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

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.

Multi-Parameter Adaptive Notch Filter (MPANF) for Enhanced Interference Mitigation

“…However, this article focuses on FLL-based methods, as they are simple to use with the LBCA. The LBCA also synergizes with Kalman filters (Cortés et al, 2022), which is an exciting topic for future research.…”

Evaluation of Low-Complexity Adaptive Full Direct-State Kalman Filter for Robust GNSS Tracking

“…There are several KF implementation methods in STLs [ 18 ] grouped into error-state Kalman-filter (ESKF) and direct-state Kalman filter (DSKF) [ 19 ]. The former replaces the loop filter of the STL with a KF [ 20 , 21 , 22 , 23 ], whereas the latter considers the whole STL as part of the KF [ 24 , 25 , 26 , 27 , 28 ]. The implementation of the DSKF is straightforward due to the relation between the STL’s coefficients and the DSKF’s Kalman gains [ 24 ].…”

“…There has been significant research towards robust tracking solutions to solve this problem [ 30 ]. However, there are still ample opportunities to find the best technique in terms of performance and complexity [ 25 , 31 ]. Adaptive tracking methods can improve the tracking performance in time-varying scenarios.…”

“…Despite the tracking performance advantage of the KF, its implementation in real-time applications requires a high computational cost compared to the STL. Therefore, efficient low-complexity methods have been studied [ 23 , 25 ]. The complexity of the ESKF can be reduced by taking advantage of the Kalman gain convergence in the steady state [ 23 ].…”

FPGA-Based Autonomous GPS-Disciplined Oscillatorsfor Wireless Sensor Network Nodes

“…High-precision Global Positioning System (GPS)-disciplined oscillators (GPSDOs) have been designed to work as a source of reference timing, whose output is controlled to agree with the clock signals generated and broadcast by GPS in the Global Navigation Satellite System (GNSS) [1,2]. GPSDOs are widely used in measurement devices and communication systems due to their cost-effective, high-precision, and self-calibrating operation.…”