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 least-squares identification algorithms with incomplete excitation: convergence analysis and application to adaptive control

Abstract: The convergence properties of a fairly general class of adaptive recursive least-squares algorithms are studied under the assumption that the data generation mechanism is deterministic and time invariant. First, the (open-loop) identification case is considered. By a suitable notion of excitation subspace, the convergence analysis of the identification algorithm is carried out with no persistent excitation hypothesis, i.e. it is proven that the projection of the parameter error on the excitation subspace tends to zero, while the orthogonal component of the error remains bounded. The convergence of an adaptive control scheme based on the minimum variance control law is then dealt with. It is shown that under the standard minimum-phase assumption, the tracking error converges to zero whenever the reference signal is bounded. Furthermore, the control variable turns out to be bounded. >

A class of square root and division free algorithms and architectures for QRD-based adaptive signal processing

Abstract: The least squares (LS) minimization problem constitutes the core of many real-time signal processing problems, such as adaptive filtering, system identification and adaptive beamforming. Recently efficient implementations of the recursive least squares (RLS) algorithm and the constrained recursive least squares (CRLS) algorithm based on the numerically stable QR decomposition (QRD) have been of great interest. Several papers have proposed modifications to the rotation algorithm that circumvent the square root operations and minimize the number of divisions that are involved in the Givens rotation. It has also been shown that all the known square root free algorithms are instances of one parametric algorithm. Recently, a square root free and division free algorithm has also been proposed. In this paper, we propose a family of square root and division free algorithms and examine its relationship with the square root free parametric family. We choose a specific instance for each one of the two parametric algorithms and make a comparative study of the systolic structures based on these two instances, as well as the standard Givens rotation. We consider the architectures for both the optimal residual computation and the optimal weight vector extraction. The dynamic range of the newly proposed algorithm for QRD-RLS optimal residual computation and the wordlength lower bounds that guarantee no overflow are presented. The numerical stability of the algorithm is also considered. A number of obscure points relevant to the realization of the QRD-RLS and the QRD-CRLS algorithms are clarified. Some systolic structures that are described in this paper are very promising, since they require less computational complexity (in various aspects) than the structures known to date and they make the VLSI implementation easier. >

Frequency Domain Aspects of Modeling and Control in Adaptive Systems

Abstract: In this thesis various aspects of modeling and control in adaptive systems are presented from a frequency domain viewpoint.The thesis consists of three parts, where the first part contains a general introduction and background information concerning the problems that will be treated. In the second part some recursive identification algorithms are studied with respect to their ability to track time-varying systems and their disturbance sensitivity. Simple and illustrative frequency domain expressions that describe these properties are derived using asymptotic methods. The algorithms that are treated are the constant gain gradient (LMS) algorithm, the recursive least squares algorithm with constant forgetting factor and the Kalman filter respectively. The behavior of these methods when applied to FIR and ARX systems are studied. In the third part of the thesis adaptive control based on low order models is studied. The adaptive control algorithm that is investigated is the recursive least squares algorithm combined with pole placement regulator design. Starting from frequency domain expressions, that describe how a low order model obtained by system identification approximates a higher order system, the consequences for adaptive control are investigated. It is shown how a proper use of filtering in the identification part of the adaptive regulator can improve the robustness properties of the adaptive regulator with respect to unmodelled dynamics.

Nonstationary learning characteristics of least squares adaptive estimation algorithms

Abstract: This paper provides a quantitative analysis of the tracking characteristics of least squares algorithms. A comparison is made with the tracking performance of the LMS algorithm. Other algorithms that are similar to least squares algorithms, such as the gradient lattice algorithm and the Gram-Schmidt orthogonalization algorithm are also considered. Simulation results are provided to reinforce the analytical results and conclusions.

New Improved Recursive Least-Squares Adaptive-Filtering Algorithms

Abstract: Two new improved recursive least-squares adaptive-filtering algorithms, one with a variable forgetting factor and the other with a variable convergence factor are proposed. Optimal forgetting and convergence factors are obtained by minimizing the mean square of the noise-free a posteriori error signal. The determination of the optimal forgetting and convergence factors requires information about the noise-free a priori error which is obtained by solving a known L1-L2 minimization problem. Simulation results in system-identification and channel-equalization applications are presented which demonstrate that improved steady-state misalignment, tracking capability, and readaptation can be achieved relative to those in some state-of-the-art competing algorithms.