Fast moving horizon estimation for a two-dimensional distributed parameter system

• A fast MHE method is developed based on the idea of system decoupling.
• A high-dimensional system is decoupled into a set of single-dimensional systems via singular value decomposition.
• The parallelizable MHE algorithm employs an approximated penalty method to enforce an ellipsoidal constraint.
• The proposed method is tested on a 2D diffusion problem.
• The proposed method enables fast state estimation while accounting for physical constraints.

Partial differential equations (PDEs) pose a challenge for control engineers, both in terms of theory and computational requirements. PDEs are usually approximated by ordinary differential equations or difference equations via the finite difference method, resulting in a high-dimensional state-space system. The obtained system matrix is oftentimes symmetric, which allows this high-dimensional system to be decomposed into a set of single-dimensional systems using its singular value decomposition. Any linear constraints in the original problem can also be simplified by replacing it with an ellipsoidal constraint. Based on this, speedup of the moving horizon estimation is achieved by employing an analytical solution obtained by augmenting the ellipsoidal constraint into the objective function as a penalty weighted by a decreasing scaling parameter. The approximated penalty method algorithm allows for efficient parallel computation for sub-problems. The proposed algorithm is demonstrated for a two-dimensional diffusion problem where the concentration field is estimated using distributed sensors.