Globally Optimal Multisensor Distributed Random Parameter Matrices Kalman Filtering Fusion with Applications

Area of Science:

• Control Systems Engineering
• Signal Processing
• Estimation Theory

Background:

• Kalman filtering is crucial for state estimation in dynamic systems.
• Distributed filtering offers advantages in sensor networks but faces challenges with parameter uncertainty.
• Existing methods often assume fixed system parameters, limiting applicability.

Purpose of the Study:

• To develop a novel distributed Kalman filtering fusion method that explicitly handles random parameter matrices.
• To demonstrate the theoretical equivalence between the proposed distributed method and centralized Kalman filtering under specific conditions.
• To extend the applicability of Kalman filtering to systems with uncertain observations and randomly varying dynamics.

Main Methods:

• Proposed a distributed Kalman filtering fusion algorithm incorporating random state transition and measurement matrices.
• Provided a mathematical proof demonstrating the equivalence of the fused estimate to centralized Kalman filtering.
• Applied the framework to scenarios including false alarm probabilities and multiple dynamic models.

Main Results:

• The fused state estimate from the proposed distributed method is equivalent to centralized Kalman filtering.
• This equivalence ensures the achievement of optimal estimation performance.
• Numerical examples confirmed significant performance degradation when parameter randomness is ignored.

Conclusions:

• The developed distributed Kalman filtering fusion method effectively addresses random parameter matrices.
• The approach guarantees optimal estimation performance, matching centralized methods.
• This work provides a robust framework for Kalman filtering in uncertain and dynamic environments.