Tag Archives: Kalman Filters

A new Kalman Filter that is more robust under certain deviations of the gaussian hypothesis

Badong Chen, Xi Liu, Haiquan Zhao, Jose C. Principe, Maximum correntropy Kalman filter, Automatica, Volume 76, February 2017, Pages 70-77, ISSN 0005-1098, DOI: 10.1016/j.automatica.2016.10.004.

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean vector and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is also given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm.

Analysis of the deterioration of several Kalman Filters depending on the amount of uncertainty in the observations, when the observation model is non-linear

Mark R. Morelande and Ángel F. García-Fernández, Analysis of Kalman Filter Approximations for Nonlinear Measurements, IEEE Transactions on signal processing, vol. 61, no. 22, 2013 DOI: 10.1109/TSP.2013.2279367.

A theoretical analysis is presented of the correction step of the Kalman filter (KF) and its various approximations for the case of a nonlinear measurement equation with additive Gaussian noise. The KF is based on a Gaussian app roximation to the joint density of the state and the measurement. The analysis metric is the Kullback-Leibler divergence of this approximation from the true joint density. The purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the KF and its variants in nonlinear scenarios. This is illustrated using a numerical example.