Performance analysis of derivative-free estimation methods from the perspective of attitude estimation influenced by real data

Abstract

The main difference between the Extended Kalman Filter (EKF) and the non-linear estimators that make use of the so-called Sigma Points is the need or not of linearizing the equations that compose the whole dynamic system, a process that requires the calculation of the Jacobian matrices composed of partial derivatives. In this study, an analysis of the Central Difference Kalman Filter (CDKF) efficiency is performed, as compared to other derivative-free estimators and the standard EKF, when real data from on-board satellite sensors are processed by the filters. However, the use of real data can generate problems, not only regarding errors and uncertainties of different natures that can lead the filter to inaccurate results, but also regarding the difficulty in validating the results due to the absence of reference values. In this case, results of the attitude estimated by filters, such as EKF, Unscented Kalman Filter (UKF), and Cubature Kalman Filter (CKF), already validated in previous papers served as the basis for the comparisons made with the CDKF. It was observed that the performance of CDKF is superior to the conventional EKF and equivalent to filters that make use of the sigma points, while still maintaining an adequate processing time for real applications.