A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs

Almeida, Sérgio; Bermudez, J.C.M.; Bershad, N.J.; Costa, Márcio Holsbach

doi:10.1109/tcsi.2005.851720

Cited by 82 publications

(66 citation statements)

References 9 publications

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“…Now we consider the APA algorithm. Under the assumption that there exists a true adaptive filter weight vector w 0 of dimension N , based on (5) and [5], the iterated error of the APA algorithm can be written as…”

Section: Regressive Estimated Error Analysismentioning

confidence: 99%

“…Based on [5], under the situation that the input process {x n } is assumed to be zeromean wide-sense stationary autoregressive inputs of order p and the number of the most recent input vectors m ≥ p, the following result can be obtained:…”

Section: Stability Analysismentioning

confidence: 99%

“…And it can be concluded that the steady-state weights of the APA-REE algorithm are unbiased and consist. Furthermore, based on [5], if the input process {x n } is assumed to be zero-mean wide-sense stationary autoregressive inputs of order p and the number of the most recent input vectors m ≥ p, the direction vector {ϕ n } and the estimated weight vector {w n } are statistically independent, and the direction vector {ϕ n } is a zero-mean Gaussian random vector, so the results of (15) and (29) can also be obtained to be equal to zeros.…”

Section: Steady-state Weightsmentioning

confidence: 99%

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Affine Projection Algorithm Using Regressive Estimated Error

Zhang

Zhi

2011

ISRN Signal Processing

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An affine projection algorithm using regressive estimated error (APA-REE) is presented in this paper. By redefining the iterated error of the affine projection algorithm (APA), a new algorithm is obtained, and it improves the adaptive filtering convergence rate. We analyze the iterated error signal and the stability for the APA-REE algorithm. The steady-state weights of the APA-REE algorithm are proved to be unbiased and consist. The simulation results show that the proposed algorithm has a fast convergence rate compared with the APA algorithm.

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Section: Regressive Estimated Error Analysismentioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

Section: Steady-state Weightsmentioning

confidence: 99%

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Affine Projection Algorithm Using Regressive Estimated Error

Zhang

Zhi

2011

ISRN Signal Processing

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“…For the ship tracking, the dynamic model is given in (1). All the density distributions are Gaussian so we can analytically obtain some function values.…”

Section: ) Combination Of Neural Network and Particle Filtersmentioning

confidence: 99%

“…These methods have been very popular over the past few years in statistics and related fields, and they are improved greatly in implementations [11], [16], [17], [28], [30], [32]. They are also used widely in various fields, such as econometrics [15], signal processing [20], [27], noise analysis [14], circuit analysis [23], [36], communications [19], [21], [22], performance analysis of wavelet transforms [33], statistical analysis of the affine project algorithm [1], robotics [26], and so on. Particle filters approximate the sequence of probability distributions of interest using a set of random samples called particles.…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo Particle Model Associated with Neural Networks for Tracking Problem

Pang

Liu

Jin

et al. 2008

IEEE Trans. Circuits Syst. I

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Abstract-Sequential Monte Carlo (SMC) methods, namely, particle filters, are powerful simulation techniques for sampling sequentially from a complex probability distribution. SMC can be used to solve some problems associated with nonlinear non-Gaussian probability distribution. Sampling is a key step for these methods and has vital effects on simulation results. Various sampling strategies have been proposed to improve the simulation results of SMC methods, but degeneracy of particles sometimes is very severe so that there are only a few particles having significant weights. Diversity of particle samples is reduced significantly so that only a few particles are used to represent the corresponding probability distribution. This kind of sampling is not reasonable to approximate probability distribution. This paper addresses a new method which can avoid the phenomenon of particle degeneracy. We split particles with very big weights into two small ones and use the strategy of neural network to adjust positions of tail particles in order to increase their weights. Another advantage is that this method can efficiently make simulation results approach the actual object. Our simulation results of the typical tracking problem show that not only the phenomenon of particle degeneracy is effectively avoided but also tracking results are much better than those of the traditional particle filters. Compared with the move-resample method, our method shows better results under the same conditions.

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On the Convergence Behavior of Affine Projection Algorithm with Direction Error

Zhi¹,

Zheng²,

Li³

2013

Asian Journal of Control

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An affine projection algorithm with direction error (AP-DE) is presented to solve the nonconformity between the iterated direction of the adaptive filter and the direction caused by the iteration error. A statistical analysis model is shown to analyze the AP-DE algorithm for autoregressive input signals. Deterministic recursive equations for the mean weight error and for the mean-square error in the iterated direction are derived. We also analyze the steady-state mean-square error in the iterated direction for the AP-DE algorithm. Simulation results are provided to corroborate the analytical results.

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A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs

Cited by 82 publications

References 9 publications

Affine Projection Algorithm Using Regressive Estimated Error

Affine Projection Algorithm Using Regressive Estimated Error

A Monte Carlo Particle Model Associated with Neural Networks for Tracking Problem

On the Convergence Behavior of Affine Projection Algorithm with Direction Error

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