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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]

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 cooperative localization for autonomous underwater vehicles (AUVs), the practical stochastic noise may be heavy-tailed, and nonstationary distributed because of acoustic speed variation, multipath effect of acoustic channel, and changeable underwater environment. To address such noise, a novel heavy-tailed mixture (HTM) distribution is first proposed in this article, and then expressed as a hierarchical Gaussian form by employing a categorical distributed auxiliary vector. Based on that, a novel HTM distribution based robust Kalman filter is proposed, where the one-step prediction, and measurement likelihood probability density functions are, respectively, modeled as an HTM distribution, and a Normal-Gamma-inverse Wishart distribution. The proposed filter is verified by a lake experiment about cooperative localization for AUVs. Compared with the cutting-edge filter, the proposed filter has been improved by 50.27% in localization error but no more than twice computational time is required. [ABSTRACT FROM AUTHOR]

In cooperative localization for autonomous underwater vehicles (AUVs), the practical state and measurement noises may be non-stationary non-Gaussian distributed because of sensor outliers, multi-path effect of acoustic channel, and changeable underwater environment. In this paper, a couple of novel mixture distributions, i.e., the Gaussian-Slash mixture distribution and the Gaussian-generalized hyperbolic skew Student’s t mixture distribution, are proposed to model such state and measurement noises, respectively. By introducing two Bernoulli distributed random variables, both the proposed mixture distributions can be expressed as hierarchically Gaussian forms. Based on this, a novel mixture distributions based robust Kalman filter (MDRKF) is derived by exploiting the variational Bayesian inference. A lake experiment about the cooperative localization for AUVs demonstrated that the proposed MDRKF has better localization accuracy but higher computational complexity than the existing state-of-the-art filtering algorithms. [ABSTRACT FROM AUTHOR]

A slide window variational adaptive Kalman filter is presented in this brief based on adaptive learning of inaccurate state and measurement noise covariance matrices, which is composed of the forward Kalman filtering, the backward Kalman smoothing, and the online estimates of noise covariance matrices. By imposing an approximation on the smoothing posterior distribution of slide window state vectors, the posterior distributions of noise covariance matrices can be analytically updated as inverse Wishart distributions by exploiting the variational Bayesian method, which avoids the fixed-point iterations and achieves good computational efficiency. Simulation comparisons demonstrate that the proposed method has better filtering accuracy and consistency than the existing cutting-edge method. [ABSTRACT FROM AUTHOR]

To better solve the filtering problem of transfer alignment with an inaccurate measurement noise covariance matrix, a novel computationally efficient version of existing variational adaptive Kalman filter is proposed in this paper, in which an equivalent variational iteration process of the measurement noise covariance matrix is derived. The proposed filter is identical to the existing variational adaptive Kalman filter, but the total computational complexity of algorithm implementation is significantly reduced, which facilitates the application of variational adaptive Kalman filter to transfer alignment. Simulation and experiment results of transfer alignment demonstrate that the computational complexity of the proposed filter is reduced by 55.4% as compared with existing variational adaptive Kalman filter. [ABSTRACT FROM AUTHOR]

This article proposes a new skewed outlier-robust localization algorithm that is based on time-difference of arrival (TDOA) measurements at an airport. A new outlier-robust filtering framework is derived based on the skew Gaussian-gamma mixture (SGGM) distribution, where the state, a mixing parameter, a shape parameter, a scale matrix, and the degrees of freedom (DOFs) are inferred simultaneously using variational Bayesian (VB) approach. An interacting multiple-model (IMM) filter with different kinematic system models is implemented to handle the multimodal dynamics of the vehicle, yielding the IMM-SGGM algorithm. In particular, a new measurement likelihood based on the SGGM distribution is derived utilizing VB inference for the combination procedure in the proposed IMM-SGGM algorithm. Car-mounted experiments using TDOA measurements at an airport were conducted to verify the effectiveness of the proposed algorithm. The performance of the proposed IMM-SGGM algorithm is evaluated through comparisons with the state-of-the-art approaches. The experimental results demonstrate that the proposed IMM-SGGM algorithm has better localization accuracy and robustness to skewed outlier measurements than the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

In this article, we focus on addressing the nonlinear filtering problem with large prior uncertainty but high measurement accuracy, which may be encountered in the application of tightly coupled global navigation satellite system (GNSS)/inertial navigation system (INS) integration. Although the existing methods, such as progressive Gaussian approximate filter (PGAF), can address this problem, it has poor estimation accuracy. To improve the estimation accuracy of PGAF, the step sizes as well as the measurement noise covariance matrix (MNCM) are jointly estimated based on the variational Bayesian approach, from which a novel PGAF with variable step size is developed. Tightly coupled GNSS/INS integration simulations illustrate that the proposed filter outperforms the existing methods both in estimation accuracy and rate of convergence. [ABSTRACT FROM AUTHOR]

This article proposes a novel outlier-robust localization algorithm that is based on time difference of arrival measurements at an airport for multilateration surveillance. An outlier-robust filtering scheme is derived based on Student's- $t$ -distribution, where the state, a scale matrix, and a degree of freedom parameter are estimated simultaneously using variational Bayesian (VB) inference. An interacting multiple model (IMM) filter with different system models is implemented to handle the multimodal dynamics of the aircraft, yielding the IMM-VB algorithm. Specifically, the likelihood function is newly derived using VB inference for the combination procedure in the proposed IMM-VB algorithm. The experimental results obtained from a flight test using a commercial aircraft at an airport demonstrate that the proposed IMM-VB algorithm has better localization accuracy and robustness to outlier measurements than the existing state-of-the-art approaches. [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, a new outlier-robust Student's t based Gaussian approximate filter is proposed to address the heavy-tailed process and measurement noises induced by the outlier measurements of velocity and range in cooperative localization of autonomous underwater vehicles (AUVs). The state vector, scale matrices, and degrees of freedom (DOF) parameters are jointly estimated based on the variational Bayesian approach by using the constructed Student's t based hierarchical Gaussian state-space model. The performances of the proposed filter and existing filters are tested in the cooperative localization of an AUV through a lake trial. Experimental results illustrate that the proposed filter has better localization accuracy and robustness than existing state-of-the-art outlier-robust filters. [ABSTRACT FROM PUBLISHER]

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]

Novel Student?s t based approaches for formulating a filter and smoother, which utilize heavy tailed process and measurement noise models, are found through approximations of the associated posterior probability density functions. Simulation results for manoeuvring target tracking illustrate that the proposed methods substantially outperform existing methods in terms of the root mean square error. [ABSTRACT FROM AUTHOR]

In this letter, a robust Gaussian approximate (GA) fixed-interval smoother for nonlinear systems with heavy-tailed process and measurement noises is proposed. The process and measurement noises are modeled as stationary Student’s t distributions, and the state trajectory and noise parameters are inferred approximately based on the variational Bayesian (VB) approach. Simulation results show the efficiency and superiority of the proposed smoother as compared with existing smoothers. [ABSTRACT FROM PUBLISHER]