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This paper addresses the issue of Unconditional or Stochastic Maximum likelihood (SML) estimation of directions-of-arrival (DOA) finding using sensors with arbitrary array configuration. The conventional SML estimation is formulated without an important condition that the covariance matrix of signal components must be non-negative definite. An likelihood function can not be evaluated exactly for all possible sets of directions. First, this paper reveals that the conventional SML has three problems due to the lack of the condition. 1) Solutions in the noise-free case are not unique. 2) Global solution in the noisy case becomes ambiguous occasionally. 3) There exist situations that any local solution does not satisfy the condition of the non-negative definiteness. We propose an exact formulation of the SML estimation of DOA to evaluate an likelihood function exactly for any possible set of directions. The proposed formulation can be utilized without any theoretical difficulty. The three problems of the conventional SML are solved by the proposed exact SML estimation. Furthermore we show a local search technique in the conventional SML has a good chance to find an optimal or suboptimal DOA although the suboptimal solutions violate the condition of the non-negative definiteness. Finally some simulation results are shown to demonstrate good estimation properties of the exact SML estimation.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.11 pp.2141-2152

- Publication Date
- 2010/11/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E93.A.2141

- Type of Manuscript
- Special Section PAPER (Special Section on Smart Multimedia & Communication Systems)

- Category

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Haihua CHEN, Masakiyo SUZUKI, "Exact Formulation for Stochastic ML Estimation of DOA" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 11, pp. 2141-2152, November 2010, doi: 10.1587/transfun.E93.A.2141.

Abstract: This paper addresses the issue of Unconditional or Stochastic Maximum likelihood (SML) estimation of directions-of-arrival (DOA) finding using sensors with arbitrary array configuration. The conventional SML estimation is formulated without an important condition that the covariance matrix of signal components must be non-negative definite. An likelihood function can not be evaluated exactly for all possible sets of directions. First, this paper reveals that the conventional SML has three problems due to the lack of the condition. 1) Solutions in the noise-free case are not unique. 2) Global solution in the noisy case becomes ambiguous occasionally. 3) There exist situations that any local solution does not satisfy the condition of the non-negative definiteness. We propose an exact formulation of the SML estimation of DOA to evaluate an likelihood function exactly for any possible set of directions. The proposed formulation can be utilized without any theoretical difficulty. The three problems of the conventional SML are solved by the proposed exact SML estimation. Furthermore we show a local search technique in the conventional SML has a good chance to find an optimal or suboptimal DOA although the suboptimal solutions violate the condition of the non-negative definiteness. Finally some simulation results are shown to demonstrate good estimation properties of the exact SML estimation.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.2141/_p

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@ARTICLE{e93-a_11_2141,

author={Haihua CHEN, Masakiyo SUZUKI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Exact Formulation for Stochastic ML Estimation of DOA},

year={2010},

volume={E93-A},

number={11},

pages={2141-2152},

abstract={This paper addresses the issue of Unconditional or Stochastic Maximum likelihood (SML) estimation of directions-of-arrival (DOA) finding using sensors with arbitrary array configuration. The conventional SML estimation is formulated without an important condition that the covariance matrix of signal components must be non-negative definite. An likelihood function can not be evaluated exactly for all possible sets of directions. First, this paper reveals that the conventional SML has three problems due to the lack of the condition. 1) Solutions in the noise-free case are not unique. 2) Global solution in the noisy case becomes ambiguous occasionally. 3) There exist situations that any local solution does not satisfy the condition of the non-negative definiteness. We propose an exact formulation of the SML estimation of DOA to evaluate an likelihood function exactly for any possible set of directions. The proposed formulation can be utilized without any theoretical difficulty. The three problems of the conventional SML are solved by the proposed exact SML estimation. Furthermore we show a local search technique in the conventional SML has a good chance to find an optimal or suboptimal DOA although the suboptimal solutions violate the condition of the non-negative definiteness. Finally some simulation results are shown to demonstrate good estimation properties of the exact SML estimation.},

keywords={},

doi={10.1587/transfun.E93.A.2141},

ISSN={1745-1337},

month={November},}

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TY - JOUR

TI - Exact Formulation for Stochastic ML Estimation of DOA

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2141

EP - 2152

AU - Haihua CHEN

AU - Masakiyo SUZUKI

PY - 2010

DO - 10.1587/transfun.E93.A.2141

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E93-A

IS - 11

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - November 2010

AB - This paper addresses the issue of Unconditional or Stochastic Maximum likelihood (SML) estimation of directions-of-arrival (DOA) finding using sensors with arbitrary array configuration. The conventional SML estimation is formulated without an important condition that the covariance matrix of signal components must be non-negative definite. An likelihood function can not be evaluated exactly for all possible sets of directions. First, this paper reveals that the conventional SML has three problems due to the lack of the condition. 1) Solutions in the noise-free case are not unique. 2) Global solution in the noisy case becomes ambiguous occasionally. 3) There exist situations that any local solution does not satisfy the condition of the non-negative definiteness. We propose an exact formulation of the SML estimation of DOA to evaluate an likelihood function exactly for any possible set of directions. The proposed formulation can be utilized without any theoretical difficulty. The three problems of the conventional SML are solved by the proposed exact SML estimation. Furthermore we show a local search technique in the conventional SML has a good chance to find an optimal or suboptimal DOA although the suboptimal solutions violate the condition of the non-negative definiteness. Finally some simulation results are shown to demonstrate good estimation properties of the exact SML estimation.

ER -