Nanoforce estimation based on Kalman filtering and applied to a force sensor using diamagnetic levitation

Nanoforce sensors based on passive diamagnetic levitation with a macroscopic seismic mass are a possible alternative to classical Atomic Force Microscopes when the force bandwidth to be measured is limited to a few Hertz. When an external unknown force is applied to the levitating seismic mass, this one acts as a transducer that converts this unknown input into a displacement that is the measured output signal. Because the under-damped and long transient response of this kind of macroscopic transducer cannot be neglected for time-varying force measurement, it is then necessary to deconvolve the output to correctly estimate the unknown input force. The deconvolution approach proposed in this paper is based on a Kalman filter that use an uncertain a priori model to represent the unknown nanoforce to be estimated. The main advantage of this approach is that the end-user can directly control the unavoidable trade-off that exists between the wished resolution on the estimated force and the response time of the estimation.