Performance Evaluation of Adaptive Tracking Techniques with Direct-State Kalman Filter

Iñigo Cortés; Johannes Rossouw van der Merwe; Elena Simona Lohan; Jari Nurmi; Wolfgang Felber

doi:10.3390/s22020420

Performance Evaluation of Adaptive Tracking Techniques with Direct-State Kalman Filter

Sensors (Basel). 2022 Jan 6;22(2):420. doi: 10.3390/s22020420.

Authors

Iñigo Cortés^{1

2}, Johannes Rossouw van der Merwe¹, Elena Simona Lohan², Jari Nurmi², Wolfgang Felber¹

Affiliations

¹ Satellite Based Positioning Systems Department, Fraunhofer IIS, Nordostpark 84, 90411 Nuremberg, Germany.
² Electrical Engineering, Tampere University, 33014 Tampere, Finland.

Abstract

This paper evaluates the performance of robust adaptive tracking techniques with the direct-state Kalman filter (DSKF) used in modern digital global navigation satellite system (GNSS) receivers. Under the assumption of a well-known Gaussian distributed model of the states and the measurements, the DSKF adapts its coefficients optimally to achieve the minimum mean square error (MMSE). In time-varying scenarios, the measurements' distribution changes over time due to noise, signal dynamics, multipath, and non-line-of-sight effects. These kinds of scenarios make difficult the search for a suitable measurement and process noise model, leading to a sub-optimal solution of the DSKF. The loop-bandwidth control algorithm (LBCA) can adapt the DSKF according to the time-varying scenario and improve its performance significantly. This study introduces two methods to adapt the DSKF using the LBCA: The LBCA-based DSKF and the LBCA-based lookup table (LUT)-DSKF. The former method adapts the steady-state process noise variance based on the LBCA's loop bandwidth update. In contrast, the latter directly relates the loop bandwidth with the steady-state Kalman gains. The presented techniques are compared with the well-known state-of-the-art carrier-to-noise density ratio (C/N0)-based DSKF. These adaptive tracking techniques are implemented in an open software interface GNSS hardware receiver. For each implementation, the receiver's tracking performance and the system performance are evaluated in simulated scenarios with different dynamics and noise cases. Results confirm that the LBCA can be successfully applied to adapt the DSKF. The LBCA-based LUT-DSKF exhibits superior static and dynamic system performance compared to other adaptive tracking techniques using the DSKF while achieving the lowest complexity.

Keywords: adaptive tracking techniques; direct-state Kalman filter (DSKF); global navigation satellite system (GNSS); lookup table direct-state Kalman filter (LUT-DSKF); loop-bandwidth control algorithm (LBCA); scalar tracking loop (STL).