In a simplicial complex-based sensor network, sensors, pairwise measurement relationships, and higher-order measurements are represented as nodes, edges, and higher-order simplices, allowing the network to exploit both local measurements and topological constraints. In this project, the Hodge decomposition will be used to separate consistent information from higher-order errors, for accurate state estimation and the detection and localization of faulty or conflicting sensor measurements.
- Task 1: Simplicial sensor-network modelling
- Model sensors, pairwise measurement relationships, and higher-order measurement groups as a simplicial complex, and construct the corresponding weighted Hodge Laplacians.
- Task 2: Hodge-based data-fusion algorithm
- Develop a distributed estimation algorithm that uses the Hodge Laplacian to combine local sensor measurements and enforce consistency across overlapping measurement groups.
- Task 3: Inconsistency and fault detection
- Use the gradient, curl, and harmonic components of the Hodge decomposition to identify conflicting measurements and distinguish local sensor faults from network-wide inconsistencies.
- Task 4: Robustness and convergence analysis
- Establish conditions for convergence, estimation accuracy, and robustness under measurement noise, sensor failures, communication losses, and changes in network topology.
- Task 5: Numerical and experimental validation
- Evaluate the method on a representative sensor-network application and compare it with conventional graph-based consensus and distributed estimation techniques.