Cramer-Rao Bound on Passive Source Localization for General Gaussian Noise

This paper focuses on the development of Cramer-Rao Bound (CRB) expressions for passive source location estimation in various Gaussian noise environments. The scenarios considered involve an unknown deterministic source signal with a short time duration, and additive general Gaussian noise. The mathematical derivation procedure presented is applicable to non-stationary Gaussian noise problems. Specifically, explicit closed-form CRB expressions are presented using the spectrum representation of the signal and noise for stationary Gaussian noise cases.

[1]  J. Eric Salt,et al.  Error Analysis of a Localization Algorithm for Finite-Duration Events , 2007, IEEE Transactions on Signal Processing.

[2]  A. Prugger,et al.  Microearthquake location: A nonlinear approach that makes use of a simplex stepping procedure , 1988 .

[3]  K. C. Ho,et al.  A simple and efficient estimator for hyperbolic location , 1994, IEEE Trans. Signal Process..

[4]  David N. Swingler.  Approximate bounds on frequency estimates for short cisoids in colored noise , 1998, IEEE Trans. Signal Process..

[5]  Hao Ye,et al.  Maximum likelihood DOA estimation and asymptotic Cramer-Rao bounds for additive unknown colored noise , 1995, IEEE Trans. Signal Process..

[6]  Mingui Sun,et al.  Classification of abnormal cortisol patterns by features from Wigner spectra , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[7]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[8]  Michael Savic,et al.  Digital signal processing aids cholesterol plaque detection , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[9]  G. Carter,et al.  The generalized correlation method for estimation of time delay , 1976 .

[10]  J. Smith,et al.  The spherical interpolation method of source localization , 1987 .

[11]  Kok-Kwang Phoon,et al.  Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes , 2001 .

[12]  H. C. Schau,et al.  Passive source localization employing intersecting spherical surfaces from time-of-arrival differences , 1987, IEEE Trans. Acoust. Speech Signal Process..

[13]  Georgios B. Giannakis,et al.  Hybrid FM-polynomial phase signal modeling: parameter estimation and Cramer-Rao bounds , 1999, IEEE Trans. Signal Process..

[14]  Jacob Benesty,et al.  Real-time passive source localization: a practical linear-correction least-squares approach , 2001, IEEE Trans. Speech Audio Process..

[15]  G. Carter.  Coherence and time delay estimation , 1987, Proceedings of the IEEE.

[16]  Hing-Cheung So,et al.  A multidimensional scaling framework for mobile location using time-of-arrival measurements , 2005, IEEE Transactions on Signal Processing.

[17]  Joseph M. Francos,et al.  Bounds for estimation of complex exponentials in unknown colored noise , 1995, IEEE Trans. Signal Process..

[18]  F. Waldhauser,et al.  Optimizing Correlation Techniques for Improved Earthquake Location , 2004 .

[19]  David Newland,et al.  Application of Time-Frequency Analysis to Transient Data from Centrifuge Earthquake Testing , 2000 .

[20]  Kung Yao,et al.  Maximum-likelihood source localization and unknown sensor location estimation for wideband signals in the near-field , 2002, IEEE Trans. Signal Process..

[21]  J. Ortega.  Matrix Theory: A Second Course , 1987 .

[22]  Michael S. Brandstein,et al.  A closed-form location estimator for use with room environment microphone arrays , 1997, IEEE Trans. Speech Audio Process..

[23]  J. Delmas,et al.  Gaussian Cramer-Rao bound for direction estimation of noncircular signals in unknown noise fields , 2005, IEEE Transactions on Signal Processing.

[24]  Steven A. Tretter,et al.  Optimum processing for delay-vector estimation in passive signal arrays , 1973, IEEE Trans. Inf. Theory.

[25]  Jacob Benesty,et al.  Passive acoustic source localization for video camera steering , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[26]  Jean Pierre Delmas,et al.  Stochastic Crame/spl acute/r-Rao bound for noncircular signals with application to DOA estimation , 2004, IEEE Transactions on Signal Processing.

[27]  Ananthram Swami,et al.  Cramer-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals , 1999, IEEE Trans. Signal Process..

[28]  Marco Luise,et al.  Cramer-Rao bounds in the parametric estimation of fading radiotransmission channels , 1998, IEEE Trans. Commun..