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 senses 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 e xplore the use of a least squares estimate for this nonlinear estimation pr oblem and give several approximate recursive algorithms for practical reali zation. Stability results for these algorithms are also given. Simulation r esults compare the new algorithms with the Extended Kalman Filter (EKF) and Iterated Kalman Filter (IKF).