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A study of a two-dimensional state-space balance (2D SSB) method for estimating direction of arrival (DOA) for uniform rectangular array (URA) is presented in this letter. The comprehensive utilization of controllability and observability matrices and automatic pairing technique are considered in this method by using the single snapshot. Therefore, the DOAs of elevation angle and azimuth angle can pair automatically and acquire better estimation performance compared with 2D matrix pencil method or unitary matrix pencil method. In addition, the proposed method can handle correlated signals directly without preprocessing. Simulation is conducted to verify the effectiveness of the proposed method.

In array signal processing, target direction of arrival (DOA) estimation has been widely applied in radar, sonar, wireless indoor positioning [

This paper presents a two-dimensional state-space balance (2D SSB) method that is applied to the DOA estimation in order to get better DOA estimation than the 2D MP/UMP method. On one hand, the comprehensive utilization of controllability and observability matrices has been considered to improve direction abilities. On the other hand, this method can obtain the elevation angle and azimuth angle without pair matching process via automatic pairing technique.

The uniform rectangular array (URA) in Figure

Array geometry of the URA.

Suppose

Equation (

Considering the singular value decomposition (SVD) of matrix

Construct the Hankel matrices

Use the singular value decomposition of Hankel matrix

Construct the controllability matrix

Use (

Use eigenvalue pairing technique to get the diagonal matrices

Use (

Firstly, two far-field narrowband signals impinge on the

RMSEs of azimuth and elevation angles against with SNR for the dispersed sources, where

Secondly, the challenging scenario of closely positioned sources impinging on the same URA is taken into consideration with

RMSEs of azimuth and elevation angles against with SNR for the closely positioned sources, where

Thirdly, same scenario with correlated signals and uncorrelated signals is also taken into consideration in Figures

RMSEs of azimuth and elevation angles against with SNR for correlated sources, where

RMSEs of azimuth and elevation angles against with SNR for uncorrelated sources, where

In the last simulation, 9 incident signals impinge on the same URA. The 2D DOA estimation results for 300 Monte Carlo simulations are shown in Figures

2D DOA estimation results of 9 incident signals, SNR = −5 dB.

2D DOA estimation results of 9 incident signals, SNR = 5 dB.

A 2D SSB method is proposed in this paper to estimate the angles of azimuth and elevation. This algorithm indicates high performance by using both observability and controllability matrices. Additionally, this method can provide automatically paired 2D direction cosine estimates without matching pair and deal with the correlated signals directly. Simulations demonstrate the effectiveness of our method.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China (Grants nos. 61671035 and 61501012).