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Sensors 2014, 14(10), 18053-18074; doi:10.3390/s141018053

Statistical Process Control of a Kalman Filter Model

1
Unit for Surveying and Geoinformation, University of Innsbruck, Technikerstr. 13, Innsbruck 6020, Austria
2
Department of Applied Mathematics, University of Tabriz, 29 Bahman Blvd, 5166616471 Tabriz, Iran
3
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)
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Abstract

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
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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).

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

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