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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 paper, an improved variational adaptive Kalman filter for cooperative localization with inaccurate prior information is proposed, in which the prior scale matrix of the one-step prediction error covariance matrix is adaptively estimated by using the expectation-maximization algorithm. A novel alternate iteration strategy is proposed to reduce the computational complexity of the proposed method. Convergence analysis and theoretical comparisons with the existing advanced adaptive Kalman filtering methods are also provided. Based on this, a new master-slave cooperative localization method is proposed. Lake experiment results of cooperative localization for autonomous underwater vehicles demonstrate the advantages of the proposed method over existing methods. Compared with the cutting-edge adaptive master-slave cooperative localization method, the proposed method has been improved by 22.52% in average localization error but no more than twice computational time is needed. [ABSTRACT FROM AUTHOR]

In this brief, an improved Kalman filter is proposed for a linear system with one-step randomly delayed measurement and unknown latency probability. The measurement likelihood function which is a weighted sum of two Gaussian distributions is transformed into an exponential multiplication form via importing a discrete Bernoulli random variable. Then, an hierarchical Gaussian form of the state-space model is established. Finally, an improved Kalman filter is deduced to estimate jointly the augmented state vector and the unknown parameters employing the variational Bayesian and state augmentation approaches. Simulation study indicates that the improved method has superior performance in estimation accuracy than the existing methods on the basis of accurate estimation of the unknown and time-varying latency probability. [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, in order to improve the Student's t-matching accuracy, a novel Kullback-Leibler divergence (KLD) minimization-based matching method is firstly proposed by minimizing the upper bound of the KLD between the true Student's t-density and the approximate Student's t-density. To improve the Student's t-modelling accuracy, a novel KLD minimization-based adaptive method is then proposed to estimate the scale matrices of Student's t-distributions, in which the modified evidence lower bound is maximized. A novel KLD minimization-based adaptive Student's t-filter is derived via combining the proposed Student's t-matching technique and the adaptive method. A manoeuvring target tracking example is provided to demonstrate the effectiveness and potential of the proposed filter. [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]

The probability hypothesis density (PHD) filter is well known for addressing the problem of multiple human tracking for a variable number of targets, and the sequential Monte Carlo implementation of the PHD filter, known as the particle PHD filter, can give state estimates with nonlinear and non-Gaussian models. Recently, Mahler et al. have introduced a PHD smoother to gain more accurate estimates for both target states and number. However, as highlighted by Psiaki in the context of a backward-smoothing extended Kalman filter, with a nonlinear state evolution model the approximation error in the backward filtering requires careful consideration. Psiaki suggests that to minimize the aggregated least-squares error over a batch of data. We instead use the term retrodiction PHD filter to describe the backward filtering algorithm in recognition of the approximation error proposed in the original PHD smoother, and we propose an adaptive recursion step to improve the approximation accuracy. This step combines forward and backward processing through the measurement set and thereby mitigates the problems with the original PHD smoother when the target number changes significantly and the targets appear and disappear randomly. Simulation results show the improved performance of the proposed algorithm and its capability in handling a variable number of targets. [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]