Novel Computational Methods for State Space Filtering

The state-space formulation for time-dependent models has been long used invarious applications in science and engineering. While the classical Kalman filter(KF) provides optimal posterior estimation under linear Gaussian models, filteringin nonlinear and non-Gaussian environments remains challenging.Based on the Monte Carlo approximation, the classical particle filter (PF) can providemore precise estimation under nonlinear non-Gaussian models. However, it suffers fromparticle degeneracy. Drawing from optimal transport theory, the stochastic map filter(SMF) accommodates a solution to this problem, but its performance is influenced bythe limited flexibility of nonlinear map parameterisation. To account for these issues,a hybrid particle-stochastic map filter (PSMF) is first proposed in this thesis, wherethe two parts of the split likelihood are assimilated by the PF and SMF, respectively.Systematic resampling and smoothing are employed to alleviate the particle degeneracycaused by the PF. Furthermore, two PSMF variants based on the linear and nonlinearmaps (PSMF-L and PSMF-NL) are proposed, and their filtering performance is comparedwith various benchmark filters under different nonlinear non-Gaussian models.Although achieving accurate filtering results, the particle-based filters require expensive computations because of the large number of samples involved. Instead, robustKalman filters (RKFs) provide efficient solutions for the linear models with heavy-tailednoise, by adopting the recursive estimation framework of the KF. To exploit the stochasticcharacteristics of the noise, the use of heavy-tailed distributions which can fit variouspractical noises constitutes a viable solution. Hence, this thesis also introduces a novelRKF framework, RKF-SGαS, where the signal noise is assumed to be Gaussian and theheavy-tailed measurement noise is modelled by the sub-Gaussian α-stable (SGαS) distribution. The corresponding joint posterior distribution of the state vector and auxiliaryrandom variables is estimated by the variational Bayesian (VB) approach. Four differentminimum mean square error (MMSE) estimators of the scale function are presented.Besides, the RKF-SGαS is compared with the state-of-the-art RKFs under three kinds ofheavy-tailed measurement noises, and the simulation results demonstrate its estimationaccuracy and efficiency.One notable limitation of the proposed RKF-SGαS is its reliance on precise modelparameters, and substantial model errors can potentially impede its filtering performance. Therefore, this thesis also introduces a data-driven RKF method, referred to asRKFnet, which combines the conventional RKF framework with a deep learning technique. An unsupervised scheduled sampling technique (USS) is proposed to improve theistability of the training process. Furthermore, the advantages of the proposed RKFnetare quantified with respect to various traditional RKFs

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

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

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

Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond

This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since 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

Robust state estimation methods for robotics applications

State estimation is an integral component of any autonomous robotic system. Finding the correct position, velocity, and orientation of an agent in its environment enables it to do other tasks like mapping and interacting with the environment, and collaborating with other agents. State estimation is achieved by using data obtained from multiple sensors and fusing them in a probabilistic framework. These include inertial data from Inertial Measurement Unit (IMU), images from camera, range data from lidars, and positioning data from Global Navigation Satellite Systems (GNSS) receivers. The main challenge faced in sensor-based state estimation is the presence of noisy, erroneous, and even lack of informative data. Some common examples of such situations include wrong feature matching between images or point clouds, false loop-closures due to perceptual aliasing (different places that look similar can confuse the robot), presence of dynamic objects in the environment (odometry algorithms assume a static environment), multipath errors for GNSS (signals for satellites jumping off tall structures like buildings before reaching receivers) and more. This work studies existing and new ways of how standard estimation algorithms like the Kalman filter and factor graphs can be made robust to such adverse conditions without losing performance in ideal outlier-free conditions. The first part of this work demonstrates the importance of robust Kalman filters on wheel-inertial odometry for high-slip terrain. Next, inertial data is integrated into GNSS factor graphs to improve the accuracy and robustness of GNSS factor graphs. Lastly, a combined framework for improving the robustness of non-linear least squares and estimating the inlier noise threshold is proposed and tested with point cloud registration and lidar-inertial odometry algorithms followed by an algorithmic analysis of optimizing generalized robust cost functions with factor graphs for GNSS positioning problem

Maximum Correntropy Based Unscented Particle Filter for Cooperative Navigation with Heavy-Tailed Measurement Noises

In this paper, a novel robust particle filter is proposed to address the measurement outliers occurring in the multiple autonomous underwater vehicles (AUVs) based cooperative navigation (CN). As compared with the classic unscented particle filter (UPF) based on Gaussian assumption of measurement noise, the proposed robust particle filter based on the maximum correntropy criterion (MCC) exhibits better robustness against heavy-tailed measurement noises that are often induced by measurement outliers in CN systems. Furthermore, the proposed robust particle filter is computationally much more efficient than existing robust UPF due to the use of a Kullback-Leibler distance-resampling to adjust the number of particles online. Experimental results based on actual lake trial show that the proposed maximum correntropy based unscented particle filter (MCUPF) has better estimation accuracy than existing state-of-the-art robust filters for CN systems with heavy-tailed measurement noises, and the proposed MCUPF has lower computational complexity than existing robust particle filters