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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]

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]

• By introducing a Bernoulli random variable and using state augmentation approach, the conditional likelihood function is transformed into an exponential multiplication form. • The augmentation state vector together with the auxiliary random variables and the Bernoulli random variable are inferred based on variational Bayesian approach. • The superiority of the proposed filter as compared with the existing filters is demonstrated in a target tracking simulation. In this paper, a novel robust Student's t-based Gaussian approximate filter (RSTGAF) is proposed to solve the filtering problem of the nonlinear system with one-step randomly delayed measurements (ORDM) and heavy-tailed measurement noise. The conditional likelihood function is transformed into an exponential multiplication form after using state augmentation approach and introducing a Bernoulli random variable, and then the augmentation state vector, the auxiliary random variables and the Bernoulli random variable are jointly estimated based on the variational Bayesian (VB) approach. The simulation results demonstrate the superiority of the proposed filter, as compared with the existing filters, to address the ORDM and heavy-tailed measurement noise. [ABSTRACT FROM AUTHOR]