A robust direction of arrival estimation method based on the chaotic MUSIC algorithm

www.nature.com/scientificreports OPEN A robust direction of arrival estimation method based on the chaotic MUSIC algorithm Bijaya Kumar Muni1,2,9, Tahesin Samira Delwar3,9, Trilochan Panigrahi1, Prasanta Kumar Pradhan7, In-Ho Ra4, Hyung-Jin Kim8, Maninder Kaur6, A. S. M. Sanwar Hosen5 & Jee-Youl Ryu3 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. Keywords Direction of arrival, Multiple signal classification, Source localization, Sensor network, Robust, Tukey Biweight Signal processing is a concept that focuses on analyzing, modifying, and synthesizing signals such as sound, seismic data, and altimeter measurements. The fundamental challenges in signal processing include: a) determining how best the signal is sensed to ensure accurate and efficient data acquisition, b) maximizing system performance while minimizing cost to achieve optimal resource utilization, and c) extracting the original information from the signal with high fidelity for accurate interpretation and application. There are many applications of signal processing like wireless sensor networks (WSN), acoustics, sonar, video processing etc. WSN is a self-configured system comprises of sensor nodes designed for monitoring remotely for a specific purpose. Wireless source localization has many applications such as target tracking, wireless security, signal routing, emergency response and interference alignment1. Source localization involves in estimating the position of the source, from the signal received at the sensor nodes, where each sensor in the array receives the signal data to estimate the position (source location) of the source2. Direction of arrival (DOA) is one of the key issues in array signal processing for analysing source location. This DOA can be used for determining either a single source or multiple sources by using a sensor array. A sensor array (or array of sensors) is group of sensors, arranged in certain geometric patterns, used in many fields of science and engineering, particularly where the 1Department of Electronics and Communication Engineering, National Institute of Technology Goa, Farmagudi, Ponda, India. 2Department of Electronics and Communication Engineering, J B Institute of Engineering and Technology, Hyderabad, India. 3Department of Information and Communication Engineering, Pukyong National University, Busan 48513, Republic of Korea. 4Department of AI Convergence, Kunsan National University, Gunsan, South Korea. 5Department of Artificial Intelligence and Big Data, Woosong University, Daejeon 34606, South Korea. 6Department of Computer Science and Engineering, Thapar Institute of Engineering and Technology, Patiala Punjab, India. 7Present address: Department of Electronics and Communication Engineering, J B Institute of Engineering and Technology, Hyderabad, India. 8Present address: Department of IT Applied System Engineering, Jeonbuk National University, Jeonju, South Korea. 9Bijaya Kumar Muni and Tahesin Samira Delwar: These authors contributed equally to this work. email: ; Scientific Reports | (2026) 16:15877 | https://doi.org/10.1038/s41598-026-40266-3 1 www.nature.com/scientificreports/ goal is to study propagating fields. Numerous techniques have been developed in the array signal processing for estimating the DOA of the signals by using different algorithms for different array models such as linear array, rectangular array, non-uniform and other arbitrary arrays. Over the past few decades DOA has been extensively studied and numerous algorithms have been presented. Algorithms for DOA estimation are mainly divided into three different categories namely classical, sub-space and maximum likelihood (ML) techniques2. Among the most popular methods, multiple signal classification (MUSIC) algorithm part of the subspace method are widely used which involves the estimation of co-variance matrix and its eigen decomposition3. MUSIC is a well analysed and mostly used algorithm and also computationally efficient as compared to maximum-likelihood (ML) method. It is essentially used for calculating the DOA of signal impinge on the array. The MUSIc algorithm perform well for narrow-band signal with normal distributed noise, whereas the perfoamnce degraded for coherent signals and non-Gaussian noise environment4,5. In fact, real-time signals contain unpredictable noise or variations in parameters, making them inherently non-deterministic in nature. In literature, many variants of MUSIC algorthms are proposed to make robust against different noise environment [6]. The DOA is estimated from the signal covariance matrix and it is sensitive to the non-Gaussian noise and other disturbances present in the channel. Deep learning methods are used now to estimate the DOA in multipath and impulse noise wireless environment6. Recently, researchers were used Tukey Biweight cost function to minimize the error. The same cost function can be used to estimate the robust covariance matrix to make the MUSIC algorithm robust. Chaotic signal models are employed to represent complex real-world phenomena. A chaotic signal arises from a nonlinear autonomous deterministic system whose dynamics are highly sensitive to initial conditions. By introducing structured randomness, such models bridge the gap between purely random noise and fully predictable signals7. In array signal processing, chaotic signals have been applied to tasks such as weak signal detection and beamforming, exploiting their sensitivity to initial conditions and inherent nonlinearity8. The use of chaotic modeling enhances the robustness of covariance-based DOA estimation algorithms against noise, signal correlat (...truncated)