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This study introduces a globally optimal sequential fusion Kalman filter for multi-sensor linear systems with correlated noise. The new filter achieves strict equivalence to centralized fusion, solving a long-standing problem in state estimation.

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Area of Science:

  • Control Systems Engineering
  • Signal Processing
  • Estimation Theory

Background:

  • State estimation in multi-sensor linear systems is challenged by correlated process and measurement noise.
  • Existing sequential fusion Kalman filters lack strict equivalence to centralized fusion for these systems.
  • Directly decorrelating process and measurement noise is a significant hurdle.

Purpose of the Study:

  • To design a truly globally optimal sequential fusion Kalman filter for linear systems with cross-correlated noise.
  • To achieve strict equivalence between sequential and centralized fusion Kalman filters.
  • To address the unsolved problem of sequential fusion for systems with mutually correlated measurement noises.

Main Methods:

  • An innovative indirect decorrelation method for process and measurement noise.
  • Rewriting measurement equations using the Gram-Schmidt orthogonalization principle to achieve noise independence.
  • Establishing a sequential fusion Kalman filter based on the transformed measurement equations.

Main Results:

  • A novel sequential fusion Kalman filter is developed, achieving global optimality.
  • Theoretical proof rigorously establishes the equivalence between the proposed sequential filter and centralized fusion.
  • The filter's effectiveness is demonstrated through a constant velocity target tracking simulation.

Conclusions:

  • The proposed method successfully designs a globally optimal sequential fusion Kalman filter for complex noise scenarios.
  • The established equivalence provides a practical and efficient alternative to centralized fusion for state estimation.
  • This work offers a significant advancement in sequential data fusion for multi-sensor systems.