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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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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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Variational adaptive Gaussian approximation filter for nonlinear systems with generalized unknown disturbances.

Yuemei Qin1, Jincheng Lv1, Shuying Li1

  • 1School of Automation, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.

Iscience
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Summary

This study introduces a new filter for nonlinear systems with unknown disturbances and noise. The variational adaptive Gaussian approximation filter (VAGAF) improves state estimation accuracy in target tracking.

Keywords:
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Area of Science:

  • Control Systems Engineering
  • Signal Processing
  • Statistical Inference

Background:

  • Nonlinear systems often face challenges with unknown disturbances and measurement noise.
  • Accurate state estimation is crucial for applications like target tracking.
  • Existing methods struggle with generalized unknown disturbances (GUDs) and unknown noise covariance (UNC).

Purpose of the Study:

  • To develop a method for joint estimation and identification in discrete-time nonlinear systems.
  • To address the challenges posed by GUDs and UNC.
  • To improve the accuracy of state estimation in complex systems.

Main Methods:

  • A variational adaptive Gaussian approximation filter (VAGAF) is proposed.
  • Recursive state estimation is performed using a Gaussian approximation filter.
  • Variational Bayesian inference is employed to identify the UNC.
  • Matrix eigenvalue decomposition approximates innovation covariance.
  • Statistical linear regression (SLR) estimates measurement noise covariance online.

Main Results:

  • The VAGAF achieves high-precision state estimation by utilizing identified measurement noise covariance and constructed innovation covariance.
  • Target-tracking simulations show superior estimation accuracy compared to existing filters.
  • The proposed filter does not require a finely designed model set for effective operation.

Conclusions:

  • The VAGAF effectively handles discrete-time nonlinear systems with GUDs and UNC.
  • The method offers improved estimation accuracy and robustness in target tracking scenarios.
  • It provides a practical solution for state estimation problems with unmodeled dynamics and noise characteristics.