Maximum Likelihood Direction-of-Arrival Estimation of Underwater Acoustic Signals Containing Sinusoidal and Random Components

We consider the problem of maximum-likelihood (ML) direction-of-arrival (DOA) estimation of underwater acoustic signals from ships, submarines, or torpedoes, which contain both sinusoidal and random components, and are called mixed signals in this paper. We model the mixed signals as the mixture of deterministic sinusoidal signals and stochastic Gaussian signals, and derive the ML DOA estimator for the mixed signals under spatially white noise. We compute the asymptotic error covariance matrix of the proposed ML estimator, as well as that of the typical stochastic estimator assuming zero-mean Gaussian signals, for DOA estimation of mixed signals. Our analytical comparison and numerical examples show that the proposed ML estimator, which takes advantage of the sinusoidal components in the mixed signals, improves the DOA estimation accuracy for the mixed signals compared with the typical stochastic estimator assuming zero-mean Gaussian signals.

[1]  Frankie K. W. Chan,et al.  Accurate frequency estimation for real harmonic sinusoids , 2004, IEEE Signal Processing Letters.

[2]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[3]  Aleksandar Dogandzic,et al.  Space-time fading channel estimation and symbol detection in unknown spatially correlated noise , 2002, IEEE Trans. Signal Process..

[4]  S. Kay Fundamentals of statistical signal processing: estimation theory , 1993 .

[5]  R. E. Hudson,et al.  Stochastic Maximum-Likelihood DOA Estimation in the Presence of Unknown Nonuniform Noise , 2008, IEEE Transactions on Signal Processing.

[6]  Miriam A. Doron,et al.  Wavefield modeling and array processing. III. Resolution capacity , 1994, IEEE Trans. Signal Process..

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

[8]  Anthony J. Weiss,et al.  Maximum-Likelihood Direction Finding of Wide-Band Sources , 1993, IEEE Trans. Signal Process..

[9]  M. Kupperman Linear Statistical Inference and Its Applications 2nd Edition (C. Radhakrishna Rao) , 1975 .

[10]  Petre Stoica,et al.  Performance study of conditional and unconditional direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[11]  Steven M. Kay,et al.  Mean likelihood frequency estimation , 2000, IEEE Trans. Signal Process..

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

[13]  Anthony J. Weiss,et al.  Direction finding using noise covariance modeling , 1995, IEEE Trans. Signal Process..

[14]  Robert J. Urick,et al.  Principles of underwater sound , 1975 .

[15]  Venkatesh Nagesha,et al.  Maximum likelihood estimation for array processing in colored noise , 1996, IEEE Trans. Signal Process..

[16]  Petre Stoica,et al.  Array processing for signals with non-zero means in colored noise fields , 2004, Digit. Signal Process..

[17]  J. Bohme,et al.  Accuracy of maximum-likelihood estimates for array processing , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[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]  N. L. Johnson,et al.  Linear Statistical Inference and Its Applications , 1966 .

[20]  James P. Reilly,et al.  Maximum likelihood direction-finding in unknown noise environments , 1994, IEEE Trans. Signal Process..

[21]  Arye Nehorai,et al.  Maximum Likelihood Direction Finding in Spatially Colored Noise Fields Using Sparse Sensor Arrays , 2011, IEEE Transactions on Signal Processing.

[22]  A. V. D. Vaart,et al.  Asymptotic Statistics: U -Statistics , 1998 .

[23]  Marius Pesavento,et al.  Maximum-likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise , 2001, IEEE Trans. Signal Process..

[24]  A. V. D. Vaart,et al.  Asymptotic Statistics: Frontmatter , 1998 .

[25]  Aleksandar Dogandzic,et al.  Generalized multivariate analysis of variance - A unified framework for signal processing in correlated noise , 2003, IEEE Signal Process. Mag..

[26]  Malcolm J. Crocker,et al.  Handbook of Acoustics , 1998 .

[27]  Björn E. Ottersten,et al.  Further results and insights on subspace based sinusoidal frequency estimation , 2001, IEEE Trans. Signal Process..

[28]  Miriam A. Doron,et al.  Wavefield Modeling and Array Processing, Part 111-Resolution Capacity , 1994 .

[29]  A. G. Jaffer,et al.  Maximum likelihood direction finding of stochastic sources: a separable solution , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[30]  Petre Stoica,et al.  Maximum-likelihood bearing estimation with partly calibrated arrays in spatially correlated noise fields , 1996, IEEE Trans. Signal Process..

[31]  B. B. Bauer,et al.  Fundamentals of acoustics , 1963 .

[32]  Kung Yao,et al.  Maximum Likelihood DOA Estimation of Multiple Wideband Sources in the Presence of Nonuniform Sensor Noise , 2008, EURASIP J. Adv. Signal Process..

[33]  T. Kailath,et al.  Efficient estimation of closely spaced sinusoidal frequencies using subspace-based methods , 1997, IEEE Signal Processing Letters.

[34]  Erik G. Larsson,et al.  Stochastic Cramer-Rao bound for direction estimation in unknown noise fields , 2002 .

[35]  David E. Booth,et al.  Applied Multivariate Analysis , 2003, Technometrics.

[36]  Sergiy A. Vorobyov,et al.  Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays , 2005, IEEE Transactions on Signal Processing.