Efficient algorithm for estimating the parameters of two dimensional chirp signal

Lahiri, Ananya; Kundu, Debasis; Mitra, Amit

doi:10.1007/s13571-012-0048-x

Cited by 11 publications

(7 citation statements)

References 13 publications

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“…The different sample sizes we use are n = 250, n = 500 and n = 1000 and for each n we replicate the process, that is generate the data and obtain the estimates 1000 times. We estimate the parameters by the least squares estimation method, the approximate least squares estimation method and using the efficient algorithm as proposed by Lahiri et al, [2013].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Similar to the periodogram estimators, these estimators can also be used as initial guesses to find the least squares estimators of the unknown parameters. We perform some numerical simulations to see the performance of the proposed estimators and compare them with the least squares estimators and the estimators proposed by Lahiri et al, [2013]. We have analysed two real data sets for illustrative purposes.…”

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confidence: 99%

“…Recently, Lahiri et al, [2013], proposed an efficient algorithm to compute the estimators of the unknown parameters of the chirp model. We perform numerical simulations to compare the proposed ALSEs with the LSEs and the estimators obtained by the efficient algorithm.…”

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confidence: 99%

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On approximate least squares estimators of parameters of one-dimensional chirp signal

2018

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In this paper, we address the problem of parameter estimation of a 2-D chirp model under the assumption that the errors are stationary. We extend the 2-D periodogram method for the sinusoidal model, to find initial values to use in any iterative procedure to compute the least squares estimators (LSEs) of the unknown parameters, to the 2-D chirp model. Next we propose an estimator, known as the approximate least squares estimator (ALSE), that is obtained by maximising a periodogram-type function and is observed to be asymptotically equivalent to the LSE. Moreover the asymptotic properties of these estimators are obtained under slightly mild conditions than those required for the LSEs. For the multiple component 2-D chirp model, we propose a sequential method of estimation of the ALSEs, that significantly reduces the computational difficulty involved in reckoning the LSEs and the ALSEs. We perform some simulation studies to see how the proposed method works and a data set has been analysed for illustrative purposes.

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Section: Numerical Experimentsmentioning

confidence: 99%

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On approximate least squares estimators of parameters of one-dimensional chirp signal

2018

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“…Minimising R 1 (α), we obtain α and replacing α by α in (9), we get the linear parameter estimates Ã and B.…”

Section: Sequential Least Squares Estimatorsmentioning

confidence: 99%

Chirp-like model and its parameters estimation

Grover

Kundu

Mitra

2018

2018 International Conference on Computing, Power and Communication Technologies (GUCON)

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We propose a chirp-like signal model as an alternative to a chirp model and a generalisation of the sinusoidal model, which is a fundamental model in the statistical signal processing literature. It is observed that the proposed model can be arbitrarily close to the chirp model. The propounded model is similar to a chirp model in the sense that here also the frequency changes linearly with time. However, the parameter estimation of a chirp-like model is simpler compared to a chirp model. In this paper, we consider the least squares and the sequential least squares estimation procedures and study the asymptotic properties of these proposed estimators. These asymptotic results are corroborated through simulation studies and analysis of four speech signal data sets have been performed to see the effectiveness of the proposed model, and the results are quite encouraging.

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“…Parameter estimation of a 2-D chirp signal is an important statistical signal processing problem. Recently Zhang et al [8], Lahiri et al [11] and Grover et al [18] proposed some estimation methods of note. For instance, Zhang et al [8] proposed an algorithm based on the product cubic phase function for the estimation of the frequency rates of the 2-D chirp signals under low signal to noise ratio and the assumption of stationary errors.…”

Section: Introductionmentioning

confidence: 99%

An efficient methodology to estimate the parameters of a two-dimensional chirp signal model

Grover¹,

Kundu²,

Mitra³

2019

Preprint

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In various capacities of statistical signal processing two-dimensional (2-D) chirp models have been considered significantly, particularly in image processing− to model grayscale and texture images, magnetic resonance imaging, optical imaging etc. In this paper we address the problem of estimation of the unknown parameters of a 2-D chirp model under the assumption that the errors are independently and identically distributed (i.i.d.). The key attribute of the proposed estimation procedure is that it is computationally more efficient than the least squares estimation method. Moreover, the proposed estimators are observed to have the same asymptotic properties as the least squares estimators, thus providing computational effectiveness without any compromise on the efficiency of the estimators. We extend the propounded estimation method to provide a sequential procedure to estimate the unknown parameters of a 2-D chirp model with multiple components and under the assumption of i.i.d. errors we study the large sample properties of these sequential estimators. Simulation studies and a synthetic data analysis show that the proposed estimators perform satisfactorily.

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Efficient algorithm for estimating the parameters of two dimensional chirp signal

Cited by 11 publications

References 13 publications

On approximate least squares estimators of parameters of one-dimensional chirp signal

On approximate least squares estimators of parameters of one-dimensional chirp signal

Chirp-like model and its parameters estimation

An efficient methodology to estimate the parameters of a two-dimensional chirp signal model

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