Array Error Calibration And Direction Finding Algorithms Research

Both the classical superresolution algorithms and the sparse refactor-based algorithms have superresolution direction-finding performance under the premise of ideal array manifold.However,in practical application,array errors often exist due to various reasons,such as array element position errors,channel amplitude and phase errors,and mutual coupling between array elements.The existence of these errors will cause the array manifold to deviate significantly from the ideal case,thus making these superresolution direction finding algorithms seriously deteriorate or even fail.Therefore,it is of great theoretical significance and practical value to study the direction-of-arrival(DOA)estimation algorithms with array errors,and it is also an important direction in array signal processing in recent years.The main work of the dissertation is as follows:1.In view of the problem that array errors lead to the performance degradation or even failure of the high-resolution direction finding algorithms,we proposed offline array errors correction methods based on invasive weed optimization(IWO)for the position errors,gain-phase errors and mutual coupling,respectively.By using an auxiliary signal source with known azimuth,and combining the basic principle of subspace and the IWO,we transform the array errors solution into the parameter optimization problem,and modify the original steering vector with the estimated array errors.After correction of position errors of linear arrays,gain-phase errors of linear arrays,and mutual coupling of linear arrays and circular arrays,good DOA estimation performances are obtained.The proposed array error calibration methods are superior to genetic algorithm(GA)and particle swarm optimization(PSO)in both the convergence and the estimation accuracy of array errors and DOAs.Moreover,the root-mean-square error(RMSE)curves of the proposed methods for DOA estimation are closer to Cramér–Rao bound(CRB)curves.In addition,the proposed methods have no special requirements on array structure,and can be extended to the errors calibration of other arbitrary arrays.2.Combining the search depth of PSO algorithm and the search breadth of IWO algorithm,an offline correction method for gain-phase errors based on IWO-PSO algorithm is proposed.The proposed method is obviously better than GA algorithm and PSO algorithm in convergence.Moreover,regardless of the magnitude of the gain-phase errors,the accuracy of DOA and gain-phase errors estimation of the proposed method is better than that of other calibration methods based on optimization algorithms,and the traditional algorithm which relies on the initial value of the gain-phase errors.Furthermore,an offline algorithm,based on IWO-PSO for joint correction of gain-phase errors and mutual coupling,is proposed.Firstly,a known correction source is used to establish an objective function containing both gain-phase errors and mutual coupling coefficient,and then the IWO-PSO algorithm is used to search for the gain-phase errors and mutual coupling coefficient satisfying the optimal value of the objective function through an alternating iteration procedure.The proposed method does not need prior knowledge of array errors,and has good estimation performance of DOA and array errors.Compared with other calibration methods based on optimization algorithms,the RMSE curve of the proposed method for DOA estimation is closer to the CRB curve.3.An on-grid self-calibration method based on the covariance fitting criteria is presented for unknown gain-phase errors.The proposed method does not require the presence of calibration sources and previous calibration information,unlike offline ways.In the both cases of uncorrelaed signal sources and correlated sources,it has good performance within a certain range of phase errors,and overcomes the problems of the traditional algorithms that they need prior correction information and fail when the signal sources are correlated.Firstly,the gain errors are estimated by using the diagonal of the covariance matrix subtracting the noise term.Secondly,an on-grid sparse technique based on the covariance fitting criteria is reformulated aiming at gain-phase errors to obtain DOA and the corresponding source power.Finally,we estimate the phase errors by introducing an exchange matrix.The exchange matrix is a special case of forward and backward space smoothing method and can reduce the correlation between signal sources.Furthermore,the proposed method is applied to solve the problem of performance degradation in the sparse and parametric approach(SPA)under the condition of gain-phase errors.The problem is addressed by combining the proposed method and the SPA.However,because the proposed method is an alternating iterative algorithm,it is easy to fall into local optimization when the phase errors are big,and its computational complexity is high.4.A gridless sparse self-calibration method based on covariance fitting criterion is proposed for unknown gain-phase errors.Firstly,the discrete angle domain is transformed into the continuous range and a mathematical model is established in the continuous range.The objective function based on covariance fitting criterion is transformed into semidefinite programming problem(SDP),and DOA estimates and gain-phase errors estimates are derived.Next,the estimated gain-phase errors are used to compensate the SDP objective function,and then get the more accurate DOA estimation through convex optimization.The proposed algorithm does not need to discretize the angle domain to avoid the problem of grid mismatch,does not need alternative iteration,and has low computational complexity.Moreover,compared with the on-grid self-calibartion method,the proposed method has higher DOA and phase estimation accuracy.Furthermore,DOA estimation based on partially calibrated array is studied in the case of nonuniform noise.Combining with the covariance fitting criterion and the ESPRIT-Like algorithm,a unified mathematical model is established for both cases of uncorrelated signal sources and correlated signal sources.The proposed method is without alternative iteration,and has good robustness to signals correlation and non-uniform noise.In the cases of low signal-to-noise ratio(SNR)and high worst-noise-power ratio(WNPR),the estimation accuracies of DOA and gain-phase errors of the proposed method are higher than that of the ESPRIT-Like algorithm and the gridless sparse self-calibration algorithm,and the RMSE curve of the proposed method for DOA is closer to the CRB curve,...