<p>This article proposes a robust direction of arrival (DOA) estimation method in which the traditional MUSIC algorithm is enhanced with the Tukey Biweight cost function. The proposed scheme is specifically designed to perform well in chaotic signal situations. The chaotic nature of real world signal environments is modeled using a chebyshev-based chaotic number generator, which effectively captures signal variability and non-linearity. To assess the performance of the proposed methods, extensive Monte Carlo simulations have been performed on four configurations: standard multiple signal classification (MUSIC), MUSIC with Tukey Biweight, Chaotic MUSIC, and Chaotic MUSIC with Tukey Biweight. In this work, performance was measured using root mean square error (RMSE) and probability of resolution (PR) metrics. The simulation results demonstrate that the incorporation of chaotic signal modeling combined with the robust Tukey Biweight function significantly enhances DOA estimation accuracy, especially in challenging scenarios with low signal-to-noise ratio (SNR) and high signal correlation. Among the tested techniques, Chaotic MUSIC with Tukey Biweight consistently outperformed others, showing improved resolution capability and robustness. In practical wireless communication and radar systems, the proposed approach presents a strong candidate for reliable DOA estimation.</p>