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In this article, a novel normal-skew mixture (NSM) distribution is presented to model the normal and/or heavy-tailed and/or skew nonstationary distributed noises. The NSM distribution can be formulated as a hierarchically Gaussian presentation by leveraging a Bernoulli distributed random variable. Based on this, a novel robust Kalman filtering framework can be developed utilizing the variational Bayesian method, where the one-step prediction and measurement-likelihood densities are modeled as NSM distributions. For implementation, several exemplary robust Kalman filters (KFs) are derived based on some specific cases of NSM distribution. The relationships between some existing robust KFs and the presented framework are also revealed. The superiority of the proposed robust Kalman filtering framework is validated by a target tracking simulation example. [ABSTRACT FROM AUTHOR]

As a powerful tool for real-time battery management, the extended Kalman filter (EKF) can achieve an online estimation for state of charge (SOC). The EKF, however, may yield biased estimates since the measured system suffers from the abnormal operation conditions, i.e., sensor faults, sensor bias and sensor noise. Thus, this paper proposes a robust extended Kalman filter based on maximum multi-kernel correntropy (MMKC-EKF) for SOC estimate when the system is subjected to complex non-Gaussian disturbances. To derive MMKC-EKF, a batch-mode regression is formulated by integrating the uncertainties of process and measurement, which is solved by using maximum multi-kernel correntropy (MMKC) criterion to suppress the influences of abnormal conditions. An effective optimization method is introduced to determine the free parameters of MMKC, and a fixed-point iteration method gives the state estimation. Then, the posterior error covariance matrix is updated with the help of total influence function, which contributes to the robustness improvement. In addition, a novel filtering scheme is presented for reducing computational complexity, which is beneficial for solving battery pack state estimation in practice. Extensive simulations are carried out for SOC estimate to validate the accuracy and robustness of the proposed MMKC-EKF in the Gaussian and non-Gaussian distributed process and measurement noises. • In MMKC-EKF, a batch-mode regression is established, which is optimized by the MMKC. • The fixed-point iteration algorithm and total influence are used to update the posterior state and error covariance matrix, respectively. • An effective optimization method is introduced to determine the free parameters of MMKC. • A novel design scheme is also adopted to save the computational time. [ABSTRACT FROM AUTHOR]

Existing robust state estimation methods are generally unable to distinguish model uncertainties (state outliers) from measurement outliers as they only exploit the current measurement. In this article, the measurements in a sliding window are, therefore, utilized to better distinguish them, and an adaptive method is embedded, leading to a sliding window variational outlier-robust Kalman filter based on Student’s t-noise modeling. Target tracking simulations and experiments show that the tracking accuracy and consistency of the proposed filter are superior to those of the existing state-of-the-art outlier-robust methods thanks to the improved ability to identify the outliers but at a cost of greater computational burden. [ABSTRACT FROM AUTHOR]

In this paper, elliptically contoured (EC) distributions are used to model outlier-contaminated measurement noises. Exploiting a heuristic approach to introduce an unknown parameter, we present an analytical update form of the joint posterior probability density function of the state vector and auxiliary random variable, from which a novel robust EC distributions-based Kalman filtering framework is first derived. To illustrate the effectiveness of the proposed framework, the convergence, robustness, optimality and computational complexity analyses of the proposed method are then given. In addition, to cope with complex noise environments, the interaction multiple model is employed to achieve the adaptive selection of EC distributions such that well-behaved estimation performance can be obtained for different noise cases. Simulation results demonstrate the validity and superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this article, a new position loci-based in-motion initial alignment method is proposed for a low-cost attitude and heading reference system (AHRS). A new sliding-window-based position integration method is proposed to construct the position vector observations, which weakens the accumulated errors induced by the inertial measurement unit (IMU) bias errors in vector observations. Also, a new closed-loop method is proposed to jointly estimate the time-varying body attitude matrix and the unknown IMU biases and global position system (GPS) lever-arm based on the Kalman filter. The estimates of the time-varying body attitude matrix, IMU biases, and GPS lever-arm are all used to construct and compensate for the position vector observations, which improves the alignment accuracy. Both the simulation and car-mounted test results illustrate that the proposed alignment method can achieve better alignment accuracy than these existing methods for a position loci-aided low-cost AHRS. [ABSTRACT FROM AUTHOR]

Purpose: Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion. Design/methodology/approach: This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model. Findings: While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination. Practical implications: The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models. Originality/value: The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation. [ABSTRACT FROM AUTHOR]

In order to improve the computational efficiency and alignment accuracy of a microelectromechanical system (MEMS)-based strap-down inertial navigation system (SINS), this article proposes a high-accuracy global positioning system (GPS)-aided coarse alignment method. The attitude matrix between current and initial body frames and the unknown gyro bias, accelerometer bias, and lever arm are jointly estimated based on the proposed closed-loop approach, where the attitude error and unknown parameters are jointly inferred based on the derived linear state-space model using the Kalman filter. Simulation and experimental results illustrate that the proposed GPS-aided coarse alignment method can achieve better accuracy than existing state-of-the-art coarse alignment methods for MEMS-based SINS. [ABSTRACT FROM AUTHOR]

