An Improved GDE Source Number Estimation Method Based on Kurtosis

In the field of signal processing, estimating the number of sources is extremely crucial. However, traditional methods like AIC and GDE have significant drawbacks. In high signal-to-noise ratio (SNR) conditions, the accuracy of the AIC method drops sharply due to the characteristics of its penalty function. For the GDE method, the uncertainty in the value of the adjustment factor D(L) leads to fluctuations in the results. To address these issues, this paper proposes a GDE method improved based on kurtosis. By analyzing the characteristic differences in kurtosis, a higher-order statistic, between sound signals and noise, a formula for D(L) that is dynamically related to the kurtosis of the collected signals is constructed. Its calculation involves operations such as eigenvalue decomposition of the covariance matrix, and the estimation is completed according to the Gerschgorin disk criterion. Experiments demonstrate that in different noise environments and scenarios, this method significantly outperforms traditional methods in terms of estimation accuracy, noise resistance, and stability. It shows particularly prominent advantages in high SNR real-world scenarios, providing a better means for estimating the number of sources.