Distributed Field Estimation Using Sensor Networks Based on H_∞ Consensus Filtering.

Area of Science:

• Control Systems and Signal Processing
• Distributed Estimation
• Partial Differential Equations

Background:

• Sensor networks are crucial for monitoring spatially-distributed physical processes.
• Accurate field estimation from distributed measurements presents significant challenges.
• Classical centralized Kalman filtering can be computationally intensive and suboptimal.

Purpose of the Study:

• To design a local filter for each sensor node enabling distributed field estimation.
• To leverage network-wide measurements for enhanced process estimation.
• To improve upon the performance of traditional centralized filtering techniques.

Main Methods:

• Discretization of infinite-dimensional processes described by partial differential equations using the finite element method.
• Establishment of an approximate finite-dimensional linear system.
• Application of sparse ℓ 1 -regularized H ∞ filtering to address the estimation problem, exploiting source function sparsity.

Main Results:

• The proposed ℓ 1 -regularized H ∞ filtering method demonstrates effectiveness in distributed field estimation.
• The method offers potential performance advantages compared to centralized Kalman filtering.
• A numerical example validates the practical applicability and accuracy of the developed approach.

Conclusions:

• The developed local filter design effectively addresses distributed field estimation in sensor networks.
• Sparse ℓ 1 -regularized H ∞ filtering provides a robust and accurate solution for complex physical processes.
• The proposed method enhances the capabilities of sensor networks for real-time physical process monitoring.