Dimension-Reduction Maximum Likelihood Sensor Array Calibration Using Inaccurate Cooperative Sources

The state-of-the-art auxiliary calibration algorithms can perform comprehensive calibration of various array non-ideal characteristics, such as mutual coupling, gain/phase uncertainties, and sensor position errors, employing a set of cooperative calibration sources with known direction of arrival (D...

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Published in	IEEE sensors journal Vol. 24; no. 6; p. 1
Main Authors	Song, Shuoshuo, Ma, Xiaofeng, Sheng, Weixing
Format	Journal Article
Language	English
Published	New York IEEE 15.03.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects	Algorithms Ambiguity Calibration dimension-reduction Direction of arrival Direction-of-arrival estimation global optimization inaccurate calibration sources Local optimization Lower bounds Mathematical models Maximum likelihood estimation Mutual coupling Normal distribution Optimization methods Parameters Performance degradation Position errors Position sensing Reduction sensor array calibration Sensor arrays Sensor phenomena and characterization Sensors Two dimensional analysis Uncertainty
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ISSN	1530-437X 1558-1748
DOI	10.1109/JSEN.2024.3360471

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Abstract	The state-of-the-art auxiliary calibration algorithms can perform comprehensive calibration of various array non-ideal characteristics, such as mutual coupling, gain/phase uncertainties, and sensor position errors, employing a set of cooperative calibration sources with known direction of arrival (DOA). However, the task of deploying calibration sources at precisely measured DOAs is complex. Otherwise, the calibration source DOA errors would seriously degrade the performance of these algorithms. In this paper, a dimension-reduction maximum likelihood calibration algorithm with inaccurate cooperative sources is proposed to overcome this issue. First, a maximum likelihood calibration model is established including both the unknown array non-ideal parameters and 2-D DOAs of all calibration sources. Next, the ambiguity of sensor position estimation caused by inaccurate 2-D DOAs of calibration sources is analyzed. Furthermore, a dimension-reduction maximum likelihood calibration model is proposed to resolve the ambiguity under the zero mean Gaussian distribution assumption of the calibration source elevation errors. Then, since the proposed multi-parameter dimension-reduction model is non-convex and multimodal, a new filled function method is proposed to cope with its local extrema attractors. The proposed single-parameter filled function has a single form without an exponential term and is second-order continuously differentiable, which is stable for numerical calculations and easy to optimize by local optimization tools. Finally, the closed-form hybrid Cramer-Rao lower-bound expressions of array parameters under unknown source DOAs are derived in detail. Numerical results verify the effectiveness of the proposed algorithm.
AbstractList	The state-of-the-art auxiliary calibration algorithms can perform comprehensive calibration of various array nonideal characteristics, such as mutual coupling, gain/phase uncertainties, and sensor position errors, employing a set of cooperative calibration sources with known direction of arrival (DOA). However, the task of deploying calibration sources at precisely measured DOAs is complex. Otherwise, the calibration source DOA errors would seriously degrade the performance of these algorithms. In this article, a dimension-reduction maximum likelihood calibration algorithm (MLCA) with inaccurate cooperative sources is proposed to overcome this issue. First, a maximum likelihood (ML) calibration model is established including both the unknown array of nonideal parameters and 2-D DOAs of all calibration sources. Next, the ambiguity of sensor position estimation caused by inaccurate 2-D DOAs of calibration sources is analyzed. Furthermore, a dimension-reduction ML calibration model is proposed to resolve the ambiguity under the zero mean Gaussian distribution assumption of the calibration source elevation errors. Then, since the proposed multiparameter dimension-reduction model is nonconvex and multimodal, a new filled function method (FFM) is proposed to cope with its local extrema attractors. The proposed single-parameter filled function (SPFF) has a single form without an exponential term and is second-order continuously differentiable, which is stable for numerical calculations and easy to optimize by local optimization tools. Finally, the closed-form hybrid Cramer–Rao lower-bound (CRB) expressions of array parameters under unknown source DOAs are derived in detail. Numerical results verify the effectiveness of the proposed algorithm. The state-of-the-art auxiliary calibration algorithms can perform comprehensive calibration of various array non-ideal characteristics, such as mutual coupling, gain/phase uncertainties, and sensor position errors, employing a set of cooperative calibration sources with known direction of arrival (DOA). However, the task of deploying calibration sources at precisely measured DOAs is complex. Otherwise, the calibration source DOA errors would seriously degrade the performance of these algorithms. In this paper, a dimension-reduction maximum likelihood calibration algorithm with inaccurate cooperative sources is proposed to overcome this issue. First, a maximum likelihood calibration model is established including both the unknown array non-ideal parameters and 2-D DOAs of all calibration sources. Next, the ambiguity of sensor position estimation caused by inaccurate 2-D DOAs of calibration sources is analyzed. Furthermore, a dimension-reduction maximum likelihood calibration model is proposed to resolve the ambiguity under the zero mean Gaussian distribution assumption of the calibration source elevation errors. Then, since the proposed multi-parameter dimension-reduction model is non-convex and multimodal, a new filled function method is proposed to cope with its local extrema attractors. The proposed single-parameter filled function has a single form without an exponential term and is second-order continuously differentiable, which is stable for numerical calculations and easy to optimize by local optimization tools. Finally, the closed-form hybrid Cramer-Rao lower-bound expressions of array parameters under unknown source DOAs are derived in detail. Numerical results verify the effectiveness of the proposed algorithm.
Author	Ma, Xiaofeng Sheng, Weixing Song, Shuoshuo
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SubjectTerms	Algorithms Ambiguity Calibration dimension-reduction Direction of arrival Direction-of-arrival estimation global optimization inaccurate calibration sources Local optimization Lower bounds Mathematical models Maximum likelihood estimation Mutual coupling Normal distribution Optimization methods Parameters Performance degradation Position errors Position sensing Reduction sensor array calibration Sensor arrays Sensor phenomena and characterization Sensors Two dimensional analysis Uncertainty
Title	Dimension-Reduction Maximum Likelihood Sensor Array Calibration Using Inaccurate Cooperative Sources
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