# Outlier-robust Kalman filters with mixture correntropy

## TL;DR

This paper introduces two novel robust Kalman filters based on mixture correntropy to effectively handle outliers in nonlinear measurement data, improving estimation accuracy in challenging scenarios.

## Contribution

The work develops two new robust filters using mixture correntropy, enhancing traditional Kalman filtering for outlier resistance in nonlinear systems.

## Key findings

- The proposed filters outperform existing robust methods in numerical tests.
- Mixture correntropy effectively mitigates measurement outliers.
- The methods maintain reasonable estimates when measurement errors are small.

## Abstract

We consider the robust filtering problem for a nonlinear state-space model with outliers in measurements. To improve the robustness of the traditional Kalman filtering algorithm, we propose in this work two robust filters based on mixture correntropy, especially the double-Gaussian mixture correntropy and Laplace-Gaussian mixture correntropy. We have formulated the robust filtering problem by adopting the mixture correntropy induced cost to replace the quadratic one in the conventional Kalman filter for measurement fitting errors. In addition, a tradeoff weight coefficient is introduced to make sure the proposed approaches can provide reasonable state estimates in scenarios where measurement fitting errors are small. The formulated robust filtering problems are iteratively solved by utilizing the cubature Kalman filtering framework with a reweighted measurement covariance. Numerical results show that the proposed methods can achieve a performance improvement over existing robust solutions.