A novel robust Rauch–Tung–Striebel smoothing framework is proposed based on a generalized Gaussian scale mixture (GGScM) distribution for a linear state-space model with heavy-tailed and/or skew noises. The state trajectory, mixing parameters, and unknown distribution parameters are jointly inferred using the variational Bayesian approach. As such, a major contribution of this paper is unifying results within the GGScM distribution framework. Simulation and experimental results demonstrate that the proposed smoother has better accuracy than existing smoothers. [ABSTRACT FROM AUTHOR]

A novel variational Bayesian (VB)-based adaptive Kalman filter (AKF) is proposed to solve the filtering problem of a linear system with unknown probability of measurement loss. The sum of two likelihood functions is transformed into an exponential multiplication form, and the state vector, the Bernoulli random variable and the probability of measurement loss are jointly inferred based on the VB approach. Simulation results demonstrate the superiority of the proposed AKF as compared with the existing filtering algorithms with unknown probability of measurement loss. [ABSTRACT FROM AUTHOR]

In this paper, a new robust Kalman filtering framework for a linear system with non-Gaussian heavy-tailed and/or skewed state and measurement noises is proposed through modeling one-step prediction and likelihood probability density functions as Gaussian scale mixture (GSM) distributions. The state vector, mixing parameters, scale matrices, and shape parameters are simultaneously inferred utilizing standard variational Bayesian approach. As the implementations of the proposed method, several solutions corresponding to some special GSM distributions are derived. The proposed robust Kalman filters are tested in a manoeuvring target tracking example. Simulation results show that the proposed robust Kalman filters have a better estimation accuracy and smaller biases compared to the existing state-of-the-art Kalman filters. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive Kalman filter is proposed for a linear Gaussian state-space model with inaccurate noise statistics based on the variational Bayesian (VB) approach. Both the prior joint probability density function (PDF) of the one-step prediction and corresponding prediction error covariance matrix and the joint PDF of the mean vector and covariance matrix of measurement noise are selected as Normal-inverse-Wishart (NIW), from which a new NIW-based hierarchical Gaussian state-space model is constructed. The state vector, the one-step prediction and corresponding prediction error covariance matrix, and the mean vector and covariance matrix of measurement noise are jointly estimated based on the constructed hierarchical Gaussian state-space model using the VB approach. Simulation results show that the proposed filter has better estimation accuracy than existing state-of-the-art adaptive Kalman filters. [ABSTRACT FROM AUTHOR]

To solve the problem of unknown noise covariance matrices inherent in the cooperative localization of autonomous underwater vehicles, a new adaptive extended Kalman filter is proposed. The predicted error covariance matrix and measurement noise covariance matrix are adaptively estimated based on an online expectation-maximization approach. Experimental results illustrate that, under the circumstances that are detailed in the paper, the proposed algorithm has better localization accuracy than existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the in-motion coarse alignment (IMCA) for odometer-aided strap-down inertial navigation system (SINS) is investigated with the main focus on compensating for the dynamic errors of gyroscope induced by severe maneuvering. A new Kalman-filtering-based IMCA method for an odometer-aided SINS is presented. A novel closed-loop approach to estimating the attitude matrix from the current body frame to the initial body frame is proposed, in which the attitude error between the closed-loop calculation and the true attitude matrix is first estimated, and then, the estimated attitude matrix is obtained by refining the closed-loop calculation with the estimated attitude error. A linear state-space model for the attitude error is derived, and then, a Kalman filter is employed to track the attitude error. Experimental results illustrate that the proposed closed-loop approach can estimate the attitude matrix from the current body frame to the initial body frame better than the existing open-loop approach, which results in improved alignment accuracy as compared with the existing optimization-based alignment method for the odometer-aided SINS when the vehicle maneuvers severely. [ABSTRACT FROM AUTHOR]

A novel robust Student's t-based Kalman filter is proposed by using the variational Bayesian approach, which provides a Gaussian approximation to the posterior distribution. Simulation results for a manoeuvring target tracking example illustrate that the proposed filter has smaller root mean square error and bias than existing filters. [ABSTRACT FROM PUBLISHER]

In this study, the authors focus on improving measurement update of existing nonlinear Kalman approximation filter and propose a new sigma-point Kalman filter with recursive measurement update. Statistical linearization technique based on sigma transformation is utilized in the proposed filter to linearize the nonlinear measurement function, and linear measurement update is applied gradually and repeatedly based on the statistically linearized measurement equation. The total measurement update of the proposed filter is nonlinear, and the proposed filter can extract state information from nonlinear measurement better than existing nonlinear filters. Simulation results show that the proposed method has higher estimation accuracy than existing methods. [ABSTRACT FROM AUTHOR]

The choice of free parameter in embedded cubature Kalman filter (ECKF) is important, and it is difficult to choose an optimal value in practice. To solve this problem, an adaptive method is proposed to determine the value of free parameter of ECKF based on maximum likelihood criterion. By incorporating this method in the third-degree ECKF, a new third-degree adaptive ECKF (AECKF) algorithm is obtained. To further improve the accuracy of the third-degree AECKF, a new fifth-degree AECKF based on the fifth-degree embedded cubature rule is developed. Simulation results show that the proposed algorithms have higher estimation accuracy than existing methods. [ABSTRACT FROM AUTHOR]