Research On Distributed Sources Direction-of-Arrival Estimation

In the conventional research on direction-of-arrival (DOA) estimation, thesource is usually assumed to be a point. But from the time of 90s of last century, theresearch on distributed sources DOA estimation has been paid much attention. Nomatter the theoretical model establishment or DOA estimator, there have manyproductions been proposed. From the point source to distributed sources, the form oftheir model, estimation algorithm and the computational cost have change greatly.This is a new research area and a challenge for researchers. This thesis will discussdistributed sources problem. The main content and innovations are as the follows:1. Introducing some fundamental concepts and theories of distributed sources.As the development of array signal processing, researchers found that the distributedsources model can reflect the reality more properly in the case of near field, largeamount of multipath and high speed movement. The target in the distributed sourcestheory is always considered with volume or spatial power distribution. The spatialpower distribution can be continuous or discrete. Now, researchers have proposedmany kinds of distributed sources models and corresponding DOA estimators.2. Introducing the distributed sources model. In the model establishment theoryof distributed sources, the spatial power distribution of the target is usually abstractedto many point sources. According to the relativity in space domain and time domainof these points, the distributed sources can be divided into coherent distributed (CD)model, incoherent distributed (ID) model and partial coherent (PD) model. This thesismainly discusses the discrete ID model.3. Making a summary of the proposed distributed sources DOA estimationmethods. For many years of research on distributed sources, there have manyproductions been proposed. In this thesis, these methods, which being divided bytheir basic theory, are called subspace methods, beamforming methods, maximumlikelihood methods, covariance fitting methods and low complexity methods.4. Proposing a beam domain high resolution DOA estimation method fordistributed sources. The computational cost is usually very large for distributedsources DOA methods. In order to reduce the computational cost, a popular techniqueis making a pretreatment of these methods in beam domain. When the array sample istransformed from array domain to beam domain, it will be filtered in advance and thesignal-to-noise ratio will be enhanced. Then the high resolution method will be used.Because the freeness of sample in beam domain is much less than it in array domain,the computational cost will be reduced greatly.In this thesis, the basic theories of narrowband beamforming and beam domain DOA estimation are introduced first. Then the beam domain technique is associatedwith distributed sources DOA estimation method and a new method is derived.5. Proposing a simplified maximum likelihood estimation (MLE) method fordistributed sources. The former MLE method for distributed sources parameterestimation is a four dimensional nonlinear optimization method. Its computationalcost is very large and is called as four dimensional MLE in this thesis. In order toreduce its computational complexity, here proposes a lower dimensional MLEmethod. This new method is three dimensional nonlinear optimization method and iscalled three dimensional MLE. The theoretical analysis shows that the computationalcost of the new method will be reduced greatly. So the efficiency of the searchalgorithm is improved and more memory is saved. The CRB for the new MLEalgorithm is proposed, its computational cost is reduced also. The computersimulation validates that the estimation accuracy of these two MLE methods aresimilar. The new algorithm not only reduces the computational cost but also avoidsthe loss of performance, so it has higher practicability and real time capability.6. Proposing a new non-symmetric and large angular spread distributed sourcesmodel and the corresponding DOA estimation method. In former distributed sourcesresearch, the spatial angular spread is always assumed to be very small andsymmetric. This is an ideal assumption and usually not fitting in reality.In this thesis, a non-symmetric and large angular spread distributed sourcesmodel is proposed with Jacobi-Anger (JA) series expansion and Gaussian mixturetechniques. The new model will not be restricted by the distribution form and spatialangular spread. The former distributed sources models can be regarded as the specialcases of this new model.Using the JA series expansion technique, the model error will only relate withthe series order and have no relationship with the spatial angular spread. Furthermore,the model error can be very small if the series order is high enough. In theoreticalmodel establishment, the non-symmetric distribution is usually described as thesummation of many symmetric distributions. Here the non-symmetric distribution isconstructed with Gaussian mixtures technique, its shape can be changed when theparameters of mixtures is altered. Then the new model is associated with the steepestdescent algorithm and a new DOA estimation method is derived. Finally, dataanalysis validated the exactness of the theory.7. Proposing a distributed sources model with two orders Taylor series expansionand the corresponding low order approximation SMVDR algorithms. With theassumption of small spatial angular spread, the distributed sources model can bederived with low order Taylor series expansion approximately. Generalized arraymanifold uses one order Taylor series expansion and is called one order approximation distributed sources model here. Research on this thesis show that themodel error generated by neglecting high order items is distinct and the performanceof DOA estimation algorithm will degrade as a result. A two orders approximationdistributed sources model is proposed with two orders Taylor series expansion. Thenew model can reduce the model error and enhance the performance of DOAestimation. Here the distributed sources models with one order approximation andtwo orders approximation are called low order approximation model together. Thesemodels have no relationship with the form of spatial angular distribution. Thecorresponding DOA estimation algorithms have simple forms, low computationalcost, and good estimation performance.Then the distributed sources models of one order approximation model, twoorders approximation model, spatial frequency model and low order JA seriesexpansion model are compared with respect to the model accuracy. The conclusion isthat the spatial frequency model has the best accuracy. The accuracies of one orderapproximation model and two orders approximation model are close and have thesame order with low JA series expansion model.