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.

Recursive identification and adaptive prediction in linear stochastic systems

Abstract: By making use of extended stochastic Lyapunov functions and martingale limit theorems, established herein are certain basic properties of adaptive d-step ahead predictors associated with the extended least squares, stochastic gradient (without interlacing), and monitored recursive maximum likelihood algorithms for recursive identification of an ARMAX system. Both the direct (or implicit) and indirect (or explicit) approaches to adaptive prediction are considered within a unified framework involving stochastic regression models. Applications to adaptive control of ARMAX systems are also discussed.

Fast coupled adaptation for sparse impulse responses using a partial haar transform

Abstract: This work presents a novel scheme for identifying the impulse response of a sparse channel. The scheme consists of two adaptive filters operating sequentially. The first adaptive filter adapts using a partial Haar transform of the input and yields an estimate of the location of the peak of the sparse impulse response. The second adaptive filter is then centered about this estimate. Both filters are short in comparison to the delay uncertainty of the unknown channel. The principle advantage of this scheme is that two short adaptive filters can be used instead of one long adaptive filter, resulting in faster overall convergence and reduced computational complexity and storage. The scheme is analyzed in detail for a least mean squares (LMS) LMS-LMS type of structure, although it can be implemented using any combination of adaptive algorithms. Monte Carlo simulations are shown to be in good agreement with the theoretical model for the behavior of the peak estimating filter as well as for the mean square error (MSE) behavior of the second filter.

Fast-Converging Blind Adaptive Channel-Shortening and Frequency-Domain Equalization

Abstract: Orthogonal frequency-division multiplexing (OFDM) is a popular transmission format for emerging wireless communication systems, including satellite radio, various wireless local area network (LAN) standards, and digital broadcast television. Single-carrier cyclic-prefixed (SCCP) modulation is similar to OFDM, but with all frequency-domain operations performed at the receiver. Systems employing OFDM and SCCP perform well in the presence of multipath provided that the channel delay spread is shorter than the guard interval between transmitted blocks. If this condition is not met, a channel-shortening equalizer can be used to shorten the channel to the desired length. In modestly time-varying environments, an adaptive channel shortener is of interest. All existing adaptive channel shorteners require renormalization to restrain the channel shortener away from zero. In this paper, we study the use of a unit-tap constraint rather than a unit-norm constraint on the adaptive channel shortener. We use this constraint to manipulate existing algorithms into a framework analogous to the recursive least squares algorithm, and we develop adaptation rules for blind and semiblind frequency domain equalizers for SCCP receivers. Simulations of the proposed algorithms show an order of magnitude improvement in convergence speed, as well as a reduced asymptotic bit error rate

Linear fractional order system identification using adjustable fractional order differentiator

Abstract: In previous decades, it has been observed that many physical systems are well characterised by fractional order models. Hence, their identification is attracting more and more interest of the scientific community. However, they pose a more difficult identification problem, which requires not only the estimation of model coefficients but also the determination of fractional orders with the tedious calculation of fractional order derivatives. This study focuses on an identification scheme, in the time domain, of dynamic systems described by linear fractional order differential equations. The proposed identification method is based on the recursive least squares algorithm applied to an ARX structure derived from the linear fractional order differential equation using adjustable fractional order differentiators. The basic ideas and the derived formulations of the identification scheme are presented. Illustrative examples are presented to validate the proposed linear fractional order system identification approach.

DCD-Based Recursive Adaptive Algorithms Robust Against Impulsive Noise

Abstract: The dichotomous coordinate descent (DCD) algorithm has been successfully used for significant reduction in the complexity of recursive least squares (RLS) algorithms. In this brief, we generalize the application of the DCD algorithm to RLS adaptive filtering in impulsive noise scenarios and derive a unified update formula. By employing different robust strategies against impulsive noise, we develop novel computationally efficient DCD-based robust recursive algorithms. Furthermore, to equip the proposed algorithms with the ability to track abrupt changes in unknown systems, a simple variable forgetting factor mechanism is also developed. Simulation results for channel identification scenarios in impulsive noise demonstrate the effectiveness of the proposed algorithms.