Sequential noise-boosted M-estimation for robust parameter estimation under impulsive noise

We propose a sequential noise-boosted M-estimation algorithm for estimating system parameters in environments characterized by impulsive (heavy-tailed) noise. This algorithm extends the conventional M-estimation framework by strategically injecting artificial noise into the observations, thereby facilitating the estimation procedure and ensuring convergence to the desired estimator. A fundamental criterion theorem is established to determine the conditions under which injecting scale-family noise enhances the efficacy of the M-estimator in heavy-tailed background noise. For cases where noise injection is beneficial, it is rigorously proved that the sequential noise-boosted M-estimation algorithm converges with probability one. Experimental results demonstrate that the proposed algorithm outperforms traditional M-estimation methods, both under a given injected noise intensity and when the noise injection is adaptively optimized via Bayesian optimization. Furthermore, it is observed that the proposed algorithm can asymptotically achieve the performance of the maximum likelihood estimator (MLE) for system parameter estimation.