Abstract: Aiming at the precision loss problem of most low-complexity Root-MUSIC algorithms at present， a low-complexity Root-MUSIC algorithm with precision compensation ability is studied and proposed. The algorithm reconstructs the autocorrelation matrix with Toeplitz shape according to the first row of the approximate data observation matrix obtained by finite snapshots， so that the reconstructed autocorrelation matrix has Hermitian property. After decomposing the reconstructed autocorrelation matrix， the noise subspace is obtained， the noise subspace is flipped and split， a new root-finding polynomial is reconstructed， and then the DOA estimated value is obtained by the root-finding method. The algorithm proposed in this paper using Toeplitz matrix reconstruction and root polynomial reduction effectively improves the DOA estimation accuracy of the improved Root-MUSIC algorithm. And the time complexity of the improved algorithm is no higher than that of previous algorithms. Under different incident sources and sampling snapshots， the algorithm proposed in this paper also shows stronger robustness and stability.

Key words: Root-MUSIC algorithm; precision loss; reconstructing Toeplitz matrix; noise subspace; flip and split; root polynomial reduction; robustness and stability