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Modified recursive extended least squares identification algorithms
2013 25th Chinese Control and Decision Conference (CCDC), 2013For ARMAX models, modified recursive extended least squares identification algorithms are presented. The basic idea lies in two aspects. One is to decompose the original system into two subsystems. The other is that the most recent information is used to update the parameters, which is different from the hierarchical principle.
Ai-Guo Wu, Zhi-Guang Wang
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Recursive least squares lattice algorithms--A geometrical approach
IEEE Transactions on Automatic Control, 1981Several time-recursive least squares algorithms have been developed in recent years. In this paper a geometrical formalism is defined which utilizes a nested family of metric spaces indexed by the data time interval. This approach leads to a simplified derivation of the so-called recursive least squares lattice algorithms (recursive in time and order).
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LEVINSON‐TYPE RECURSIVE ALGORITHMS FOR LEAST‐SQUARES AUTOREGRESSION
Journal of Time Series Analysis, 1990Abstract. A set of formulae for calculating the least‐squares autoregressive coefficients is given. It can be used for stable, unstable and explosive models. The calculations needed by this algorithm are less than those of the Burg and Marple algorithms. The method used to deduce these formulae has general significance. For example, it is also used to
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Fast recursive least-squares algorithms: Preventing divergence
ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005The fast recursive least-squares algorithms are known to exhibit unstable behaviours and sudden divergences, due to round-off noise in finite-precision implementation. This key problem occurs when a forgetting factor is introduced to make the algorithms adaptive.
P. Fabre, C. Gueguen
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Data-Reuse Recursive Least-Squares Algorithms
IEEE Signal Processing Letters, 2022Constantin Paleologu +2 more
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Recursive Update Algorithm for Least Squares Support Vector Machines
Neural Processing Letters, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chi, Hoi-Ming, Ersoy, Okan K.
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Error Propagation Properties of Recursive Least Squares Adaptation Algorithms
IFAC Proceedings Volumes, 1984Many algorithms giving effective estimations of the coefficients of the equation \(y(t)+a_ 1y(t-1)+...+a_ ny(t-n)=e(t),\) \(t=0,1,..\). for observation data y(t) are known. Here e(t) is, for example, white noise. It is shown that some of the known algorithms are stable and some are unstable (exponentially) with respect to roundoff error.
Ljung, Stefan, Ljung, Lennart
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Pure order recursive least-squares ladder algorithms
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1986The new class of pure order recursive ladder algorithms (PORLA) is presented in this paper. The new method obtains the true, not approximate, least-squares (LS) ladder solution by performing two steps. First, the covariance matrix of the estimated signal is calculated time recursively, and second, the reflection coefficients of the ladder form are ...
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Analysis of a Recursive Least-Squares Signal-Processing Algorithm
SIAM Journal on Scientific and Statistical Computing, 1986This paper concerns a popular recursive least-squares algorithm for beamforming. The way in which the method's stability depends on the condition of a special matrix is analyzed in detail, and a new procedure for estimating the error in the computed solution is presented.
Franklin T. Luk, Sanzheng Qiao
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Fast Recursive Least-Squares Ladder Algorithms
1990Chapters 7 and 8 have illuminated the classes of ladder algorithms that are based on a pure order recursive construction of the ladder form. In this type of algorithm, the central problem appeared to be the order recursive updating of the covariance Cm(t) according to $$ {{{\text{C}}}_{{\text{m}}}}{\text{(t)}}{\mkern 1mu} {\mkern 1mu} {\text{ = }}{\
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