Analysis of a frequency estimator for a class of laser signals with time-varying amplitude

The authors address the problem of estimating a particle's velocity in the vicinity of an aircraft by means of a laser velocimeter. A model for the signal generated by a particle of air passing through a probe volume consisting of equidistant bright and dark fringes is given. From this model, a frequency estimator based on the phase of the correlation sequence of the signal is proposed. A theoretical analysis of the frequency estimator is presented. In particular, a formula for the variance of the estimate is derived under the assumption of small estimation errors. Numerical examples confirm the validity of the analysis. It is reported that this estimator, although simpler than the maximum likelihood approach, comes close to the Cramer-Rao bound. Finally, the effectiveness of the proposed algorithm is demonstrated on real data.

[1]  Petre Stoica,et al.  Estimation of the parameters of a random amplitude sinusoid by correlation fitting , 1996, IEEE Trans. Signal Process..

[2]  K Sasaki,et al.  Laser Doppler particle measuring system using nonsinusoidal forced vibration and bispectral analysis. , 1978, Applied optics.

[3]  Hongya Ge,et al.  Estimating the frequencies of two sinusoids using only the phase angles of complex-valued data , 1993, IEEE Trans. Signal Process..

[4]  Steven Kay,et al.  A Fast and Accurate Single Frequency Estimator , 2022 .

[5]  Joseph M. Francos,et al.  Estimation of amplitude and phase parameters of multicomponent signals , 1995, IEEE Trans. Signal Process..

[6]  Petros Maragos,et al.  Energy separation in signal modulations with application to speech analysis , 1993, IEEE Trans. Signal Process..

[7]  Petar M. Djuric,et al.  Parameter estimation of chirp signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

[8]  Torbjörn Wigren,et al.  Performance analysis of a correlation based single tone frequency estimator , 1995, Signal Process..

[9]  Steven A. Tretter,et al.  Estimating the frequency of a noisy sinusoid by linear regression , 1985, IEEE Trans. Inf. Theory.

[10]  Yoram Bresler,et al.  Exact maximum likelihood parameter estimation of superimposed exponential signals in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[11]  Robert Boorstyn,et al.  Single tone parameter estimation from discrete-time observations , 1974, IEEE Trans. Inf. Theory.

[12]  Petre Stoica,et al.  Asymptotic properties of the high-order Yule-Walker estimates of sinusoidal frequencies , 1989, IEEE Trans. Acoust. Speech Signal Process..

[13]  Petre Stoica,et al.  Sinusoidal signals with random amplitude: least-squares estimators and their statistical analysis , 1995, IEEE Trans. Signal Process..

[14]  Petre Stoica.  List of references on spectral line analysis , 1993, Signal Process..

[15]  R. Kumaresan,et al.  Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood , 1982, Proceedings of the IEEE.

[16]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[17]  Petros Maragos,et al.  On amplitude and frequency demodulation using energy operators , 1993, IEEE Trans. Signal Process..

[18]  Frédéric Galtier,et al.  Estimating particles velocity from laser measurements: maximum likelihood and Cramer-Rao bounds , 1996, IEEE Trans. Signal Process..

[19]  Thomas Kailath,et al.  ESPRIT-A subspace rotation approach to estimation of parameters of cisoids in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[20]  Michael P. Fitz,et al.  Further results in the fast estimation of a single frequency , 1994, IEEE Trans. Commun..