Abstract
In this paper, comprehensive methods to apply several formulations of nonlinear estimators to integrated navigation problems are considered and developed. The problem of linear and nonlinear filters such as Kalman Filter (KF) and Extended Kalman Filter (EKF) is stated. Analog solution which is based on fisher information matrix propagation for linear and nonlinear filtering is also developed. Additionally, the idea of iterations is included through the update step both for Kalman filters and Information filters in order to improve accuracy. Through this development, two new formulations of High order Kalman filters and High order Information filters are presented. Finally, in order to compare these different nonlinear filters, special applications are analyzed by using the proposed techniques to estimate two well-known mathematical state space models, which are based on nonlinear time series used to apply these estimation algorithms. A criterion used for comparison is the root mean square error RMSE and several simulations under specific conditions are illustrated.
Highlights
Different kinds of filters exist and were developed in order to ensure high quality measurement in input-output systems and permit more accurate control system in several fields such as in Aerospace, for aircraft’s navigation, ship, spacecraft, tracking etc
Through simulations based on two well-known mathematical state space models, it is possible to appreciate the difference between the classic formulations of the nonlinear filters such as Extended Kalman Filter (EKF), Extended Information Filter (EIF), 2nd OK compared with the proposed information filters
More accurate estimate is due to high nonlinearity both in system and measurement equations using new formulations of iterative extended Kalman filter, 2nd order information filter and 2nd order iterative information filter
Summary
Different kinds of filters exist and were developed in order to ensure high quality measurement in input-output systems and permit more accurate control system in several fields such as in Aerospace, for aircraft’s navigation, ship, spacecraft, tracking etc. Information filters present several other advantages when the state space model input is a combination of several sensors as in data fusion or multi-sensors fusion, it was proven that comparing with Kalman filter and extended Kalman filter both for linear and nonlinear case, the information filters are more easy to implement in real time application with multiple information combination [9,10,11,12]. We apply these different nonlinear filters to dynamical state models such as references. It is expected that this work could serve in investigate integrated navigation system INS (Inertial navigation System)/GNSS (Global Navigation by Satellite System) problems, in order to show possible application in the field of aerospace
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