Parameter estimation of autoregressive signals from observations corrupted with colored noise

Mahmoudi, Alimorad; Karimi, Mahmood

doi:10.1016/j.sigpro.2009.06.005

Cited by 25 publications

(19 citation statements)

References 12 publications

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“…Unlike the additive white noise case, few papers deal with this issue. To our knowledge, this problem has been investigated by looking at two cases: when the additive noise is a moving average (MA) process [19,20] or when it is a first-order AR process [21]. Note that the first resulting algorithms are based on [4] while the second algorithm is based on [6].…”

Section: Introductionmentioning

confidence: 99%

“…It is based on the prediction error method (PEM), which is known to be asymptotically unbiased and efficient in the Gaussian case [22,23]. 2) We compare our approach with [20].…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 recalls the main concepts of the prediction error method and describes how the PEM can be applied to the case of AR models corrupted by MA processes. In Section 4, a comparative study between our approach and that introduced in [20] is carried out by means of Monte Carlo simulations.…”

Section: Introductionmentioning

confidence: 99%

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Prediction error method to estimate the ar parameters when the AR process is disturbed by a colored noise

Diversi

Ishiguro

Grivel

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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Estimating the autoregressive parameters from noisy observations has been addressed by various authors for the last decades. Although several on-line or off-line approaches have been proposed when the additive noise is white, few papers deal with the additive moving average noise. In this paper, we suggest estimating the model parameters by using the prediction error method. Despite its high computational cost, the method has the advantage of being efficient in the Gaussian case. A comparative study with existing methods is then carried out and points out the efficiency of our approach especially when the number of samples is small.

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Section: Introductionmentioning

confidence: 99%

“…It is based on the prediction error method (PEM), which is known to be asymptotically unbiased and efficient in the Gaussian case [22,23]. 2) We compare our approach with [20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Prediction error method to estimate the ar parameters when the AR process is disturbed by a colored noise

Diversi

Ishiguro

Grivel

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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“…In [12], an improved least-squares based method is proposed for a noisy autoregressive (AR) signal using observations corrupted with colored noise.…”

Section: Introductionmentioning

confidence: 99%

Design of RLS Wiener Smoother and Filter for Colored Observation Noise in Linear Discrete-Time Stochastic Systems

Nakamori¹

2012

JSIP

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“…The method is based on convex optimization, and no exact answer can be provided. Mahmoudi and Karimi propose an LS-based method to estimate AR parameters from noisy data [19]. The method exploites YW equations, but this method also does not provide the explicit solution to the equations.…”

Section: Introductionmentioning

confidence: 99%

Linear Estimation of Stationary Autoregressive Processes

Dianat

Marvasti

2011

ISRN Signal Processing

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Consider a sequence of an mth-order Autoregressive (AR) stationary discrete-time process and assume that at least m − 1 consecutive neighboring samples of an unknown sample are available. It is not important that the neighbors are from one side or are from both the left and right sides. In this paper, we find explicit solutions for the optimal linear estimation of the unknown sample in terms of the neighbors. We write the estimation errors as the linear combination of innovation noises. We also calculate the corresponding mean square errors (MSE). To the best of our knowledge, there is no explicit solution for this problem. The known solutions are the implicit ones through orthogonality equations. Also, there are no explicit solutions when fewer than m−1 samples are available. The order of the process (m) and the feedback coefficients are assumed to be known.

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Parameter estimation of autoregressive signals from observations corrupted with colored noise

Cited by 25 publications

References 12 publications

Prediction error method to estimate the ar parameters when the AR process is disturbed by a colored noise

Prediction error method to estimate the ar parameters when the AR process is disturbed by a colored noise

Design of RLS Wiener Smoother and Filter for Colored Observation Noise in Linear Discrete-Time Stochastic Systems

Linear Estimation of Stationary Autoregressive Processes

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