A class of nonlinear filtering problems arising from drifting sensor gains

This paper considers a state estimation problem where the nominal system is linear but the sensor has a time-varying gain component, giving rise to a bilinear output equation. This is a general sensor self-calibration problem and is of particular interest in the problem of estimating wafer thickness and etch rate during semiconductor manufacturing using reflectometry. We explore the use of a least squares estimate for this nonlinear estimation problem and give several approximate recursive algorithms for practical realization. Stability results for these algorithms are also given. Simulation results for comparing the new algorithms with the extended Kalman filter and iterated Kalman filter are given.