 shows this principle.

Figure 1: Standard loop (STL) compared to vector tracking loops (VTL)

An extended Kalman filter, which processes all measurements of code phase deviation and carrier frequency deviation in combination, is used as a loop filter in the VTL. The change of the position, the speed, the clock bias and the clock drift of the receiver is internally estimated. The computational complexity of this filter has been reduced by particular adaptations, which allows a real-time implementation:

1. Simplified parameterization of the temporal changes of the pseudoranges due to satellite movements
2. Reduction of the required update rate of the system model
3. Elimination of the matrix inversion in the Kalman filter by scalarization
4. The use of the existing intermediate results from the low-rate PVT calculation in the tracking algorithm
5. Feedback of the model errors assessed in the PVT calculation into tracking, in order to avoid an error increas

Simulation results: The designed tracking algorithm has been tested with both synthetic and recorded data. In the following, evaluation results of test in Aldenhoven Testing Center (ATC) are exemplarily shown. In this case, shadowing effects were artificially generated. Figure 2 shows the satellite constellation at the time of data recording. There are 11 satellites visible, which are subdivided into southeastern (brown) and northwest (green) satellites.

Figure 2: Satellite constellation during data recording

Figure 3: Results with an artificial shadowing from southeast

In the first scenario (Figure 3), the simulated case consists of passing a long (and virtual) building where all satellite signals from the southeast direction are obliterated. The shadowing event is activated at the time of 65 seconds and lasts 15 seconds. Figure 3 compares the position estimations resulting from the VTL and the STL. In the case of STL, the sudden shadowing of the southeastern satellites causes a jump in the position, which is corrected only after the satellites have been visible again at the time of 80 seconds. Figure 4 shows the regulated carrier frequency and the code phase as an example for satellite PRN 18.

Figure 4: Time curve of the regulated code phase and carrier frequency for PRN18

In the case of STL, the regulation error in the code phase increases during the shadowing event up to 0.13 chips which correspond to an error of 43 m in the pseudorange. In contrast, the error of VTL, which could be corrected immediately after the southeastern satellites appear without any delay, is only 0.01 chips. That shows the VTL’s capability to regulate the code phase even during shadowing event with support of the remaining visible satellites. Analogous, the regulation error of the carrier frequency increases up to 20 Hz in the case of STL. The VTL again avoid a larger error and, therefore, prevent a possible time consuming re-acquisition of the lost satellite.

Figure 5: Results with artificial and alternating shadowing effects

In the second scenario (Figure 5), an alternating shadowing effect is applied. The direction of the shadowing changes every 5 seconds and, as a result, corresponding position jumps using STL occur while the VTL position remains consistently stable.

# REFERENCES

 [1] M. Lashley, D. M. Bevly, and J. Y. Hung, “Performance analysis of vector tracking algorithms for weak gps signals in high dynamics,” IEEE Journal of Selected Topics in Signal Processing, vol. 3, no. 4, August 2009. [2] Q. Li, W. Wang, X. Guo, and D. Xu, “A design method and performance Analysis of vector-based tracking loop receiver,” in IEEE 11th International Conference on Signal Processing (ICSP), Oktober 2012. [3] H. So, T. Lee, S. Jeon, C. Kim, C. Kee, T. Kim, and S. Lee2, “Implementation of a vector-based tracking loop receiver in a pseudolite navigation system,” Sensors (Basel), vol. 10, no. 7, Juni 2010. [4] M. Lashley and D. M. Bevly, “Gnss solutions: What are vector tracking loops, and what are their benefits and drawbacks?” Inside GNSS, 2009.