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The Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However, when the noises are non‐Gaussian in nature, its performance deteriorates rapidly. For non‐Gaussian noises, maximum correntropy Kalman filter (MCKF) is developed which provides a more accurate result. In a scenario, where the actual system model differs from nominal consideration, the performance of the MCKF degrades. For such cases, in this article, we have proposed a new robust filtering technique for a linear system which maximizes a cost function defined by exponential of weighted past and present errors weighted with the kernel bandwidth. During filtering, at each time step, the kernel bandwidth is selected by maximizing the correntropy function of error. Further, a convergence condition of the proposed algorithm is derived. Numerical examples are presented to show the usefulness of the proposed filtering technique. [ABSTRACT FROM AUTHOR]

This article proposes two robust Kalman filters to solve the issue of inaccurate modeling in multiplicative noise systems due to epistemic limitations. First, we construct all conceivable state/measurement transition probability densities as an ambiguity set. This ambiguity set chooses the Wasserstein distance or the moment‐based metric as the distance metric. Besides, this set is an inequality set with a chosen tolerance, which can be seen as a non‐negative radius ball. Then, by combining the robust solution of the least favorable model in that ball with the alternating direction method of multipliers or an efficient direct solution method, we propose two robust Kalman filters based on the minimum mean square error criterion. A classical example is provided to verify the effectiveness of the proposed robust filters in comparison to existing state‐of‐the‐art filters. [ABSTRACT FROM AUTHOR]