Next Article in Journal
Attitude Heading Reference System Using MEMS Inertial Sensors with Dual-Axis Rotation
Previous Article in Journal
A Survey on M2M Systems for mHealth: A Wireless Communications Perspective
Article Menu

Export Article

Open AccessArticle
Sensors 2014, 14(10), 18053-18074;

Statistical Process Control of a Kalman Filter Model

Unit for Surveying and Geoinformation, University of Innsbruck, Technikerstr. 13, Innsbruck 6020, Austria
Department of Applied Mathematics, University of Tabriz, 29 Bahman Blvd, 5166616471 Tabriz, Iran
Department of Geomatic and Surveying Engineering, College of Engineering, University of Tehran, 111554563 Tehran, Iran
Author to whom correspondence should be addressed.
Received: 20 June 2014 / Revised: 25 August 2014 / Accepted: 25 August 2014 / Published: 26 September 2014
(This article belongs to the Section Physical Sensors)
Full-Text   |   PDF [3395 KB, uploaded 29 September 2014]


For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations. View Full-Text
Keywords: consistency check; controllability; Kalman filter; measurement innovation; observability; system state consistency check; controllability; Kalman filter; measurement innovation; observability; system state
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 (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Gamse, S.; Nobakht-Ersi, F.; Sharifi, M.A. Statistical Process Control of a Kalman Filter Model. Sensors 2014, 14, 18053-18074.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Sensors EISSN 1424-8220 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top