Extended fast fixed-order RLS adaptive filters

Merched, R.; Sayed, Ali H.

doi:10.1109/78.969510

Cited by 19 publications

(14 citation statements)

References 30 publications

(62 reference statements)

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“…Now, these minimal components for the FIR case can be established, once the connection with the minimal components of fast transversal filters of all least-squares orders is recognized, thus resulting in a 2M + 1 minimal dimension (see [17]). We have shown in [3], for the general orthonormal basis of this paper, that the same defining components of the minimum state vector in a fast transversal FIR algorithm also define the minimum components of an orthonormalitybased FTF, 3 therefore, using the arguments of [17], one can conclude that this holds similarly for the order-recursive algorithms of this paper, resulting in 2M + 1 minimal parameters. The nonminimal character of the above recursions can be intuitively seen, by following their derivation.…”

Section: Backward Consistency and Minimality Issuesmentioning

confidence: 53%

“…This relation helps in reducing the redundant variables in fast RLS recursions and is one of the relations forming the manifold of S i in such recursions (as observed for the FTF algorithm in [15,16] in the case of FIR models). 4 This relation has been further extended to the general orthonormal model of [3] and has been used in the standard and it turns out that this is also the case for the lattice recursions, since we have shown that this relation holds for every order-M LS problem.…”

Section: Backward Consistency and Minimality Issuesmentioning

confidence: 75%

“…One can exploit this relation to obtain the LS solution in a fast manner. The key for extending this concept to more general structures in [1,3] was to show that, although the above equality no longer holds for general orthonormal models, it is still possible to relate the entries of {u M,N , u M,N+1 } asū…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Extended RLS Lattice Adaptive Variants: Error-Feedback, Normalized, and Array-Based Recursions

Merched

2005

EURASIP J. Adv. Signal Process.

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Error-feedback, normalized, and array-based recursions represent equivalent RLS lattice adaptive filters which are known to offer better numerical properties under finite-precision implementations. This is the case when the underlying data structure arises from a tapped-delay-line model for the input signal. On the other hand, in the context of a more general orthonormality-based input model, these variants have not yet been derived and their behavior under finite precision is unknown. This paper develops several lattice structures for the exponentially weighted RLS problem under orthonormality-based data structures, including error-feedback, normalized, and array-based forms. As a result, besides nonminimality of the new recursions, they present unstable modes as well as hyperbolic rotations, so that the well-known good numerical properties observed in the case of FIR models no longer exist. We verify via simulations that, compared to the standard extended lattice equations, these variants do not improve the robustness to quantization, unlike what is normally expected for FIR models.

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Section: Backward Consistency and Minimality Issuesmentioning

confidence: 53%

Section: Backward Consistency and Minimality Issuesmentioning

confidence: 75%

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On Extended RLS Lattice Adaptive Variants: Error-Feedback, Normalized, and Array-Based Recursions

Merched

2005

EURASIP J. Adv. Signal Process.

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“…To reduce the physiological interference, the RLS adaptive filtering algorithm was used to remove the correlated components of reference signal x(t) from signal d(t) by minimizing the following mean square error [13].…”

Section: Recursive Least-squares Adaptive Filteringmentioning

confidence: 99%

Physiological interference reduction for near infrared spectroscopy brain activity measurement based on recursive least squares adaptive filtering and least squares support vector machines

Liu

Zhang

Liú

et al. 2019

Computer Assisted Surgery

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Rolfe (2019) Physiological interference reduction for near infrared spectroscopy brain activity measurement based on recursive least squares adaptive filtering and least squares support vector machines, Computer Assisted Surgery, 24:sup1, 160-166, ABSTRACTNear infrared spectroscopy is the promising and noninvasive technique that can be used to detect the brain functional activation by monitoring the concentration alternations in the haemodynamic concentration. The acquired NIRS signals are commonly contaminated by physiological interference caused by breathing and cardiac contraction. Though the adaptive filtering method with least mean squares algorithm or recursive least squares algorithm based on multidistance probe configuration could improve the quality of evoked brain activity response, both methods can only remove the physiological interference occurred in superficial layers of the head tissue. To overcome the shortcoming, we combined the recursive least squares adaptive filtering method with the least squares support vector machine to suppress physiological interference both in the superficial layers and deeper layers of the head tissue. The quantified results based on performance measures suggest that the estimation performances of the proposed method for the evoked haemodynamic changes are better than the traditional recursive least squares method. KEYWORDSNear infrared spectroscopy; physiological interference; adaptive filtering; recursive least squares; least squares support vector machine

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“…Digital Object Identifier 10.1109/TSP.2013.2278150 instead of relying on Gauss elimination computations, recursive solutions require by exploiting the sequential least-squares structure of a given data, or even multiplications per iteration, by relying on additional data structure [8], [10]- [12]. A fast algorithm is by itself one way of proving the so-called displacement structure, tracing back the works [13]- [29] for inversion of Toeplitz matrices.…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach to Structured Covariances: Fast Generalized Sliding Window RLS Recursions for Arbitrary Basis

Merched

2013

IEEE Trans. Signal Process.

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This paper extends the existing fast RLS recursions originally intended to exponentially windowed problems for general models, to a generalized sliding window formulation (GSWRLS). From a matrix algebra perspective, we show explicitly how the displacement rank of the underlying inverse covariance matrix associated to any operator is defined as a function of the number of window breakpoints and how the fast GSWRLS calculates these rank factors in a fast manner. The recursions hold regardless of the (first order) data structure induced and show that fast fixed order and order recursive RLS algorithms can still be obtained for unwindowed data matrices exhibiting a fixed arbitrary relation between successive regressors. Our approach highlights the existence of a certain degree of freedom inherent to structured data matrices induced by general models, showing that efficient representations of their inverse covariances are not limited to factor circulants, but rather constructed from any arbitrary operator. These Bezoutians, usually expressed via reproducing kernel relations, can be represented exactly in matrix form, along with a precise correspondence to variables of a GSWRLS. As a fallout, we obtain a vector relation stating the so-called minimality property, for extended models and windows, as opposed to analogous generating function arguments normally seen in original approaches. These results pave the way to a more general framework of polynomial Vandermonde covariance decompositions which arise naturally via a proper choice of recurrence related polynomials. This has further impact on several signal processing applications, including superfast realization of equalizers in communications scenarios.

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Extended fast fixed-order RLS adaptive filters

Cited by 19 publications

References 30 publications

On Extended RLS Lattice Adaptive Variants: Error-Feedback, Normalized, and Array-Based Recursions

On Extended RLS Lattice Adaptive Variants: Error-Feedback, Normalized, and Array-Based Recursions

Physiological interference reduction for near infrared spectroscopy brain activity measurement based on recursive least squares adaptive filtering and least squares support vector machines

A Unified Approach to Structured Covariances: Fast Generalized Sliding Window RLS Recursions for Arbitrary Basis

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