Skip to main content
SpringerLink
Log in

Asymptotic properties of the least squares estimators of the parameters of the chirp signals

  • Asymptotic Theory
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Chirp signals are quite common in different areas of science and engineering. In this paper we consider the asymptotic properties of the least squares estimators of the parameters of the chirp signals. We obtain the consistency property of the least squares estimators and also obtain the asymptotic distribution under the assumptions that the errors are independent and identically distributed. We also consider the generalized chirp signals and obtain the asymptotic properties of the least squares estimators of the unknown parameters. Finally we perform some simulations experiments to see how the asymptotic results behave for small sample and the performances are quite satisfactory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abatzoglou, T. (1986). Fast maximum likelihood joint estimation of frequency and frequency rate,IEEE Transactions on Aerospace and Electronic Systems,22, 708–714.

    Google Scholar 

  • Besson, O., Ghogho, M. and Swami, A. (1999). Parameter estimation for random amplitude chirp signals,IEEE Transactions on Signal Processing,47, 3208–3219.

    Article  Google Scholar 

  • Chung, K. L. (1974).A First Course in Probability, Academic Press, New York.

    Google Scholar 

  • Djuric, P. M. and Kay, S. M. (1990). Parameter estimation of chirp signals,IEEE Transactions on Acoustics, Speech and Signal Processing,38, 2118–2126.

    Article  Google Scholar 

  • Gini, F., Montanari, M. and Verrazzani, L. (2000). Estimation of chirp signals in compound Gaussian clutter: A cyclostationary approach,IEEE Transactions on Acoustics, Speech and Signal Processing,48(4), 1029–1039.

    Google Scholar 

  • Huang, D., Sando S. and Wen, L. (1999). Least squares estimation of polynomial phase signals via stochastic tree-search, ICASSP, Phoenix, Arizona, Paper No. 1355.

    Google Scholar 

  • Jennrich, R. I. (1969). Asymptotic properties of the nonlinear least squares estimators,Annals of Mathematical Statistics,40, 633–643.

    MathSciNet  Google Scholar 

  • Kumaresan, R. and Verma, S. (1987). On estimating the parameters of chirp signals using rank reduction techniques,Proceedings of 21st Asilomar Conference, 555–558, Pacific Grove, California.

  • Kundu, D. (1991). Asymptotic properties of the complex valued nonlinear regression model,Communications in Statistics: Theory and Methods,20, 3793–3803.

    MathSciNet  Google Scholar 

  • Kundu, D. and Mitra, A. (1996). A note on the consistency of the undamped exponential signals model,Statistics,28, 25–33.

    MathSciNet  Google Scholar 

  • Rao, C. R. (1973).Linear Statistical Inferences and Its Applications 2nd ed., Wiley and Sons, New York.

    Google Scholar 

  • Rihaczek, A. W. (1969).Principles of High Resolution Radar, McGraw Hill, New York.

    Google Scholar 

  • Saha, S. and Kay, S. (2002). Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling,IEEE Transactions on Signal Processing,50, 224–230.

    Article  Google Scholar 

  • Wu, C. F. J. (1981). Asymptotic theory of the nonlinear least squares estimation,Annals of Statistics,9, 501–513.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Swagata Nandi

  2. Department of Mathematics, Indian Institute of Technology Kanpur, 208016, Kanpur, Pin, India

    Debasis Kundu

Authors
  1. Swagata Nandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Debasis Kundu
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Nandi, S., Kundu, D. Asymptotic properties of the least squares estimators of the parameters of the chirp signals. Ann Inst Stat Math 56, 529–544 (2004). https://doi.org/10.1007/BF02530540

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02530540

Key words and phrases

Search

Navigation