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In this paper, a new sequential learning algorithm is constructed by combining the Online Sequential Extreme Learning Machine (OS-ELM) and Kalman filter regression. The Kalman Online Sequential Extreme Learning Machine (KOSELM) handles the problem of multicollinearity of the OS-ELM, which can generate poor predictions and unstable models. The KOSELM learns the training data one-by-one or chunk-by-chunk by adjusting the variance of the output weights through the Kalman filter. The performance of the proposed algorithm has been validated on benchmark regression datasets, and the results show that KOSELM can achieve a higher learning accuracy than OS-ELM and its related extensions. A statistical validation for the differences of the accuracy for all algorithms is performed, and the results confirm that KOSELM has better stability than ReOS-ELM, TOSELM and LS-IELM. [ABSTRACT FROM AUTHOR]