Kronecker Product Based Modeling of Darlington Amplifier and State Estimation using Unscented Kalman Filter

Abstract

ABSTRACT This paper presents the application of unscented Kalman filter (UKF) for output voltage estimation of the Darlington amplifier (DA). Implementation of UKF requires the state-space model of DA circuit, which has been obtained using Kirchhoff’s voltage law (KVL), Kirchhoff’s current law (KCL) and the Gummel–Poon model of the bipolar junction transistor (BJT). This work uses Kronecker product for vector multiplication. The mathematical representation of nonlinear system in terms of Kronecker product helps to reduce the computational burden involved in the vector multiplication. The proposed method has the advantage that it can be used for the nonlinear region and large amplitude input signal. As the maximal precision of estimation requires modelling in terms of circuit elements and device parameters, the proposed method is able to provide an accurate estimation. We compared the UKF estimation results with the extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF). The UKF presents smaller mean square error (MSE) as compared to EKF and IEKF as UKF is accurate to the third order for any nonlinearity. In addition, IEKF presents smaller MSE as compared to EKF because the linearisation error is taken into account by IEKF.