AbstractThis paper explores a linear state estimation problem in non‐Gaussian setting and suggests a computationally simple estimator based on the maximum correntropy criterion Kalman filter (MCC‐KF). The first MCC‐KF method was developed in Joseph stabilized form. It requires two n × n and one m × m matrix inversions, where n is a dimension of unknown dynamic state to be estimated, and m is a dimension of available measurement vector. Therefore, the estimator becomes impractical when the system dimensions increase. Our previous work has suggested an improved MCC‐KF estimator (IMCC‐KF) and its factored‐from (square‐root) implementations that enhance the MCC‐KF estimation quality and numerical robustness against roundoff errors. However, the proposed IMCC‐KF and its square‐root implementations still require the m × m matrix inversion in each iteration step of the filter. For numerical stability and computational complexity reasons it is preferable to avoid the matrix inversion operation. In this paper, we suggest a new IMCC‐KF algorithm that is more accurate and computationally cheaper than the original MCC‐KF and previously suggested IMCC‐KF. Furthermore, compared with stable square‐root algorithms, the new method is also accurate, but less computationally expensive. The results of numerical experiments substantiate the mentioned properties of the new estimator on numerical examples.