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

Nano force 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 little damped and long transient response of this kind of macroscopic transducer can not be neglected, it is then necessary to deconvolve the output to correctly estimate the unknown input force. The deconvolution approach proposed in this article 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 estimatedforce and the response time of the estimation.