In the field of microscopic vision， piezoelectric-driven positioning technology has attracted significant attention due to its high precision and flexibility at the microscale. However， the presence of delays in processes such as image processing， transmission， and control during positioning introduces significant estimation errors in the image Jacobian matrix. Therefore， this paper proposed an improved extended Kalman filter algorithm to predict the image Jacobian matrix and substantially reduce the impact of time delays.Firstly， the identified Bouc-Wen model was combined with the state observation equation of the extended Kalman filter algorithm. This comprehensive consideration of the hysteresis nonlinearity of the piezoelectric platform effectively enhanced the prediction of the platform's velocity and position. Secondly， in dealing with nonlinear problems， the extended Kalman filter algorithm traditionally employed Taylor series， which may result in poor approximations for highly nonlinear functions， introducing significant errors when estimating the Jacobian matrix. To address this， the paper employed a neural network to approximate highly nonlinear functions and subsequently estimate the image Jacobian matrix. Finally， by constructing a piezoelectric-driven experimental platform for microscopic vision， position tracking experiments were conducted. Simulation experiments demonstrate that when the input signals are sinusoidal and triangular wave signals， the mean tracking errors of the improved Extended Kalman Filter algorithm are 0.199 μm and 0.132 μm， respectively， while the mean tracking errors of the Extended Kalman Filter algorithm are 0.692 μm and 0.513 μm， respectively. The results validate the superiority and feasibility of the improved algorithm.