Optimal Co-Design of Sensor Placement and State Observer for Lithography Applications

The state and output estimation accuracy depends on both the observer and the sensor locations. This paper focuses on this co-design problem in lithography applications. A theoretical formulation of this co-design problem is presented and solved for discrete-time linear stochastic models. We compare the optimal solution of two variants of the estimation problem. The first variant minimizes the transient estimation error whereas the second one minimizes the steady-state estimation error. In both cases, the Kalman filter is optimal. While solving these problems for a lithography application formulated as a 3D thermoelastic model, we observe a significant difference between the optimal sensor placements. Our results highlight the importance of designing a sensor layout in line with the desired transient or steady-state estimation performance.