On the Intrinsic Relationship Between the Least Mean Square and Kalman Filters [Lecture Notes]


The Kalman filter and the smallest amount mean square (LMS) adaptive filter are 2 of the most in style adaptive estimation algorithms that are typically used interchangeably in a range of statistical Signal Processing applications. They are sometimes treated as separate entities, with the former as a realization of the optimal Bayesian estimator and the latter as a recursive answer to the optimal Wiener filtering problem. In this lecture note, we have a tendency to take into account a system identification framework at intervals that we develop a joint perspective on Kalman filtering and LMS-type algorithms, achieved through analyzing the degrees of freedom necessary for optimal stochastic gradient descent adaptation. This approach permits the introduction of Kalman filters while not any notion of Bayesian statistics, which could be useful for many communities that don't depend on Bayesian ways [one], [a pair of].

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