Expanded co-prime matrix direct-finding estimation method based on polynomial root solving

Abstract

The invention discloses an expanded co-prime matrix direction finding estimation method based on polynomial root solving. The method comprises the following steps of establishing a mathematical modelof an array signal of an expanded co-prime linear array; solving a covariance matrix according to the established mathematical model, and performing eigenvalue decomposition on the covariance matrix to obtain a signal subspace and a noise subspace; constructing an extraction matrix according to a relationship between the expanded co-prime linear array and a one-dimensional uniform linear array, and constructing a root finding polynomial according to the relationship between the extraction matrix and the noise subspace; performing root finding through the obtained root finding polynomial, and determining a root corresponding to an information source angle; and completing one-dimensional DOA estimation. By combining the advantages of the ROOT-MUSIC algorithm and the expanded co-prime lineararray, the spatial degree of freedom can be effectively improved by utilizing the expanded co-prime linear array, and meanwhile, the algorithm complexity is reduced since the ROOT-MUSIC algorithm doesnot need to search a spectral peak, thereby obtaining the one-dimensional DOA estimation with higher precision.

Description

technical field [0001] The invention belongs to the field of array signal processing, in particular to an expanded coprime array direction finding estimation method based on polynomial root finding. Background technique [0002] The early research on DOA estimation was based on the uniform linear array, which is a one-dimensional array in which the array elements are arranged on the same straight line at equal intervals. The uniform linear array has the advantage of simple structure, but since each array element is located on the same straight line, the Only one-dimensional angle estimation can be performed. Although the traditional one-dimensional uniform linear array can perform effective DOA estimation, it has certain defects. Taking a uniform linear array as an example, a uniform linear array containing M array elements can only detect M-1 signal sources at most, that is, DOF=M, and the degree of spatial freedom is small. At the same time, in order to avoid the problem...

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