A Predictive Gradient-Based Filtering Method for State Estimation of MEMS Micromirrors

In this article, a novel dynamic filtering method called predictive gradient based filtering (PGBF) scheme is proposed for state estimation of electromagnetic scanning micromirrors (ESMs) disturbed by noise. In this method, a random state space Hammerstein model with hysteresis is established to describe the characteristic of ESM with hysteresis in random noise environment. Then, the predictive gradient-based filter based on the constructed model is developed to suppress the influence of random noise on such nonlinear systems. To cope with the impact of model uncertainty, a model error compensation mechanism (MECM) is introduced into the PGBF algorithm. Due to the predictive gradient-based optimization (PGBO) method being able to predict the gradient direction of the system cost function within certain horizon in the future, it enables the filter to make decision to avoid being trapped in some local extrema and obtain satisfactory filtering results. Then, the convergence of PGBF is analyzed. Subsequently, the proposed filtering method is applied to the state estimation of ESM disturbed by noise. The proposed filtering scheme is compared with the unscented Kalman filtering (UKF) and nonsmooth Kalman filtering (NKF) strategies. The experimental results show that the proposed PGBF method can achieve better performance in both accuracy and convergence speed of state estimation.