Robust Distributed Estimation via Equalization-Consistent Soft-Weighting for Mitigating Wireless Link Impairments

Distributed parameter estimation over wireless sensor networks is vulnerable to channel fading, path loss, and additive link noise. This letter proposes a robust diffusion algorithm that assigns soft combination weights using residuals between equalized neighbor estimates and temporally smoothed local references. The resulting observation-driven reliability measure avoids hard link-discarding decisions based on signal-to-noise-ratio thresholds. A Gaussian weighting function motivated by robust estimation maps the consistency residuals to continuous combination scores, while a median-based recursive scale estimate adjusts the kernel width to changing link conditions. A staged variable step-size strategy is further incorporated to compensate for the convergence delay introduced by temporal smoothing. Numerical simulations under several non-ideal wireless channel conditions show that the proposed method improves steady-state estimation accuracy and robustness relative to representative diffusion strategies. By continuously reducing the influence of severely distorted estimates rather than discarding entire links, the method seeks to preserve useful spatial information during distributed estimation.