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.

Fast projection algorithms with application to voice echo cancellation

Abstract: Prior to the advent of subband adaptive filtering, acoustic echo cancellation for hands-free, full-duplex speech communication was considered impractical. Adaptive filters were simply too slow, too complex, or too unstable to cope with the acoustic echo path's long, time varying impulse response. The divide and conquer approach of subband acoustic echo cancellers (SBAECs) provided relatively fast convergence, low computational complexity and stability. The main drawback of SBAECs is that for relatively distortionless transmission of the near-end (non-echoing) speech, a considerable amount of delay is inserted in the signal path. This dissertation introduces three new adaptive filtering algorithms based on the philosophy of affine projections. All three share the property of fast convergence coupled with low computational complexity and memory usage. The first algorithm combines properties of the row action projection and subband adaptive filtering algorithms to produce a new dynamic computational resource allocated subband adaptive filtering algorithm. Simulations demonstrate that the new algorithm converges faster than the conventional NLMS based subband adaptive filters. The second new algorithm is actually a small class of algorithms which are fast (low complexity) versions of the repeated normalized block least mean square (RNBLMS) and the row action projection (RAP) algorithms. Also shown, is the relationship between RNBLMS, RAP, the affine projection algorithm (APA), and its close relative, the partial rank algorithm (PRA). Specifically, the block level convergence of PRA and RNBLMS are shown to be very closely related and it is demonstrated that the significant parameters of one can be derived from the other, even to the point where the overall convergence of the two algorithms match almost exactly. The delay in this class of algorithms is relatively small compared to SBAECs. The third new algorithm is called the fast affine projection algorithm. This algorithm has the property of achieving recursive least squares (RLS) like convergence (fast) with LMS like complexity (low). In addition, FAP is easily regularized, achieving good convergence for highly colored excitations even in noisy environments. These advantages are attained without the price of adding delay in the signal. Finally, a new convergence theory for PRA is introduced. The results of this theory are directly applicable to RNBLMS, since the relationship between the key parameters of it and PRA are known. And indirectly, the results are applicable to APA, FAP, and RAP, where the relationship between the key parameters, as of now, must be determined empirically.

Recursive adaptive algorithms for fast and rapidly time-varying systems

Abstract: In this paper, some new schemes are developed to improve the tracking performance for fast and rapidly time-varying systems. A generalized recursive least-squares (RLS) algorithm called the trend RLS (T-RLS) algorithm is derived which takes into account the effect of local and global trend variations of system parameters. A bank of adaptive filters implemented with T-RLS algorithms are then used for tracking an arbitrarily fast varying system without knowing a priori the changing rates of system parameters. The optimal tracking performance is attained by Bayesian a posteriori combination of the multiple filter outputs, and the optimal number of parallel filters needed is determined by extended Akaike's Information Criterion and Minimum Description Length information criteria. An RLS algorithm with modification of the system estimation covariance matrix is employed to track a time-varying system with rare but abrupt (jump) changes. A new online wavelet detector is designed for accurately identifying the changing locations and the branches of changing parameters. The optimal increments of the covariance matrix at the detected changing locations are also estimated. Thus, for a general time-varying system, the proposed methods can optimally track its slowly, fast and rapidly changing components simultaneously.

Adaptive filtering using filter banks

Abstract: This paper derives a theory for adaptive filters which operate on filter bank outputs, here called filter bank adaptive filters (FBAFs). It is shown how the FBAFs are a generalization of transform domain adaptive filters and adaptive filters based on structural subband decompositions. The minimum mean-square error performance and convergence properties of FBAFs are determined as a function of filter bank used. A parametrization for a class of FIR perfect reconstruction filter banks is derived which is used to design FBAF's having optimal error performance given prior knowledge of the application. Simulations are performed to illustrate the derived theory and demonstrate the improved error performance of the FBAFs relative to the LMS algorithm, when prior knowledge is incorporated.

The analysis of the continuous-time LMS algorithm

Abstract: A continuous-time analog adaptive filter is suggested using the digital prototype. The continuous-time LMS (least-mean squares) algorithm is then described by a set of simultaneous first-order equations. The adaptive gain is shown to be unbounded theoretically. >