Distributed estimation in the Internet of Things (IoT) often suffers from unreliable communication links and non-Gaussian environmental noise, which significantly degrade the performance of conventional algorithms. Most existing approaches assume ideal channel conditions and Gaussian noise, making them inadequate for realistic IoT scenarios. This paper proposes a robust and communication-efficient compressed double-diffusion algorithm based on the Maximum Correntropy Criterion (MCC). The proposed method leverages MCC to effectively handle impulsive and non-Gaussian interference. Furthermore, a random projection compression strategy is incorporated to significantly reduce communication overhead while maintaining estimation accuracy, as well as to enhance resilience against wireless link noise. We provide theoretical analysis on convergence and steady-state behavior, and extensive simulations validate the superior robustness and performance of the proposed algorithm over existing MSE-based and uncompressed MCC diffusion methods. The results highlight the practical potential of our approach for resilient and scalable distributed learning in bandwidth-constrained and noise-prone IoT environments.

To further improve the performance of the kernel adaptive filtering algorithm in a non-Gaussian environment, a robust kernel least mean square algorithm is proposed, and the effectiveness of the root cost function and the convergence of the algorithm is theoretically analyzed. An improved online vector quantization criterion is then applied to the proposed algorithm to suppress the linearly growing network size. Finally, the different performances of the algorithm of this paper and other kernel adaptive filtering algorithms as well as this paper’s algorithm before and after quantization are compared in Mackey Glass chaotic time series as well as in system identification, confirming the superiority of the algorithm of this paper and the improved online vector quantization criterion.