An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes
In this paper, an improved two-dimensional (2-D) direction of arrival (DOA) estimation algorithm for L-shaped nested arrays is proposed. Unlike the approach for a classical nested array, which use the auto-correlation matrix (ACM) to increase the degrees of freedom (DOF), we utilize the cross-correl...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-05-01
|
| Series: | Sensors |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1424-8220/19/9/2176 |
| _version_ | 1798043256051728384 |
|---|---|
| author | Xiaofeng Gao Xinhong Hao Ping Li Guolin Li |
| author_facet | Xiaofeng Gao Xinhong Hao Ping Li Guolin Li |
| author_sort | Xiaofeng Gao |
| collection | DOAJ |
| description | In this paper, an improved two-dimensional (2-D) direction of arrival (DOA) estimation algorithm for L-shaped nested arrays is proposed. Unlike the approach for a classical nested array, which use the auto-correlation matrix (ACM) to increase the degrees of freedom (DOF), we utilize the cross-correlation matrix (CCM) of different sub-arrays to generate two long consecutive virtual arrays. These acquire a large number of DOF without redundant elements and eliminate noise effects. Furthermore, we reconstruct the CCM based on the singular value decomposition (SVD) operation in order to reduce the perturbation of noise for small numbers of samples. To cope with the matrix rank deficiency of the virtual arrays, we construct the full rank equivalent covariance matrices by using the output and its conjugate vector of virtual arrays. The unitary estimation of signal parameters via rotational invariance technique (ESPRIT) is then performed on the covariance matrices to obtain the DOA of incident signals with low computational complexity. Finally, angle pairing is achieved by deriving the equivalent signal vector of the virtual arrays using the estimated angles. Numerical simulation results show that the proposed algorithm not only provides more accurate 2-D DOA estimation performance with low complexity, but also achieves angle estimation for small numbers of samples compared to existing similar methods. |
| first_indexed | 2024-04-11T22:46:50Z |
| format | Article |
| id | doaj.art-0d868c7180cb421cbbeef5bc7633ccee |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-04-11T22:46:50Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-0d868c7180cb421cbbeef5bc7633ccee2022-12-22T03:58:43ZengMDPI AGSensors1424-82202019-05-01199217610.3390/s19092176s19092176An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample SizesXiaofeng Gao0Xinhong Hao1Ping Li2Guolin Li3Science and Technology on Electromechanical Dynamic Control Laboratory, School of Mechatronical Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, ChinaScience and Technology on Electromechanical Dynamic Control Laboratory, School of Mechatronical Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, ChinaScience and Technology on Electromechanical Dynamic Control Laboratory, School of Mechatronical Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, ChinaScience and Technology on Electromechanical Dynamic Control Laboratory, School of Mechatronical Engineering, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, ChinaIn this paper, an improved two-dimensional (2-D) direction of arrival (DOA) estimation algorithm for L-shaped nested arrays is proposed. Unlike the approach for a classical nested array, which use the auto-correlation matrix (ACM) to increase the degrees of freedom (DOF), we utilize the cross-correlation matrix (CCM) of different sub-arrays to generate two long consecutive virtual arrays. These acquire a large number of DOF without redundant elements and eliminate noise effects. Furthermore, we reconstruct the CCM based on the singular value decomposition (SVD) operation in order to reduce the perturbation of noise for small numbers of samples. To cope with the matrix rank deficiency of the virtual arrays, we construct the full rank equivalent covariance matrices by using the output and its conjugate vector of virtual arrays. The unitary estimation of signal parameters via rotational invariance technique (ESPRIT) is then performed on the covariance matrices to obtain the DOA of incident signals with low computational complexity. Finally, angle pairing is achieved by deriving the equivalent signal vector of the virtual arrays using the estimated angles. Numerical simulation results show that the proposed algorithm not only provides more accurate 2-D DOA estimation performance with low complexity, but also achieves angle estimation for small numbers of samples compared to existing similar methods.https://www.mdpi.com/1424-8220/19/9/21762-D DOA estimationL-shaped nested arrayssmall numbers of samplescross-correlation matrix |
| spellingShingle | Xiaofeng Gao Xinhong Hao Ping Li Guolin Li An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes Sensors 2-D DOA estimation L-shaped nested arrays small numbers of samples cross-correlation matrix |
| title | An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes |
| title_full | An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes |
| title_fullStr | An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes |
| title_full_unstemmed | An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes |
| title_short | An Improved Two-Dimensional Direction-Of-Arrival Estimation Algorithm for L-Shaped Nested Arrays with Small Sample Sizes |
| title_sort | improved two dimensional direction of arrival estimation algorithm for l shaped nested arrays with small sample sizes |
| topic | 2-D DOA estimation L-shaped nested arrays small numbers of samples cross-correlation matrix |
| url | https://www.mdpi.com/1424-8220/19/9/2176 |
| work_keys_str_mv | AT xiaofenggao animprovedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes AT xinhonghao animprovedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes AT pingli animprovedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes AT guolinli animprovedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes AT xiaofenggao improvedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes AT xinhonghao improvedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes AT pingli improvedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes AT guolinli improvedtwodimensionaldirectionofarrivalestimationalgorithmforlshapednestedarrayswithsmallsamplesizes |