Robust estimation of high-order phase dynamics using Variational Bayes inference

Abstract

Cycle slips strongly impact the performance of phase tracking algorithm leading, in the worst case, to a permanent loss of lock of the signal. In this paper, we propose a new nonlinear phase estimator to obtain more robust tracks. The latter stems from a Variational Bayes (VB) approximation used within the optimal Bayesian filtering formulation in case of highorder phase dynamics. A comparison with a more conventional technique, namely a Kalman filter based PLL (Phase Lock Loop), is performed in terms of mean square error of the phase estimate and mean time to first slip. Results show that the proposed method outperforms the conventional linear filter with respect to both metrics, especially at low signal-to-noise ratio.

A Tight Coupling Algorithm for Strapdown Inertial Navigation System (SINS)/Global Positioning System (GPS) Adaptive Integrated Navigation Based on Variational Bayesian

“…Its time complexity is lower than UKF, and it avoids the high-order divergence problem of EKF [7,10,11]. Additionally, it was discovered that using VB as a method for computing high-order integrals in complex measurement models or unmeasured models is possible through the process of learning from the Bayesian notion, which is the foundation of the KF algorithm [14,15]. Therefore, VB is used to realize the synchronous estimation of the state and the measurement noise variance [19].…”

“…is the set of measurements from the initial moment to moment K. According to reference [15], the core idea of Bayesian filtering is that, after the state posterior probability density function ( )…”

“…Then, the derivation defines that Y = {y 1 , y 2 , • • • y k } is the set of measurements from the initial moment to moment K. According to reference [15], the core idea of Bayesian filtering is that, after the state posterior probability density function P(x k |Y k ) at moment k is known, the state posterior probability density function at the next moment P(x k+1 |Y k+1 ) can be updated by using the measurement value z k+1 at the next moment in the process of time updating and measurement updating. In the time-updating step, the one-step state prediction probability density function p(x k+1 |Y k ) is computed by the integral of the following equation:…”

“…Additionally, the noise-tracking ability, which fluctuates independently in the covariance matrix, can be adjusted separately by modifying the weight ρ. From (15), it can be seen that the parameter to be estimated is only related to ρ, which is usually ρ ∈ (0, 1]. A lower value of ρ means that the predicted value of the variance parameter is less related to the previous time, and the actual measurement noise changes more sharply.…”