Research On 2D-DOA Estimation And Tracking Algorithm For Coprime Planar Array

Array signal processing is an important branch of signal processing and has been widely used in many civilian and military fields.As one of the vital tasks of array signal processing,the direction of arrival(DOA)estimation of signal sources has developed vigorously since the 1970 s.And a large number of super-resolution DOA estimation algorithms have emerged.However,most existing algorithms are based on compact arrays represented by uniform arrays.Due to the limitation of the spatial domain Nyquist sampling theorem,the improvement of estimation accuracy in existing algorithms must be at the cost of increasing hardware costs.At the same time,most super-resolution algorithms have high computation complexity and have difficulty in engineering implementation,which only suitable for source localization of spatial static signals and cannot realize on-line real-time tracking of two-dimensional DOA of spatial time-varying sources.Compared with traditional compact arrays,coprime arrays have the advantages of sparse perception and the unique properties of prime numbers.They can obtain larger array apertures and higher degrees of freedom while using the same number of physical array elements,that is why the signal processing technology with coprime arrays has been widely used in radar,sonar,wireless communication and other fields.Therefore,this paper concentrate on the research of two-dimensional DOA estimation and tracking algorithms for spatial signal sources with coprime planar arrays,which owns rich theoretical significance and practical value.The main work of the thesis are as follows:(1)The two-dimensional DOA estimation algorithms based on rotation invariance under coprime planar arrays are studied,including the Two-Dimensional Estimation Signal Parameters via Rotational Invariance Techniques(2D-ESPRIT)and the Two-Dimensional Propagator Method(2D-PM).This type of algorithm uses the rotation invariance of the signal subspace to obtain parameter estimates,and can realize automatic pairing of two-dimensional angles.Because of no spectral peak search is required,the computational complexity of this type of algorithm is lower than the classic source localization algorithms based on two-dimensional spectral peak search,such as the MUltiple SIgnal Classification(MUSIC)algorithm and Capon algorithm.Considering that the sparse distribution of the elements in coprime arrays increase the effective aperture of arrays,the parameter estimation performance of this kind of algorithm is better than the 2D-ESPRIT and 2D-PM in the uniform arrays with the same number of array elements.IV(2)The two-dimensional DOA estimation algorithms based on successive spectral peak search under coprime planar arrays are studied,including the successive MUSIC algorithm and the successive Capon algorithm.This type of algorithm obtains the initial parameter estimation based on the rotation invariance firstly,then breaks down the two-dimensional spectral peak search process into two onedimensional spectral peak searches to avoid the huge computational load brought by two-dimensional global search,which greatly reduce the computational complexity of the algorithm.With the same constructer of arrays,the two-dimensional angle estimation performance of this kind of algorithm is superior to that of source localization algorithms based on rotation invariance.And when the elevation(or azimuth)of multiple sources are the same,this type of algorithm can also work effectively.(3)The two-dimensional DOA estimation algorithms based on the idea of dimensionality-reduced spectral peak search under coprime planar arrays are studied,including the Reduced-Dimension MUSIC algorithm and the Reduced-Dimension Capon algorithm.This type of algorithm obtains the initial estimation of the parameters by utilizing the rotation invariance firstly,and then converts the twodimensional spectral function in the classical spectral search algorithm into a second-order optimization problem,and reduces the two-dimensional global spectral peak search to a one-dimensional local search.Compared to successive spectral peak search algorithms.the computational complexity of this kind if algorithm is further reduced.Under the same structure of array,the parameter estimation performance of this kind of algorithm is close to that of the classical two-dimensional spectral peak search algorithms,and is superior to the rotation invariance method.The algorithm can still work effectively even if the multiple sources have same elevation or azimuth angles.(4)The two-dimensional DOA estimation algorithms based on polynomial root-finding under coprime planar arrays are researched,and the Root-MUSIC algorithm and the Root-Capon algorithm are emphatically analyzed.This type of algorithm reduces the two-dimensional parameter estimation problem to one dimension firstly,and then converts the spectral function in the classical spectral peak search algorithm into the corresponding polynomial,finally,the parameters are obtained by solving the root of the polynomial.Because of no spectral peak search,the computational complexity of the proposed algorithm is lower than the algorithms proposed in the previous chapter.What’s more,the performance of DOA estimation of this kind of algorithm is superior to that of the algorithms based on rotation invariance.(5)Because the traditional high-resolution DOA estimation algorithms cannot meet the needs of real-time direction finding and tracking of dynamic targets in practical applications,the twodimensional DOA tracking algorithms for the coprime planar arrays are researched,with emphasis on DOA tracking algorithms based on the projection approximation subspace tracking(PAST)algorithm and the Projection Approximation Subspace Tracking with deflation(PASTd)algorithm,separately,and the subspace tracking algorithm based on Parallel Factor via Recursive Least Square Tracking(PARAFAC-RLST)is also studied.The front two algorithms are based on the theoretical framework that the eigen subspace can be regarded as the optimal solution of an unconstrained cost function.In the two algorithms,the signal subspaces are obtained by solving the minimum value of the corresponding unconstrained functions,and then the DOA estimations of the source can be gained.Therefore,eigenvalue decomposition processes with high computational complexity in classical DOA estimation algorithms are avoided.The subspace tracking algorithm based on adaptive PARAFAC-RLST constructs the received data as a trilinear model,and considers the carrier matrices in the trilinear model as the optimal solution of a window function,and then uses the iterative least square method to update the PARAFAC iteratively.Finally,the estimates of the direction of arrival are obtained.This algorithm uses a linear iterative update process to replace the batch processing of matrices in traditional PARAFAC algorithms,which greatly reduces the computational load.The three DOA tracking algorithms studied above can realize the on-line real-time estimation and tracking of two-dimensional direction of arrival for time-varying targets,moreover,they are suitable for a large number of practical scenarios attribute to the low computational complexity.