We consider the nonlinear robust filtering problem where the measurements are partially disturbed by outliers. A new robust Kalman filter based on a detect-and-reject idea is developed. To identify and exclude outliers automatically, each measurement is assigned an indicator variable, which is modeled by a beta-Bernoulli prior. The mean-field variational Bayesian method is then utilized to estimate the state of interest as well as the indicator in an iterative manner at each time instant. Simulation results reveal that the proposed algorithm outperforms several recent robust solutions with higher computational efficiency and better accuracy.

We consider the problem of user activity detection for grant-free massive connectivity, where a base station, equipped with a large number of antennas, serves a large number of machine type devices. Two massive multiple-input multipleoutput (mMIMO) systems are studied, namely, a collocated mMIMO with physically collocated antennas and a cell-free mMIMO with geographically separated antennas. By utilizing the sporadic transmission nature and the asymptotical orthogonality of channel vectors associated with different users, we propose a correlation-based sparse signal recovery scheme to detect active users. Simulation results are provided to evaluate the performance of the proposed method. Our results show that the cell-free mMIMO achieves much better user activity detection performance than the collocated mMIMO, and thus is more suitable for grant-free massive connectivity. An empirical analysis is performed to explain the superiority of the cell-free system over the collocated system.

We consider the problem of robust estimation involving filtering and smoothing for nonlinear state space models which are disturbed by heavy-tailed impulsive noises. To deal with heavy-tailed noises and improve the robustness of the traditional nonlinear Gaussian Kalman filter and smoother, we propose in this work a general framework of robust filtering and smoothing, which adopts a new maximum correntropy criterion to replace the minimum mean square error for state estimation. To facilitate understanding, we present our robust framework in conjunction with the cubature Kalman filter and smoother. A half-quadratic optimization method is utilized to solve the formulated robust estimation problems, which leads to a new maximum correntropy derivative-free robust Kalman filter and smoother. Simulation results show that the proposed methods achieve a substantial performance improvement over the conventional and existing robust ones with slight computational time increase.

We study the problem of joint wideband spectrum sensing and recovery of multi-band signals in a multi-antenna-based sub-Nyquist sampling framework. Specifically, the multi-band signal is composed of a number of uncorrelated narrowband signals spreading over a wide frequency band. Unlike existing works which assume the source signals impinge on the receiver via a line-of-sight (LOS) path, we consider a more practical unknown MIMO channel which results from multipath propagation. A new sub-Nyquist sampling architecture is proposed, where each antenna output passes through two channels, namely, a direct path and a delayed path with a controlled amount of time delay. The signal at each channel is then sampled by a synchronized low-rate analog-to-digital converter (ADC). We utilize the collected data samples to build a set of cross-correlation matrices with different time lags and develop a CANDECOMP/PARAFAC (CP) decomposition-based method to recover the carrier frequencies, power spectra as well as the source signals themselves. Recovery conditions of the proposed method are analyzed, and Cramér-Rao bound (CRB) results for our estimation problem are derived. Simulation results are presented to illustrate the effectiveness of the proposed method.

In real applications, non-Gaussian distributions are frequently caused by outliers and impulsive disturbances, and these will impair the performance of the Rauch-Tung-Striebel (RTS) smoother. In this study, a modified RTS smoothing algorithm combined with the minimum error entropy (MEE) criterion (MEE-RTS) is developed, and by employing the Taylor series linearization method, it is also expanded to the state estimation of nonlinear systems. The proposed methods improve the robustness of the conventional RTS smoother against complex non-Gaussian noises. In addition, we examine the MEE-RTS smoother's mean error behavior, mean square error behavior, and computational complexity, and the performance of the proposed algorithms is verified by comparing it with existing RTS -type smoothers.