To develop a reasonable transition process for physical signals with speed and acceleration limits， we propose a variable parameter linear tracking differentiator with speed and acceleration saturations. The parameter of the tracking differentiator is designed as a decreasing function of the tracking error， which avoids large acceleration shock in the initial stage when the tracking error is relatively large. Using the same set of parameters， the designed tracking differentiator can give reasonable transition signals that match the feedback capabilities of physical systems for a wide range of step signals. Simulation results show that the proposed tracking differentiator can produce nearly the same tracking effect as that of the classical nonlinear tracking differentiator and with reduced computational complexity. We applied the designed tracking differentiator to the rapid positioning of an altazimuth large area telescope. Compared with the commonly used position segmentation method， the response time was reduced by 15%–37%， thereby improving the search efficiency of the telescope. The proposed variable parameter tracking differentiator can not only play a transitional role but can also maximize the feedback capabilities of physical systems. The parameter setting of the proposed method is simple as well as easy to debug and implement in engineering practice.