Mean-square performance of a convex combination of two adaptive filters

Abstract

Abstract-Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination is adapted by means of a stochastic gradient algorithm in order to minimize the error of the overall structure. General expressions are derived that show that the method is universal with respect to the component filters, i.e., in steady-state, it performs at least as well as the best component filter. Furthermore, when the correlation between the a priori errors of the components is low enough, their combination is able to outperform both of them. Using energy conservation relations, we specialize the results to a combination of least mean-square filters operating both in stationary and in nonstationary scenarios. We also show how the universality of the scheme can be exploited to design filters with improved tracking performance.

Low-complexity approximation to the Kalman filter using convex combinations of adaptive filters from different families

“…According to [4], a convex combination approach is an interesting way to improve adaptive filter performance. In this case, the individual filters are independently adapted using their own error signals, while the combination is adapted by means of a stochastic gradient algorithm in order to minimize the error of the overall structure.…”

“…As it was shown in [4], [5], when combining filters from different families, namely LMS and RLS, it is possible to take advantage of the tracking properties from each filter and obtain a structure with better performance than if each filter were implemented individually. Combinations of Kalman Filters were also proposed using different update rules as proposed in [6] and [7].…”

Generalized CMAC adaptive ensembles for concept-drifting data streams

“…If β(t) is appropriately updated, it can be shown that the resulting model performs as well as or better than the best individual component under certain conditions [11]. The adaptation rule for β(t) is obtained as follows:…”

A Mixing Vector Based an Affine Combination of Two Adaptive Filters for Sensor Array Beamforming

“…The basic idea is that two (or more) adaptive filters with complementary capabilities combine adaptively their outputs by means of a mixing parameter, in order to obtain an overall filter of improved performance. Among these schemes, convex [28][29][30], linear [31] and affine [32,33] combinations have received attention due to their simplicity and universal behavior in steady-state, i.e., the combined estimate is at least as good as the best of the component filters. And the convex combination proposed in [34] for knowledge-aided STAP obtains a significant improvement to estimate the inverse interference covariance matrix by combining the inverse of a priori known covariance matrix and a sample covariance matrix with a scale weighting parameter.…”