Variational Bayes phase tracking for correlated dual-frequency measurements with slow dynamics

We consider the problem of estimating the absolute phase of a noisy signal when this latter consists of correlated dual-frequency measurements. This scenario may arise in many application areas such as global navigation satellite system (GNSS). In this paper, we assume a slow varying phase and propose accordingly a Bayesian filtering technique that makes use of the frequency diversity. More specifically, the method results from a variational Bayes approximation and belongs to the class of nonlinear filters. Numerical simulations are performed to assess the performance of the tracking technique especially in terms of mean square error and cycle-slip rate. Comparison with a more conventional approach, namely a Gaussian sum estimator, shows substantial improvements when the signal-to-noise ratio and/or the correlation of the measurements are low.