Stochastic filtering in fractional-order circuits

This paper presents the extended Kalman filter (EKF) and moving horizon estimation (MHE) approach-based nonlinear stochastic filtering of fractional-order complementary metal oxide semiconductor (CMOS) circuit. The fractional-order calculus is used to get better reliability of the circuit. The two metal oxide semiconductor field-effect transistors of CMOS circuit are modeled using Enz-Krummenacher-Vittoz (EKV) model, and Kirchhoff's current law (KCL) is then applied to obtain the state-space model. Ornstein-Uhlenbeck (O.U.) process is used to model the input source, which is a white Gaussian noise and Brownian process. Following are the advantages of the proposed method: (1) State estimation using EKF and MHE is real-time and can be used for the estimation purpose when parameters are slowly varying with time. (2) Fractional-order calculus leads to better flexibility in circuits. (3) Application of Kronecker product gives better and more accurate nonlinear mathematical representation. The estimated output values obtained using the proposed techniques have been compared with the wavelet transform (WT) method when nonlinear dynamics are represented using Kronecker product-based representation. The estimated output voltage using estimation algorithms is then compared with PSPICE simulated values. Simulation results validate the better disturbance rejection ability of the proposed methods.