Direction Of Arrival Estimation Algorithms In The Presence Of Array Error

As an important research branch of array signal processing, direction of arrival (DOA) estimation has been widely used in radar, sonar, communication systems, smart appliances and smart meeting systems. The vast majority of existing DOA estimation algorithms are based on the assumption that the array manifold is known precisely. However, in practical engineering applications, affected by the climate, environment and changes in the device itself, the uncertainties of the array manifold are unavoidable. Then the performance of these algorithms will deteriorate seriously, or even fail. Therefore, with important theoretical and practical value, DOA estimation in the presence of array error has become an important research area. In this paper, we focus on the problem of DOA estimation in the presence of three type of typical array errors. Several self-calibration algorithms are proposed, and the main contributions can be summarized as follows:Firstly, for channel gain and phase errors, we propose an algorithm which is based on the amplitude of the covariance matrix. From perspective of "decoupling", the gain errors, source directions and phase errors are estimated sequentially. The proposed algorithm needs no iteration and has the advantage that the performance is independent of the phase errors. For applications in the modern communication systems, the proposed algorithm can be easily extended to exploit the noncircularity of the signals. As the high-order cumulant can be used to suppress the Gaussian noise, we proposed a similar fourth-order cumulants based algorithm, which can effectively eliminate the influence of channel gain and phase errors in colored noise environment.Secondly, for mutual coupling between array elements, we proposed two self-calibration algorithms utilizing the statistical characteristics of the signals. In most existing algorithms, the mutual coupling matrix is expressed with a particular form, which can be characterized using a few of mutual coupling coefficients. In order to improve the performance, we can take advantage of the statistical properties of the signals. We proposed two algorithms:The first one assumes that all signals are uncorrelated. According to the principle of covariance matrix fitting, a cost function is defined with respect to the mutual coupling coefficients, signal directions and power. An iterative method can be used to get the minimizer of the cost function and estimate the DOAs. This algorithm can be applied to uniform linear arrays, uniform circular arrays and some other special arrays. Simulation results have shown that this algorithm can obtain performance improvements for low SNR condition. The second algorithm is designed for uniform linear arrays. A cost function is defined based on the covariance matrix and the ellipse covariance matrix. The mutual coupling coefficients can be estimated using a similar iterative method. Simulation results show that using the noncircularity of the signals can effectively improve the performance of mutual coupling self-calibration.Thirdly, for sensor location errors, we proposed an algorithm to solve the problem that the existing iterative algorithms are dependent on the initial estimates. As location errors can be expressed as direction-dependent phase errors, we define an MUSIC based spatial spectrum which is robust to phase errors. The DOAs and the steering vectors can be estimated by searching the peaks of this spectrum. Then the least squares estimate of the location errors can be got from the estimated steering vectors. Since the effect of the location errors is considered, the proposed algorithm can calibrate the array to some extent even when traditional algorithms cannot distinguish all signals. Therefore, the proposed algorithm can be used to ensure the effectiveness of the iterative algorithms.Finally, for the problem of DO A estimation and mutual coupling self-calibration for non-unifrom linear arrays, we propose a new algorithm for constructing augmented covariance matrix. The existing self-calibration algorithms just make use of the Toeplitz structure of the covariance matrix. We consider utilizing the property of the rank of the covariance matrix to improve reconstruction accuracy. Inspired by the research in the field of low-rank matrix reconstruction, we construct the augmented covariance matrix through a problem of constructing a positive semidefinite Toeplitz matrix with determined rank. This problem is simplified by the way of truncated nuclear norm regularization and a solution can be got using an iterative schema. Then the DOAs can be estimated using traditional algorithms based on the constructed augmented covariance matrix.