International Journal of Stochastic Analysis
Volume 2013 (2013), Article ID 240295, 9 pages
Research Article

Online Stochastic Convergence Analysis of the Kalman Filter

1Department of Mechanical Engineering at Lafayette College, Easton, PA 18042, USA
2Department of Mechanical and Aerospace Engineering, Morgantown, WV 26506, USA

Received 15 May 2013; Revised 26 September 2013; Accepted 26 September 2013

Academic Editor: Ravi Agarwal

Copyright © 2013 Matthew B. Rhudy and Yu Gu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents modifications to the stochastic stability lemma which is then used to estimate the convergence rate and persistent error of the linear Kalman filter online without using knowledge of the true state. Unlike previous uses of the stochastic stability lemma for stability proof, this new convergence analysis technique considers time-varying parameters, which can be calculated online in real-time to monitor the performance of the filter. Through simulation of an example problem, the new method was shown to be effective in determining a bound on the estimation error that closely follows the actual estimation error. Different cases of assumed process and measurement noise covariance matrices were considered in order to study their effects on the convergence and persistent error of the Kalman filter.