Robustness analysis of a maximum correntropy framework for linear regression

Abstract

In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based correntropy estimators as special cases. An analysis of the robustness properties is then provided. The analysis includes a quantitative characterization of the informativity degree of the regression which is appropriate for studying the stability of the estimator. Using this tool, a sufficient condition is expressed under which the parametric estimation error is shown to be bounded. Explicit expression of the bound is given and discussion on its numerical computation is supplied. For illustration purpose, two special cases are numerically studied.

Multi-Kernel Maximum Correntropy Kalman Filter for Orientation Estimation

“…The CDOE 1: Initialize S E q est,0 and b g,0 2: while k > 0 do 3: Calculate S E q w,k using ( 13) and (29) 4: Calculate q acor,k and q mcor,k using (37) 5: Accelerometer correction using (24) 6: Magnerometer correction using (26) 7: Gyroscope bias estimation using (38) 8: k = k + 1 9: end while where α ca and α cm are two correction angles to be determined. Solving (33a) and (33b) with the gradient descent strategy, we have…”

“…In this paper, we derive two computationally efficient algorithms, i.e., the CGD and CDOE, which are built upon the GD [15] and DOE [16] and utilize the MKCL as objective functions. It is notable that although the correntropy has been successfully utilized in Kalman filter [22], [23], adaptive filtering [24], and its robustness with respect to outliers or non-Gaussian noise has been investigated and analyzed [25], [26], the properties of the multi-kernel correntropy is rarely explored and has never been utilized in the orientation estimation of IMUs with a gradient descent strategy. In this paper, we demonstrate the robustness of the MKCL with respect to outliers and assemble it to the orientation estimation problem.…”