Research on the effectiveness of continuous-discrete cubature Kalman filter robust modifications

Abstract

Introduction: usually there are some outliers (abnormal measurements) in observed data, and they can significantly affect the quality of the data processing. Many dynamic processes are described with stochastic nonlinear equations. Modern nonlinear filters that include the cubature Kalman filter, which deserves a special attention, cannot effectively process data containing abnormal measurements. One of the possible solutions to this problem is to use so-called robust methods that have good performance when one has to analyze data containing outliers. The paper deals with the common situations, when the considered process is actually continuous, but the observed data is taken discretely. Purpose: identifying the most effective advanced robust modifications of the continuous-discrete cubature Kalman filter and giving the appropriate recommendations for their appliance. Results: four modifications of the continuous-discrete cubature Kalman filter have been proposed based on the variational Bayesian and correntropy robust approaches to parameter estimation for stochastic processes. All the modifications have parameters with optimal values depending on both the selected mathematical model and the considered set of observations composing the sample. These values are determined numerically by minimizing the accumulated root mean square error on some grid. The research on the effectiveness of the proposed robust modifications has been carried out for the problem of tracking a space vehicle during its reentry into the atmosphere. The stochastic and the grouped outliers have been considered. Two most effective filters that have approximately equal qualities of estimation have been derived. The correntropy filter that has one configurable parameter can be recommended for practical using.