The Kalman filter in the context of adaptive filter theory

Abstract

SUMMARYModel-based adaptive algorithms are usually derived with the help of the Wiener-Hopf equation based on empirical statistics. They are often interpreted as an extension to their model-independent counterparts, i.e. the stochastic-gradient based adaptive ÿlters. As a consequence, it is generally not considered worthwhile to show the analogy between Kalman ÿlters and adaptive ÿlters. This article pursues just these two goals. First, it tries to remove the notion that the Kalman ÿlter is a complicated and unnecessary detour from the subject of adaptive ÿltering. Second, the advantage of a deeper insight into adaptive algorithms from Kalman's viewpoint emerges from our treatment. Based on a time-varying FIR ÿlter model, the Kalman ÿlter is completely derived and serves as a general framework for the special case of model-based adaptive ÿlters.

On the quantification of heart rate variability spectral parameters using time–frequency and time-varying methods

“…The analogy between m and l becomes evident if one observes the similarity between algorithms (2.8) and (2.10). For detailed description of the relationships between RLS and Kalman filter, see Sayed & Kailath (1994) and Lippuner & Moschytz (2004).…”

A Recursive Frequency Estimator Using Linear Prediction and a Kalman-Filter-Based Iterative Algorithm

“…Consequently, the LPCs can be described as the state equation in (16a). Combining the state equation with the LP equation in (12) gives the following linear state-space model:…”

“…Therefore, an iterative algorithm based on the Kalman filter is developed to estimate the LPCs and measurement noise covariance matrix iteratively so as to further improve the tracking performance. Simulation results show that the proposed algorithm gives better tracking capabilities than the WRLS method in nonstationary environment because the latter is more sensitive to the changes of noise variance [11], [12].…”