The Study Of Parameter Estimation Based On Nystrom Method In Array Signal Processing

Uniform linear array is a class of arrays that has widely used in real life. It has much advantage over other structural with unique structural characteristics, especially in calculation process. So it is very important to improve the estimation performance of uniform linear array.Classical signal processing algorithms can be divided into two categories, one is seeking direction of arrival of the signals under known source number conditions, the representative algorithms of this kind like MUSIC algorithm, root-MUSIC algorithm, ESPRIT algorithm. Another kind of algorithm is under the condition that not known the source number, under which case that we should have to estimate the numbers of source, in this paper, we mainly focusing on the algorithm based on gerschgorin disc to estimate the number of source. The gerschgorin disc theory means taking the diagonal elements of the matrix as the center, then taking the sum of the absolute value of the other elements in the same line of the center as the radius. The cluster of the discs we call them as Gerschgorin discs. Classic gerschgorin disc algorithm is based on the unitary transformation of the covariance matrix, which can be divided the discs into signal discs and noise discs separately, in that way, it can be used to estimate the number of sources.This paper proposed a new algorithm to solve fully coherent situation of the incident signals based on nystrom method. The new method does not need eigenvalue decomposition, it can give out the signal subspace directly. The algorithm requires calculate only part of the covariance matrix, and then use the equivalence matrix of the covariance matrix to calculate the subspace, and then it can be used to estimate the DOA, which can be greatly reduces the computational complexity during the signal processing. In this paper, it has make comparison between the new method and the classical spatial smooth algorithm.This paper proposes a low complexity DOA estimation algorithm method based on Nystrom algorithm. The new algorithm which has based on replacement of the covariance matrix can significantly reduce the computational complexity. Compared the performance of the new algorithm to the classical MUSIC method under the same array aperture, when the SNR conditions is low, the new method shows advantage over the classical method with the same array aperture.Based on full analyzing of the theory of classical gerschgorin disc, in this paper, we have proposed the method which has made full use of the information covariance matrix carried. And this algorithm can estimate the source number many times. To some extent, the proposed algorithm can improve the estimating performance with the same conditions. The proposed algorithm has been simulated in this paper, the simulation results show the effectiveness of this new algorithm.