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 ()-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.
Highlights
The direct-state Kalman filter (DSKF) can be simplified considering the convergence of the Kalman gains in the steady-state, referred to as the dashed blue line
The LBCAbased DSKF, and the loop-bandwidth control algorithm (LBCA)-based lookup table (LUT)-DSKF are analyzed using the weighting function defined in Equation (48)
This study presents the first proof of the LBCA’s general applicability to any control system by implementing it in the DSKF
Summary
Global navigation satellite system (GNSS) receivers synchronize with GNSS signals to decode the navigation message, measure the pseudo-range and pseudo-range rate, and calculate a position, velocity, and time (PVT) solution [1,2]. The synchronization consists of two stages: Acquisition and tracking. Acquisition performs a coarse estimate of the synchronization parameters, whereas the tracking stage provides an improved estimate. The latter stage uses the scalar tracking loop (STL) to refine the synchronization of the incoming GNSS signals [3,4]. The STL replicates a synchronization parameter for every loop iteration. The carrier phase θ, the carrier Doppler f d , and the code phase τ are the GNSS signal parameters in which the GNSS receiver must synchronize. A correlator, a discriminator, a loop filter, and a numerically controlled oscillator (NCO)
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