Variational Bayesian learning for robust AR modeling with the presence of sparse impulse noise

A single distribution is typically used to model the innovations of an autoregressive (AR) model. However, sparse impulses may exist within the innovations which may cause outliers in the observations. These impulses cannot be modeled by a single distribution and may potentially degrade the estimation. In this study, the innovation of an AR model is modeled by using both a Gaussian noise component and a sparse impulse noise model in order to obtain robust estimation and estimation of the impulses simultaneously. The Gaussian distribution models the normal noise and the sparse impulse noise model models the sparse abnormal innovation impulses. A hierarchal Bayesian model is built for the proposed model. Automatic relevance determination (ARD) priors are set for both the coefficients and the sparse impulses. A Variational Bayesian (VB) learning algorithm is given to estimate the parameters of the model. Experimental results show that the proposed model with the learning algorithm is valid for AR models with outliers caused by sparse innovation impulses, the coefficient estimation accuracy is better than other methods, and the sparse impulses can be estimated simultaneously.     

High-resolution ISAR imaging of fast rotating targets based on pattern-coupled Bayesian strategy for multiple measurement vectors

Very high resolution inverse synthetic aperture radar (ISAR) imaging of fast rotating targets is a complicated task. There may be insufficient pulses or may introduce migration through range cells (MTRC) during the coherent processing interval (CPI) when we use the conventional range Doppler (RD) ISAR technique. With compressed sensing (CS) technique, we can achieve the high-resolution ISAR imaging of a target with limited number of pulses. Sparse representation based method can achieve the super resolution ISAR imaging of a target with a short CPI, during which the target rotates only a small angle and the range migration of the scatterers is small. However, traditional CS-based ISAR imaging method generally faced with the problem of basis mismatch, which may degrade the ISAR image. To achieve the high resolution ISAR imaging of fast rotating targets, this paper proposed a pattern-coupled sparse Bayesian learning method for multiple measurement vectors, i.e. the PC-MSBL algorithm. A multi-channel pattern-coupled hierarchical Gaussian prior is proposed to model the pattern dependencies among neighboring range cells and correct the MTRC problem. The expectation-maximization (EM) algorithm is used to infer the maximum a posterior (MAP) estimate of the hyperparameters. Simulation results validate the effectiveness and superiority of the proposed algorithm.     

Robust adaptive algorithm for nonlinear systems with unknown measurement noise and uncertain parameters by variational Bayesian inference

This paper studies an adaptive algorithm for the estimation problem of nonlinear systems with unknown or missing measurement noise and uncertain parameters using variational Bayesian (VB) inference. We combine VB inference with the Monte Carlo sampling technique to settle this problem. There are many cases of missing information, and because of the difficulty in obtaining the analytical results, the existing control methods for uncertain systems lack generality. We present a set of nonlinear recursive adaptive filtering algorithms that address the unknown parameters and probability density function. The proposed algorithms yield a separable variational approximation of the joint posterior distribution of noise parameters with uncertain parameters and states on each step separately. Estimation convergence and robustness against disturbances are guaranteed. A convergence result for VB inference is presented. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms.