Localization Algorithm For Incoherently Distributed Sources Using Multi-dimensional Fitting

The parameter estimation of the direction-of-arrival(DOA)is a generic problem concerned in array signal processing.There are various high-resolution parameter estimation algorithms of the DOA which are based on point sources for signal modeling.However,due to the existence of multi-path effects in complex application environment,the sources will expand at a certain angle in space.Thus,compared with actual signal model,the incoherently distributed source model is more applicable.At present,researchers have proposed some parameter estimation algorithms for incoherently distributed sources.But these algorithms are for antenna arrays of specific shape which lead to the limitation of application range.In order to solve the above problems,we proposed a new estimation algorithm that is appropriate for the incoherently distributed source for arbitrary array shape or large angle expansion.Firstly,we introduce several classical estimation algorithms of the DOA based on the point source model.However,the estimation algorithm for point sources cannot be applied directly to the incoherently distributed source model.There are a number of parameter estimation algorithms for the incoherently distributed sources.We briefly introduce several typical estimation algorithm of incoherently distributed sources.These algorithms are subspace-based algorithm and dispersed signal parametric estimation(DISPARE)algorithm based on subspace,generalized Capon algorithm based on beam forming and covariance fitting algorithm,respectively.We briefly describe the basic principles of these algorithms.Then we construct the array manifold vector for arbitrary based on manifold separation technique,and get the closed-form expression of the array covariance matrix.The initial estimation of the central DOA parameters and angle expansion parameters is obtained by scanning the 2-D spectral function.These initial estimates may have errors.To improve the performance of parameter estimation,we use the first-order Taylor expansion to approximate the covariance matrix.Then we use the weighted least-squares algorithm to improve the estimation performance.We get accurate estimation parameters through multi-dimensional fitting.Finally,the experiment simulation shows that the proposed algorithm has better performance than the covariance fitting algorithm and subspace-based estimation algorithm.Compared with other algorithms for incoherent distributed sources,the innovations of our algorithm are embodied in the following points:(1)The closed-form expression of the signal covariance matrix based on manifold separation technique is applicable to the case with arbitrary array geometries or large angle spreads.(2)The first-order Taylor expansion to approximate the covariance matrix is proposed for the first time,and we use the weighted least-square algorithm to improve the performance of the estimation.(3)We propose a multi-dimensional fitting approach that makes several types of parameters to be matched synchronously to obtain more accurate estimation parameters.