Abstract
We propose a two-stage estimator to estimate chirp rate and initial frequency of the chirp signals in the presence of additive white Gaussian noise. In the first stage, the chirp rate estimation problem is reformulated as a single tone frequency estimation problem. Then, the frequency of single tone is estimated through a linear prediction approach. Using the chirp rate estimate in the first stage, we can convert the linear frequency modulated signal to a single tone. Similar to the first stage, the initial frequency is estimated via the linear prediction approach. The performance of the present method is assessed by comparison with Cramer–Rao lower bound and other existing methods through computer simulations. The proposed algorithm estimates well for different values of the chirp rate and initial frequency, as well as for different number of samples. In other words, this algorithm has uniform performance for various values of the signal parameters.
Similar content being viewed by others
References
T. Abatzoglou, Fast maximum likelihood joint estimation of frequency and frequency rate. IEEE Trans. Aerosp. Electron. Syst. AES–22(6), 708–715 (1986)
O. Besson, M. Ghogho, A. Swami, Parameter estimation for random amplitude chirp signals. IEEE Trans. Signal Process. 47(12), 3208–3219 (1999)
J. Cao, N. Zhang, L. Song, A fast algorithm for the chirp rate estimation, in IEEE International Symposium on Electronic Design, Test and Applications (2008), p. 45–48
C.E. Davila, A subspace approach to estimation of autoregressive parameters from noisy measurements. IEEE Trans. Signal Process. 46(2), 531–534 (1998)
Z.M. Deng, L.M. Ye, M.Z. Fu, S.J. Lin, Y.X. Zhang, Further investigation on time-domain maximum likelihood estimation of chirp signal parameters. IET Signal Proc. 7(5), 444–449 (2013)
P.M. Djuric, S.M. Kay, Parameter estimation of chirp signals. IEEE Trans. Acoust. Speech Signal Process. 38(12), 2118–2126 (1990)
I. Djurovic, Viterbi algorithm for chirp-rate and instantaneous frequency estimation. Sig. Process. 91(5), 1308–1314 (2011)
I. Djurovic, A WD-RANSAC instantaneous frequency estimator. IEEE Signal Process. Lett. 23(5), 757–761 (2016)
I. Djurovic, QML-RANSAC: PPS and FM signals estimation in heavy noise environments. Signal Process. 130(1), 142–151 (2017)
I. Djurovic, M. Simeunovic, S. Djukanovic, P. Wang, A hybrid CPF–HAF estimation of polynomial-phase signals: detailed statistical analysis. IEEE Trans. Signal Process. 60(10), 5010–5023 (2012)
K. Heydari, P. Azmi, B. Abbasi, A. Heydari, Determining the parameters of chirp signals using cyclostationary method in presence of the interference. J. Fundam. Appl. Sci. 8(4), 478–486 (2016)
M.Z. Ikram, K. Abed-Meraim, Y. Hua, Estimating the parameters of chirp signals: an iterative approach. IEEE Trans. Signal Process. 46(12), 3436–3441 (1998)
M. Jankiraman, Design of Multi-frequency CW Radars (SciTech Publishing, New York, 2007)
Y. Li, H. Fu, P.Y. Kam, Improved, approximate, time-domain ML estimators of chirp signal parameters and their performance analysis. IEEE Trans. Signal Process. 57(4), 1260–1272 (2009)
Y. Li, P.Y. Kam, Improved chirp parameter estimation using signal recovery method, in IEEE Vehicular Technology Conference (2010), pp. 1–5
Z. Li, W. Sheng-Li, N. Jin-Lin, L. Guo-Sui, Doppler frequency rate estimation for sar using match Fourier transform. Int. Conf. Neural Netw. Signal Process. 2, 1109–1112 (2003)
R.G. McKilliam, B.G. Quinn, I.V.L. Clarkson, B. Moran, B.N. Vellambi, Polynomial phase estimation by least squares phase unwrapping. IEEE Trans. Signal Process. 62(8), 1962–1975 (2014)
A. Papoulis, S.U. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw-Hill Education, New York, 2002)
L. Qi, R. Tao, S. Zhou, Y. Wang, Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform. Proc. Sci. China Ser. F: Inf. Sci. 47(2), 184–198 (2004)
A. Springer, M. Huemer, L. Reindl, C.C. Ruppel, A. Pohl, F. Seifert, W. Gugler, R. Weigel, A robust ultra-broad-band wireless communication system using saw chirped delay lines. IEEE Trans. Microw. Theory Tech. 46(12), 2213–2219 (1998)
S. Saha, S.M. Kay, Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling. IEEE Trans. Signal Process. 50(2), 224–230 (2002)
A. Serbes, O. Aldimashki, A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform. EUSIPCO 190(1), 95–101 (2017)
P. Stoica, R.L. Moses, Spectral Analysis of Signals (Prentice Hall, Upper Saddle River, 2005)
P. Wang, P.V. Orlik, K. Sadamoto, W. Tsujita, F. Gini, Parameter estimation of hybrid sinusoidal FM-polynomial phase signal. IEEE Signal Process. Lett. 24(1), 66–70 (2017)
H. Zhang, G. Zhang, J. Wang, \(\cal{H} _ {\infty } \) Observer design for LPV systems with uncertain measurements on scheduling variables: application to an electric ground vehicle. IEEE/ASME Trans. Mechatron. 21(3), 1659–1670 (2016)
E.C. Zaugg, D.G. Long, Theory and application of motion compensation for LFM-CW SAR. IEEE Trans. Geosci. Remote Sens. 46(10), 2990–2998 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gholami, S., Mahmoudi, A. & Farshidi, E. Two-Stage Estimator for Frequency Rate and Initial Frequency in LFM Signal Using Linear Prediction Approach. Circuits Syst Signal Process 38, 105–117 (2019). https://doi.org/10.1007/s00034-018-0843-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-018-0843-3