Parameter estimation in dynamic Casimir force measurements with known periodicity

It is important to have an accurate estimate of the unknown parameters such as the separation distance between interacting materials in Casimir force measurements. Current methods tend to produce large estimation errors. In this Letter, we present a novel method based on an adaptive control approach to estimate the unknown parameters using large amplitude dynamic Casimir measurements at separation distances of below 1 μm where both electrostatic force and Casimir force are significant. The estimate is proved to be accurate and the effectiveness of our method is demonstrated via a numerical example.

► Unknown parameters like separation gap are nonlinearly parameterized in Casimir force measurements
► A two-stage parameter estimation method is proposed to estimate unknown parameters accurately.
► Our method is proved to be effective by theoretical derivation and simulations.
► Our method can be applied to a broad range of nonlinear parameter estimation problems.