Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation

Disturbance observers have been attracting continuing research efforts and are widely used in many applications. Among them, the Kalman filter-based disturbance observer is an attractive one since it estimates both the state and the disturbance simultaneously, and is optimal for a linear system with Gaussian noises. Unfortunately, The noise in the disturbance channel typically exhibits a heavy-tailed distribution because the nominal disturbance dynamics usually do not align with the practical ones. To handle this issue, we propose a generalized multi-kernel maximum correntropy Kalman filter for disturbance estimation, which is less conservative by adopting different kernel bandwidths for different channels and exhibits excellent performance both with and without external disturbance. The convergence of the fixed point iteration and the complexity of the proposed algorithm are given. Simulations on a robotic manipulator reveal that the proposed algorithm is very efficient in disturbance estimation with moderate algorithm complexity.Comment: in IEEE Transactions on Automatic Control (2023

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

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

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

LQ non-Gaussian Control with I/O packet losses

The paper concerns the Linear Quadratic non-Gaussian (LQnG) sub-optimal control problem when the input and output signals travel through an unreliable network, namely Gilbert-Elliot channels. In particular, the input/output packet losses are modeled by Bernoulli sequences, and we assume that the moments of the non-Gaussian noises up to the fourth order are known. By mean of a suitable rewriting of the system through an intermittent output injection term, and by considering an augmented system with the second-order Kronecker power of the measurements, a simple solution is provided by substituting the Kalman predictor with intermittent observations of the LQG control law with a quadratic optimal predictor. Numerical simulations show the effectiveness of the proposed method

Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis

The maximum correntropy criterion (MCC) has been employed to design outlier-robust adaptive filtering algorithms, among which the recursive MCC (RMCC) algorithm is a typical one. Motivated by the success of our recently proposed proportionate recursive least squares (PRLS) algorithm for sparse system identification, we propose to introduce the proportionate updating (PU) mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC (CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination of two PRMCC filters. For PRMCC, its stability condition and mean-square performance were analyzed. Based on the analysis, optimal parameter selection in nonstationary environments was obtained. Performance study of CPRMCC was also provided and showed that the CPRMCC performs at least as well as the better component PRMCC filter in steady state. Numerical simulations of sparse system identification corroborate the advantage of proposed algorithms as well as the validity of theoretical analysis

Maximum Correntropy Filtering for Complex Networks With Uncertain Dynamical Bias: Enabling Componentwise Event-Triggered Transmission

10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 62203016, U2241214, T2121002 and 61933007);; 10.13039/501100002858-China Postdoctoral Science Foundation (Grant Number: 2021TQ0009); Royal Society, U (Grant Number: 0000DONOTUSETHIS0000.K); Alexander von Humboldt Foundation of Germany