Robust Methods for Estimation Problems

Abstract—Estimation in conventional signal processing is often based on strong assumptions on the probability distribution of the sensor noise, stationarity, linearity, or independence and identical distribution of random variables. Many a time engineering problems rely on Gaussian distribution of the data and noise. This is sometimes well justified and enables a simple derivation of optimal estimators. But sometimes, these assumptions do not hold in practice and nominal optimality becomes useless. A slight deviation from the assumed distribution may result in drastic degradation of the estimator. Hence there is a need for statistically robust methods of estimation. In this paper, we elaborate on some of the important robust methods for estimation problems for both single channel and multi-channel cases, particulary the generalized M-estimators and the sequential M-estimators. Further, robust Kalman filter based estimation is also highlighted. I