基于改善特征值离散度的信源数目估计

Source number estimation based on improved dispersion of eigenvalues

摘要:

相比于传统的信源数目估计方法，基于特征值差值法的信源数目估计具有较小运算量的优点，但是因为在低信噪比时效果差，且在色噪声下效果不稳定等多种缺点一直未能在实际中应用。因此分析了特征值离散度对差值法估计的影响，提出一种基于对数函数拟合改善特征值发散程度的方法，并利用拟合特征值进行差值法进行估计。该算法很大程度上减少了相邻信源特征值之间的差值，使信源特征值和噪声特征值之间的差值更加明显，大大提升了差值法的估计性能，同时保证了较小的运算量。经实验仿真表明，该方法在白噪声和色噪声下都能进行稳定估计，在较低信噪比和低快拍数下依然具有良好估计性能的优点。

Abstract:

Compared with the traditional method of source number estimation , the source number estimation based on the eigenvalue-difference method has the advantage of less computational complexity, but because of the poor performance at low SNR and the unstable effects under color noise, etc. Various shortcomings make it have not been applied in practice. This paper analyzes the influence of the dispersion of eigenvalues on the estimation of the eigenvalue-difference method, proposes a method to improve the divergence of eigenvalues based on logarithmic functions, and uses the fitted eigenvalues to estimate the source number. The algorithm greatly reduces the difference between the adjacent source eigenvalues, makes the difference between the source eigenvalue and the noise eigenvalue more obvious, greatly improves the estimation performance of the eigenvalue-difference method, and guarantees the smaller amount of operations. Experimental simulations show that the proposed method can perform stable estimation under both white noise and color noise, and still has the advantage of good performance under low signal-to-noise ratio and low-speed shots.