Sparse array DOA estimation method based on improved ALM algorithm

The invention discloses a sparse array DOA estimation method based on an improved ALM algorithm, and the method comprises the following steps: reconstructing echo snapshot data sampled by a sparse array into a Toeplitz matrix, and assigning a reconstructed matrix value to an observation matrix D; filling the sparse matrix by using an improved ALM algorithm to obtain a full-rank matrix A; a full-rank matrix X is obtained after filling of all data is completed, the covariance R 'XX of each subarray is solved through a backward spatial smoothing algorithm, a covariance matrix RXX is obtained after the covariance R' XX is averaged, and finally direction-of-arrival angle estimation is completed through a conventional DOA estimation algorithm. According to the improved ALM algorithm, the full-rank receiving matrix can be well recovered under the conditions that the number of array elements is relatively small and the array elements are sparse, and good direction finding performance can still be kept under the condi