Research On Array Errors Calibration And Direction Of Arrival Estimation

DOA(direction of arrival)estimation techniques play an important role in the field of electronic reconnaissance and electronic warfare,etc.Spatial spectrum estimation technology can estimate the DOA of multiple radiation signals,which has wide application in direction finding system and therefore attracts extensive attention from scholars.Usually,spatial spectrum estimation algorithms have excellent performance in ideal direction finding conditions with the premise of an exact characterization of the array manifold.However,array errors are inevitable in the real direction finding system due to the effects of ambient temperature,humidity,inconsistent electromagnetic properties of each element in the antenna array,and other factors.The performance of spatial spectrum estimation algorithms will be greatly degraded in the presence of array errors.Therefore,array errors restrict the development of spatial spectrum estimation techniques from theoretical research to practical application.This paper studies array errors in real passive array direction finding systems and proposes several self-correction algorithms for array gain/phase errors,mutual coupling errors,gain/phase errors and mutual coupling errors of the real passive array direction finding system,so as to realize correct estimation of DOA of radiation signals.Firstly,for the problems of array gain/phase errors in the real passive array direction finding system,an estimation method of array gain/phase error coefficients and one-dimensional DOA is proposed based on uniform linear array;an estimation method of array gain/phase error coefficients and two-dimensional DOA is proposed based on L-shaped array.The DOA and array gain/phase coefficients can be estimated by applying a group of auxiliary sensors with consistent gain/phase characteristic,based on the traditional idea of orthogonal linear transformation,converting array manifold in the presence of array gain/phase errors and combined with the least square method.In the proposed algorithm,spectral peak searching and operational characteristics of decomposition are not required,so small computational algorithms and low complexity are available.Simulation results show that good performance of DOA estimation and higher accuracy of gain/phase coefficients estimation can be obtained by this method,thus realizing rapid calibration of array.Secondly,for the problems of array mutual coupling errors in the real passive array direction finding system,an cascade estimation method of array mutual coupling error coefficients and one-dimensional DOA is proposed on the basis that mutual coupling error matrix for uniform linear array is in the form of complex symmetric band Toeplitz matrix;an cascade estimation method of array mutual coupling coefficients and two-dimensional DOA is proposed on the basis that mutual coupling error matrix for uniform circle array is in the form of complex symmetric cycle band Toeplitz matrix.The DOA and array mutual coupling coefficients can be estimated by researching each coefficient,decomposing mutual coupling error matrix into mutual coupling coefficient vector and position matrix,transforming array manifold,constructing objective function,and solving the objective function under linear constrained,so as to realize self-calibration of array mutual coupling errors.It is not necessary to do multidimensional iteration calculation,without initial iterative selection and setup issues,so the complexity of the proposed method is lower.Meanwhile,the calibration performance,necessary conditions of parameter identifiability and computational complexity of the method are analyzed.By simulation experiments and tested data analysis,it is verified that such method is effective and has higher performance in DOA estimation and mutual coupling error coefficient estimation,which can effectively calibrate array mutual coupling errors and enhance estimation performance.Thirdly,in practical situations,various sources of array errors may be present simultaneously,but the aforesaid calibration methods are capable of analyzing statistical performance of circumstances where only one array error model presents,so the calibration performance of some methods is not ideal.Considering this case,the mathematical model of array gain/phase errors and mutual coupling errors is established,an estimation method of array gain/phase error coefficients and mutual coupling error coefficients and DOAs is proposed.By applying a group of independent auxiliary sensors,we first estimate DOA and array gain/phase error coefficient.During this process,we convert matrixes to make steering vector unrelated to mutual coupling coefficient and do decoupling to estimate mutual coupling error coefficient and get a correct estimation of DOA and array gain/phase error coefficient and mutual coupling error coefficient.No calibration source,pectral search or iteration is required in this method,so the complexity is low and computational algorithm is small.It is verified by simulation experiments that this method has a good DOA estimation performance and higher accuracy and stability in estimating array gain/phase error coefficient and mutual coupling coefficient when SNR reaches certain threshold,thus illustrating the effectiveness of the proposed method in calibrating array gain/phase and mutual coupling errors.