Robust Semiparametric Amplitude Estimation of Sinusoidal Signals: The Multi-Sensor Case

The problem of robust estimation of the complex amplitudes of sinusoidal signals using multiple sensors, in an unknown heavy-tailed, spatially and temporally i.i.d. noise environement is considered. A semiparametric approach for this case is presented, where non-parametric estimation of the noise density is succeeded by maximum likelihood estimation incorporating the estimated density. The suggested approach adapts to the sensor measurements using a compact, and conceptually simple non-parametric transformation density estimation. Simulation results are provided, which illustrate the improvement of the presented approach over classical robust or non-robust estimation procedures, e.g. Huber's minimax estimator or the least-squares estimator.