Recursive least squares filter

About: Recursive least squares filter is a research topic. Over the lifetime, 8907 publications have been published within this topic receiving 191933 citations.

Complex Correntropy: Probabilistic Interpretation and Application to Complex-Valued Data

Abstract: Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher order statistical moments in non-Gaussian noise environments. Although correntropy has been used with complex data, no theoretical study was pursued to elucidate its properties, nor how to best use it for optimization. By using a probabilistic interpretation, this work presents a novel similarity measure between two complex random variables, which is defined as complex correntropy. A new recursive solution for the maximum complex correntropy criterion is introduced based on a fixed-point solution. This technique is applied to a system identification, and the results demonstrate prominent advantages when compared against three other algorithms: the complex least mean square, complex recursive least squares, and least absolute deviation. By the aforementioned probabilistic interpretation, correntropy can now be applied to solve several problems involving complex data in a more straightforward way.

The time-sequenced adaptive filter

Abstract: A new form of adaptive filter is proposed which is especially suited for the estimation of a class of nonstationary signals. This new filter, called the time-sequenced adaptive filter, is an extension of the least mean-square error (LMS) adaptive filter. Both the LMS and time-sequenced adaptive filters are digital filters composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive algorithm. For stationary stochastic inputs the mean-square error, which is the expected value of the squared difference between the filter output and an externally supplied "desired response," is a quadratic function of the weights-a paraboloid with a single fixed minimum point which can be sought by gradient techniques, such as the LMS algorithm. For nonstationary inputs however the minimum point, curvature, and orientation of the error surface could be changing over time. The time-sequenced adaptive filter is applicable to the estimation of that subset of nonstationary signals having a recurring (but not necessarily periodic) statistical character, e.g., recurring pulses in noise. In this case there are a finite number of different paraboloidal error surfaces, also recurring in time. The time-sequenced adaptive filter uses multiple sets of adjustable weights. At each point in time, one and only one set of weights is selected to form the filter output and to be adapted using the LMS algorithm. The index of the set of weights chosen is synchronized with the recurring statistical character of the filter input so that each set of weights is associated with a single error surface. After many adaptations of each set of weights, the minimum point of each error surface is reached resulting in an optimal time-varying filter. For this procedure, some a priori knowledge of the filter input is required to synchronize the selection of the set of weights with the recurring statistics of the filter input. For pulse-type signals, this a priori knowledge could be the location of the pulses in time; for signals with periodic statistics, knowledge of the period is sufficient. Possible applications of the time-sequenced adaptive filter include electrocardiogram enhancement and electric load prediction.

A Relative Off set Orthogonality Convergence Criterion for Nonlinear least Squares

Abstract: An orthogonality convergence criterion using relative offset is proposed. This criterion is compared to currently used criteria and its advantages are discussed.

On least squares algorithms for system parameter identification

Abstract: A new least squares solution for obtaining asymptotically unbiased and consistent estimates of unknown parameters in noisy linear systems is presented. The proposed algorithms are in many ways more advantageous than generalized least squares algorithm. Extensions to on-line and multivariable problems can be easily implemented. Examples are given to illustrate the performance of these new algorithms.