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Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs.

Yali Ruan1, Yingting Luo2, Yunmin Zhu3

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Summary
This summary is machine-generated.

This study introduces an optimal algorithm for state estimation in dynamic systems with unknown inputs, improving accuracy and reducing computation. The new method is independent of initial input values, unlike traditional approaches.

Keywords:
augmented state Kalman filtering (ASKF)distributed fusionoptimal estimateunknown inputs

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Area of Science:

  • Control Systems Engineering
  • Signal Processing
  • Dynamic Systems Analysis

Background:

  • State estimation is crucial for dynamic systems, but unknown inputs complicate traditional methods.
  • Existing algorithms often struggle with accuracy and computational load when dealing with unknown inputs.
  • Autoregressive (AR(1)) processes are frequently used to model unknown inputs in dynamic systems.

Purpose of the Study:

  • To develop an optimal state estimation algorithm for dynamic systems with unknown inputs modeled as AR(1) processes.
  • To address the challenges of computational complexity and initial value dependency in existing methods.
  • To extend the proposed algorithm to multisensor dynamic systems and compare its performance with centralized approaches.

Main Methods:

  • A novel difference method is employed to effectively eliminate unknown inputs from the state estimation process.
  • The proposed algorithm is designed to achieve optimality in the mean square error sense.
  • For multisensor systems, a distributed fused state estimation approach is developed and shown to be equivalent to centralized Kalman filtering.

Main Results:

  • The proposed algorithm significantly reduces computational complexity compared to traditional augmented state algorithms.
  • Numerical examples demonstrate that the new algorithm maintains good performance irrespective of the initial value of unknown inputs.
  • The distributed fused state estimate for multisensor systems achieves optimal performance, equivalent to centralized Kalman filtering.

Conclusions:

  • The developed algorithm offers an optimal and computationally efficient solution for state estimation in dynamic systems with unknown AR(1) inputs.
  • The method's independence from initial unknown input values provides robustness and superior performance over traditional algorithms.
  • The extension to multisensor systems confirms the effectiveness and optimality of the distributed fused state estimation approach.