## Optimal Kalman filtering fusion with cross-correlated sensor noises.(English)Zbl 1130.93427

Summary: When there is no feedback from the fusion center to local sensors, we present a distributed Kalman filtering fusion formula for linear dynamic systems with sensor noises cross-correlated, and prove that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements, therefore, it achieves the best performance. Then, for the same dynamic system, when there is feedback, a modified Kalman filtering fusion with feedback for distributed recursive state estimators is proposed, and prove that the fusion formula with feedback is, as the fusion without feedback, still exactly equivalent to the corresponding centralized Kalman filtering fusion formula; the various $$P$$ matrices in the feedback Kalman filtering at both local filters and the fusion center are still the covariance matrices of tracking errors; the feedback does reduce the covariance of each local tracking error.

### MSC:

 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 93E24 Least squares and related methods for stochastic control systems
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### References:

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