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.

On the BIBO Stability Condition of Adaptive Recursive FLANN Filters With Application to Nonlinear Active Noise Control

Abstract: In this paper, a bounded-input bounded-output (BIBO) stability condition for the recursive functional link artificial neural network (FLANN) filter, based on trigonometric expansions, is derived. This filter is considered as a member of the class of causal shift-invariant recursive nonlinear filters whose output depends linearly on the filter coefficients. As for all recursive filters, its stability should be granted or, at least, tested. The relevant conclusion we derive from the stability condition is that the recursive FLANN filter is not affected by instabilities whenever the recursive linear part of the filter is stable. This fact is in contrast with the case of recursive polynomial filters where, in general, specific limitations on the input range are required. The recursive FLANN filter is then studied in the framework of a feedforward scheme for nonlinear active noise control. The novelty of our study is due to the simultaneous consideration of a nonlinear secondary path and an acoustical feedback between the loudspeaker and the reference microphone. An output error nonlinearly Filtered-U normalized LMS adaptation algorithm, derived for the elements of the above-mentioned class of nonlinear filters, is then applied to the recursive FLANN filter. Computer simulations show that the recursive FLANN filter, in contrast to other filters, is able to simultaneously deal with the acoustical feedback and the nonlinearity in the secondary path.

Real-Time Adaptive EEG Source Separation Using Online Recursive Independent Component Analysis

Abstract: Independent component analysis (ICA) has been widely applied to electroencephalographic (EEG) biosignal processing and brain–computer interfaces. The practical use of ICA, however, is limited by its computational complexity, data requirements for convergence, and assumption of data stationarity, especially for high-density data. Here we study and validate an optimized online recursive ICA algorithm (ORICA) with online recursive least squares (RLS) whitening for blind source separation of high-density EEG data, which offers instantaneous incremental convergence upon presentation of new data. Empirical results of this study demonstrate the algorithm's: 1) suitability for accurate and efficient source identification in high-density (64-channel) realistically-simulated EEG data; 2) capability to detect and adapt to nonstationarity in 64-ch simulated EEG data; and 3) utility for rapidly extracting principal brain and artifact sources in real 61-channel EEG data recorded by a dry and wearable EEG system in a cognitive experiment. ORICA was implemented as functions in BCILAB and EEGLAB and was integrated in an open-source Real-time EEG Source-mapping Toolbox (REST), supporting applications in ICA-based online artifact rejection, feature extraction for real-time biosignal monitoring in clinical environments, and adaptable classifications in brain–computer interfaces.

An adaptive Kalman filter for dynamic estimation of harmonic signals

Abstract: In electrical railway systems there is often a need of detecting or/and predicting harmonic signals contained in measurement data for vehicle control or monitoring purpose. An efficient on-line estimation method for such applications is the Kalman filter technique. However, the performance of a standard recursive Kalman algorithm is strongly dependent on the a priori information of the process and measurement noise which is either unknown or is known only approximately in practical situations. Furthermore, a Kalman filter often suffers from the problem of "dropping off" and loses then the ability to match abrupt parameter changes. In this paper an adaptive Kalman filter based on correlation analysis is proposed to help overcome these problems. The modelling and estimation technique is described in the paper. Simulation results using measured vehicle line current demonstrate the effectiveness of the proposed method.

Least squares estimation of discrete linear dynamic systems using orthogonal transformations

Abstract: Kalman [9] introduced a method for estimating the state of a discrete linear dynamic system subject to noise. His method is fast but has poor numerical properties. Duncan and Horn [3] showed that the same problem can be formulated as a weighted linear least squares problem. Here we present a method which uses orthogonal transformations to solve the Duncan and Horn formulation by taking advantage of the special structure of the problem. This approach gives advantages in numerical accuracy over other related methods in the literature, and is similar in the number of computations required. It also gives a straightforward presentation of the material for those unfamiliar with the area.