Multi-kernel Correntropy Regression: Robustness, Optimality, and Application on Magnetometer Calibration

This paper investigates the robustness and optimality of the multi-kernel correntropy (MKC) on linear regression. We first derive an upper error bound for a scalar regression problem in the presence of arbitrarily large outliers and reveal that the kernel bandwidth should be neither too small nor too big in the sense of the lowest upper error bound. Meanwhile, we find that the proposed MKC is related to a specific heavy-tail distribution, and the level of the heavy tail is controlled by the kernel bandwidth solely. Interestingly, this distribution becomes the Gaussian distribution when the bandwidth is set to be infinite, which allows one to tackle both Gaussian and non-Gaussian problems. We propose an expectation-maximization (EM) algorithm to estimate the parameter vectors and explore the kernel bandwidths alternatively. The results show that our algorithm is equivalent to the traditional linear regression under Gaussian noise and outperforms the conventional method under heavy-tailed noise. Both numerical simulations and experiments on a magnetometer calibration application verify the effectiveness of the proposed method

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

Resilient dynamic state estimation for power system using Cauchy-kernel-based maximum correntropy cubature Kalman filter

Accurate estimation of dynamic states is the key to monitoring power system operating conditions and controlling transient stability. The inevitable non-Gaussian noise and randomly occurring denial-of-service (DoS) attacks may, however, deteriorate the performance of standard filters seriously. To deal with these issues, a novel resilient cubature Kalman filter based on the Cauchy kernel maximum correntropy (CKMC) optimal criterion approach (termed CKMC-CKF) is developed, in which the Cauchy kernel function is used to describe the distance between vectors. Specifically, the errors of state and measurement in the cost function are unified by a statistical linearization technique, and the optimal estimated state is acquired by the fixed-point iteration method. Because of the salient thick-tailed feature and the insensitivity to the kernel bandwidth (KB) of Cauchy kernel function, the proposed CKMC-CKF can effectively mitigate the adverse effect of non-Gaussian noise and DoS attacks with better numerical stability. Finally, the efficacy of the proposed method is demonstrated on the standard IEEE 39-bus system under various abnormal conditions. Compared with standard cubature Kalman filter (CKF) and maximum correntropy criterion CKF (MCC-CKF), the proposed algorithm reveals better estimation accuracy and stronger resilience

Correntropy: Answer to non-Gaussian noise in modern SLAM applications?

The problem of non-Gaussian noise/outliers has been intrinsic in modern Simultaneous Localization and Mapping (SLAM) applications. Despite numerous algorithms in SLAM, it has become crucial to address this problem in the realm of modern robotics applications. This work focuses on addressing the above-mentioned problem by incorporating the usage of correntropy in SLAM. Before correntropy, multiple attempts of dealing with non-Gaussian noise have been proposed with significant progress over time but the underlying assumption of Gaussianity might not be enough in real-life applications in robotics.Most of the modern SLAM algorithms propose the `best' estimates given a set of sensor measurements. Apart from addressing the non-Gaussian problems in a SLAM system, our work attempts to address the more complex part concerning SLAM: (a) If one of the sensors gives faulty measurements over time (`Faulty' measurements can be non-Gaussian in nature), how should a SLAM framework adapt to such scenarios? (b) In situations where there is a manual intervention or a 3rd party attacker tries to change the measurements and affect the overall estimate of the SLAM system, how can a SLAM system handle such situations?(addressing the Self Security aspect of SLAM). Given these serious situations how should a modern SLAM system handle the issue of the previously mentioned problems in (a) and (b)? We explore the idea of correntropy in addressing the above-mentioned problems in popular filtering-based approaches like Kalman Filters(KF) and Extended Kalman Filters(EKF), which highlights the `Localization' part in SLAM. Later on, we propose a framework of fusing the odometeries computed individually from a stereo sensor and Lidar sensor (Iterative Closest point Algorithm (ICP) based odometry). We describe the effectiveness of using correntropy in this framework, especially in situations where a 3rd party attacker attempts to corrupt the Lidar computed odometry. We extend the usage of correntropy in the `Mapping' part of the SLAM (Registration), which is the highlight of our work. Although registration is a well-established problem, earlier approaches to registration are very inefficient with large rotations and translation. In addition, when the 3D datasets used for alignment are corrupted with non-Gaussian noise (shot/impulse noise), prior state-of-the-art approaches fail. Our work has given birth to another variant of ICP, which we name as Correntropy Similarity Matrix ICP (CoSM-ICP), which is robust to large translation and rotations as well as to shot/impulse noise. We verify through results how well our variant of ICP outperforms the other variants under large rotations and translations as well as under large outliers/non-Gaussian noise. In addition, we deploy our CoSM algorithm in applications where we compute the extrinsic calibration of the Lidar-Stereo sensor as well as Lidar-Camera calibration using a planar checkerboard in a single frame. In general, through results, we verify how efficiently our approach of using correntropy can be used in tackling non-Gaussian noise/shot noise/impulse noise in robotics applications

Robust dynamic CPU resource provisioning in virtualized servers

We present robust dynamic resource allocation mechanisms to allocate application resources meeting Service Level Objectives (SLOs) agreed between cloud providers and customers. In fact, two filter-based robust controllers, i.e. H∞ filter and Maximum Correntropy Criterion Kalman filter (MCC-KF), are proposed. The controllers are self-adaptive, with process noise variances and covariances calculated using previous measurements within a time window. In the allocation process, a bounded client mean response time (mRT) is maintained. Both controllers are deployed and evaluated on an experimental testbed hosting the RUBiS (Rice University Bidding System) auction benchmark web site. The proposed controllers offer improved performance under abrupt workload changes, shown via rigorous comparison with current state-of-the-art. On our experimental setup, the Single-Input-Single-Output (SISO) controllers can operate on the same server where the resource allocation is performed; while Multi-Input-Multi-Output (MIMO) controllers are on a separate server where all the data are collected for decision making. SISO controllers take decisions not dependent to other system states (servers), albeit MIMO controllers are characterized by increased communication overhead and potential delays. While SISO controllers offer improved performance over MIMO ones, the latter enable a more informed decision making framework for resource allocation problem of multi-tier applications