Minimum Error Entropy Estimation Under Contaminated Gaussian Noise
Carlos Alejandro Lopez, Ferran de Cabrera, Jaume Riba · IEEE Signal Processing Letters · 2023
It is shown that R´enyi's entropy of a Gaussian mixture with entropic index α ∊ (1,∞] is upper-bounded by the cluster with minimum variance. This basic idea leads to a clean worst-case formulation of the minimum error entropy principle in the context of linear multi-sensor fusion by using a largely contaminated Gaussian distribution to model sensor errors with outliers. The obtained entropic best linear unbiased estimator leads to an operational interpretation in terms of a precision/reliability trade-off, it resonates closely with model order selection methods, and it provides a possible information theoretic root to sparsity-promoting regularization.