The interval versions of the Kalman filter and the EM algorithm

Advances in Difference Equations

J Al-Mutawa¹  M El-Gebeily¹  O Al-Gahtani²  R Agarwal² 

[1] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhaharan, Kingdom of Saudi Arabia;Department of Mathematics, King Saud University, Riyadh, Kingdom of Saudi Arabia

关键词: Probability Density Function;    Kalman Filter;    State Space Model;    Expectation Maximization Algorithm;    Interval Arithmetic;   

DOI  :  10.1186/1687-1847-2012-172

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study state space models represented by interval parameters and noise. We introduce an interval version of the Expectation Maximization (EM) algorithm for the identification of the interval parameters of the system. We also introduce a suboptimal interval Kalman filter for the identification and estimation of the state vectors. The work requires the introduction of the concept of interval random variables which we also include in this work together with a study of their interval statistical properties such as expectation, conditional expectation and variance. Although the interval Kalman filter introduced here is suboptimal, it successfully recovers the state vectors to a high precision in the simulation examples we have run.

【 授权许可】

CC BY