Ionospheric Scintillation Mitigation With Kalman PLLs Employing Radial Basis Function Networks

We investigate two adaptive Kalman phase-locked loop (PLL) structures for ionospheric scintillation mitigation for global navigation satellite systems receivers, employing radial basis function (RBF) networks to model the scintillation phase and amplitude, instead of the typically employed autoregressive (AR) models. In the first structure, the Kalman filter innovations are computed by the arctangent phase discriminator, and the state estimates are directly employed in the carrier replica generation. In the second structure, the Kalman filter measurements are the prompt correlator outputs, and the error states are computed and used by a state feedback controller to provide a control signal to drive the carrier replica generation. The nonlinear RBFs provide more flexibility to capture nonlinear dynamics evolving with time, possibly present in the scintillation phase and amplitude. The weights of the RBF networks and the covariance matrices of the process and measurement noise of the Kalman filters are estimated online in the adaptive Kalman PLL structures. Simulations with synthetic severe scintillation data show the capability of the proposed Kalman PLLs to improve robustness to scintillation effects in carrier synchronization, with performance similar to the corresponding structures employing AR scintillation models. Simulations using recorded scintillation data collected by a commercial receiver highlight the learning and generalization capability of the RBF networks to cope with evolving scintillation characteristics over time with possibly nonlinear effects. The Kalman PLL structures employing the RBF networks present reduced errors compared with the structures using AR models.