Efficient mixed-spectrum estimation with applications to target feature extraction

In this paper, we present a decoupled parameter estimation (DPE) algorithm for estimating sinusoidal parameters from both one-dimensional (1-D) and two-dimensional (2-D) data sequences corrupted by AR noise. In the first step of the DPE algorithm, we use a relaxation (RELAX) algorithm that requires simple fast Fourier transforms (FFTs) to obtain the estimates of the sinusoidal parameters. We describe how the RELAX algorithm may be used to extract radar target features from both 1-D and 2-D data sequences. In the second step of the DPE algorithm, a linear least squares approach is used to estimate the AR noise parameters. The DPE algorithm is both conceptually and computationally simple. The algorithm not only provides excellent estimation performance under the model assumptions, in which case the estimates obtained with the DPE algorithm are asymptotically statistically efficient, but is also robust to mismodeling errors.

[1]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[2]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[3]  Yoram Bresler,et al.  A compact Cramer-Rao bound expression for parametric estimation of superimposed signals , 1992, IEEE Trans. Signal Process..

[4]  Petre Stoica,et al.  Statistical analysis of two nonlinear least-squares estimators of sine-wave parameters in the colored-noise case , 1989 .

[5]  Peter T. Gough,et al.  A fast spectral estimation algorithm based on the FFT , 1994, IEEE Trans. Signal Process..

[6]  Torsten Söderström,et al.  Model-structure selection by cross-validation , 1986 .

[7]  Jeng-Kuang Hwang,et al.  Superresolution frequency estimation by alternating notch periodogram , 1993, IEEE Trans. Signal Process..

[8]  J. Kellett.  London , 1914, The Hospital.

[9]  Ilan Ziskind,et al.  Maximum likelihood localization of multiple sources by alternating projection , 1988, IEEE Trans. Acoust. Speech Signal Process..

[10]  D. Munson,et al.  A tomographic formulation of spotlight-mode synthetic aperture radar , 1983, Proceedings of the IEEE.

[11]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .

[12]  Rangasami L. Kashyap,et al.  Estimation of close sinusoids in colored noise and model discrimination , 1987, IEEE Trans. Acoust. Speech Signal Process..

[13]  Venkatesh Nagesha,et al.  Maximum likelihood estimation of signals in autoregressive noise , 1994, IEEE Trans. Signal Process..

[14]  W. D. Ray,et al.  Spectral Analysis and Time Series. Vol. 1: Univariate Series. , 1982 .

[15]  Michael I. Miller,et al.  Maximum-likelihood estimation of complex sinusoids and Toeplitz covariances , 1994, IEEE Trans. Signal Process..

[16]  J. Högbom,et al.  APERTURE SYNTHESIS WITH A NON-REGULAR DISTRIBUTION OF INTERFEROMETER BASELINES. Commentary , 1974 .

[17]  Jian Li,et al.  Efficient mixed-spectrum estimation with applications to target feature extraction , 1995 .

[18]  Petre Stoica,et al.  Maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements , 1989, IEEE Trans. Acoust. Speech Signal Process..

[19]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.

[20]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[21]  E. J. Hannan,et al.  Estimating the dimension of a linear system , 1981 .

[22]  Dale A. Ausherman,et al.  Developments in Radar Imaging , 1984, IEEE Transactions on Aerospace and Electronic Systems.

[23]  B. D. Steinberg,et al.  Reduction of sidelobe and speckle artifacts in microwave imaging: the CLEAN technique , 1988 .