Study On Source Localization Via Signal Representation Using Over-Complete Bases

This thesis mainly studies the sensor array source localization problem from the perspective of a signal representation using over-complete bases. Different from the signal subspace fitting (SSF) method, such as multiple signal classification method (MUSIC), the thesis transforms source location problem to an ill-posed inverse problem which can be solved by regularization to obtain the precise DOA. Over-complete system always shows sparse solution, so two sparsity methods are introduced- 1 norm and p norm, which later are applied to regularization as an constrain item to insure the sparse solution and the peak spectrum occurred at correct source location. The 1 regularization has some different forms due to the objective function and constrain item, fortunately however, they can be translated to conform to second order cone programming (SOC) and can be solved effectively by inner point method (IPM). The non-convex property of p regularization has to need an local optimization iterative method to approximate its global minima. The simulation shows that the above methods can obtain satisfactory estimation of DOA.In addition, under different assumption of multiple sample signals, presents several methods: the average method can be used for non-zero mean value signal, the beam-formation space method for zero mean value signal and the SVD method for both. Attribute to the absence of covariance matrix of sensor array output, the methods in this thesis can resist the influence of correlate signal which can cause order wane of signal subspace. Finally studies the property of above methods through computer simulation, including resolution, robustness to noise and robustness to correlated signals. The result shows that the methods in this paper have better resolution than the traditional SSF method under the same condition and even can perform effectively under lower signal-noise ratio and multiple correlated signals circumstance.