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Statistical Process Control (SPC) is a method used to monitor and control quality within processes, particularly in manufacturing and service delivery, by employing statistical methods. SPC aims to distinguish between natural (common cause) variation and variation due to specific changes or events (special cause), allowing for timely improvements and sustained quality. The control chart, a pivotal tool in SPC, visually displays data over time alongside a central line of upper and lower control...
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Related Experiment Video

Updated: Apr 23, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Statistical process control of a Kalman filter model.

Sonja Gamse1, Fereydoun Nobakht-Ersi2, Mohammad A Sharifi3

  • 1Unit for Surveying and Geoinformation, University of Innsbruck, Technikerstr. 13, Innsbruck 6020, Austria. sonja.gamse@uibk.ac.at.

Sensors (Basel, Switzerland)
|September 30, 2014
PubMed
Summary

This study details evaluating the Kalman filter (KF) model for time series data. It introduces rigorous statistical tests and inner confidence indicators for improved measurement accuracy in geodetic applications.

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Area of Science:

  • Geodesy
  • Data Analysis
  • Statistical Modeling

Background:

  • Kalman filtering (KF) is a common stochastic model for time series evaluation.
  • Standard KF implementation may not always ensure normal distribution of residuals or optimal parameterization.
  • Accurate measurement data evaluation requires robust model validation.

Purpose of the Study:

  • To provide a comprehensive evaluation framework for the Kalman filter model.
  • To highlight essential, yet often overlooked, statistical tests and inner confidence indicators for KF.
  • To enhance the reliability of KF in processing geodetic kinematic observations.

Main Methods:

  • Detailed description of Kalman filter evaluation procedures.
  • Inclusion of inner confidence indicators: controllability, observability, state transition matrix determinant, a posteriori covariance matrix, and Kalman gain properties.
  • Application of statistical tests: convergence of standard deviations and normal distribution of residuals.

Main Results:

  • Demonstrated the importance of computing controllability and observability matrices.
  • Emphasized verifying the normal distribution of residuals as a non-standard but crucial step.
  • Practical implementation on geodetic kinematic observations validated the proposed evaluation methods.

Conclusions:

  • Rigorous evaluation of Kalman filter models is critical for accurate measurement data processing.
  • Incorporating controllability, observability, and residual distribution tests significantly improves KF reliability.
  • The presented methodology enhances the robustness of time series analysis in geodesy.