Optimal Sequential Fusion Kalman Filter for Multi-Sensor Linear Systems with Noise Cross-Correlated

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.