Contribution in Information Signal Processing for Solving State Space Nonlinear Estimation Problems

Hamza Benzerrouk, Alexander Nebylov, Hassen Salhi

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International Institute for Advanced Aerospace Technologies, Saint-Petersburg State University of Aerospace Instrumentation, Saint Petersburg, Russia.

DOI: 10.4236/jsip.2013.44048                

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.

Keywords

Kalman Filter; Information Filter; Extended Kalman Filter; Extended Information Filter; 2nd Order Kalman Filter; 2nd Order Information Filter

Conflicts of Interest

The authors declare no conflicts of interest.

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