Robust Adaptive Generalized Correntropy-based Smoothed Graph Signal Recovery with a Kernel Width Learning

This paper proposes a robust adaptive algorithm for smooth graph signal recovery which is based on generalized correntropy. A proper cost function is defined for this purpose. The proposed algorithm is derived and a kernel width learning-based version of the algorithm is suggested which the simulation results show the superiority of it to the fixed correntropy kernel version of the algorithm. Moreover, some theoretical analysis of the proposed algorithm are provided. In this regard, firstly, the convexity analysis of the cost function is discussed. Secondly, the uniform stability of the algorithm is investigated. Thirdly, the mean convergence analysis is also added. Finally, the complexity analysis of the algorithm is incorporated. In addition, some synthetic and real-world experiments show the advantage of the proposed algorithm in comparison to some other adaptive algorithms in the literature of adaptive graph signal recovery

Robust Sensor Fusion for Indoor Wireless Localization

Location knowledge in indoor environment using Indoor Positioning Systems (IPS) has become very useful and popular in recent years. Indoor wireless localization suffers from severe multi-path fading and non-line-of-sight conditions. This paper presents a novel indoor localization framework based on sensor fusion of Zigbee Wireless Sensor Networks (WSN) using Received Signal Strength (RSS). The unknown position is equipped with two or more mobile nodes. The range between two mobile nodes is fixed as priori. The attitude (roll, pitch, and yaw) of the mobile node are measured by inertial sensors (ISs). Then the angle and the range between any two nodes can be obtained, and thus the path between the two nodes can be modeled as a curve. Through an efficient cooperation between two or more mobile nodes, this framework effectively exploits the RSS techniques. This constraint help improve the positioning accuracy. Theoretical analysis on localization distortion and Monte Carlo simulations shows that the proposed cooperative strategy of multiple nodes with extended Kalman filter (EKF) achieves significantly higher positioning accuracy than the existing systems, especially in heavily obstructed scenarios

Quantized generalized minimum error entropy for kernel recursive least squares adaptive filtering

The robustness of the kernel recursive least square (KRLS) algorithm has recently been improved by combining them with more robust information-theoretic learning criteria, such as minimum error entropy (MEE) and generalized MEE (GMEE), which also improves the computational complexity of the KRLS-type algorithms to a certain extent. To reduce the computational load of the KRLS-type algorithms, the quantized GMEE (QGMEE) criterion, in this paper, is combined with the KRLS algorithm, and as a result two kinds of KRLS-type algorithms, called quantized kernel recursive MEE (QKRMEE) and quantized kernel recursive GMEE (QKRGMEE), are designed. As well, the mean error behavior, mean square error behavior, and computational complexity of the proposed algorithms are investigated. In addition, simulation and real experimental data are utilized to verify the feasibility of the proposed algorithms

Maximum Correntropy Ensemble Kalman Filter

In this article, a robust ensemble Kalman filter (EnKF) called MC-EnKF is proposed for nonlinear state-space model to deal with filtering problems with non-Gaussian observation noises. Our MC-EnKF is derived based on maximum correntropy criterion (MCC) with some technical approximations. Moreover, we propose an effective adaptive strategy for kernel bandwidth selection.Besides, the relations between the common EnKF and MC-EnKF are given, i.e., MC-EnKF will converge to the common EnKF when the kernel bandwidth tends to infinity. This justification provides a complementary understanding of the kernel bandwidth selection for MC-EnKF. In experiments, non-Gaussian observation noises significantly reduce the performance of the common EnKF for both linear and nonlinear systems, whereas our proposed MC-EnKF with a suitable kernel bandwidth maintains its good performance at only a marginal increase in computing cost, demonstrating its robustness and efficiency to non-Gaussian observation noises.Comment: Accepted by 62nd IEEE Conference on Decision and Control (CDC 2023

Chandrasekhar-based maximum correntropy Kalman filtering with the adaptive kernel size selection

This technical note is aimed to derive the Chandrasekhar-type recursion for the maximum correntropy criterion (MCC) Kalman filtering (KF). For the classical KF, the first Chandrasekhar difference equation was proposed at the beginning of 1970s. This is the alternative to the traditionally used Riccati recursion and it yields the so-called fast implementations known as the Morf-Sidhu-Kailath-Sayed KF algorithms. They are proved to be computationally cheap because of propagating the matrices of a smaller size than $n \times n$ error covariance matrix in the Riccati recursion. The problem of deriving the Chandrasekhar-type recursion within the MCC estimation methodology has never been raised yet in engineering literature. In this technical note, we do the first step and derive the Chandrasekhar MCC-KF estimators for the case of adaptive kernel size selection strategy, which implies a constant scalar adjusting weight. Numerical examples substantiate a practical feasibility of the newly suggested MCC-KF implementations and correctness of the presented theoretical derivations