Bayesian Estimation on Lie Group With Von Mises Distribution: Application to R-Mode Phase Denoising

Several precise positioning systems rely on carrier phase measurements, which enable centimeter-level accuracy. However, these measurements are significantly affected by additive noise, degrading the performance of phase-based positioning estimators. To better capture the statistical behavior of carrier phase observations, we pro pose to model phase measurements with a von Mises distribution. Then, to perform precise navigation, it is fun damental to estimate its parameters. To ensure estimation consistency and the respect of the underlying geometric constraints, we propose to perform their estimation within a Lie group framework. Furthermore, we adopt a Bayesian approach, where prior information about the parameters is assumed within the space SO(2)×R+. The proposed method ology provides a full Bayesian formulation that incorpo rates prior knowledge, solved through a Newton algorithm on Lie groups. This approach demonstrates advantages in terms of robustness and precision, especially when dealing with a small number of observations, compared to traditional Euclidean-based and frequentist methods. Further more, we validate the approach through simulations with a real navigation dataset.