The concept of an equivalent time constant and model expansion method are introduced for the design of a synthetic stabilization acceleration autopilot. In the autopilot control loop, an extended Kalman filter is employed to estimate the time‐varying airframe parameters. The performance of the autopilot and the extended Kalman filter is investigated through computer simulations. Two main results are found: the model expansion method can efficiently specify the gains of the autopilot control loop, and good command following characteristics of the autopilot have been obtained in the computer simulations. The results also show an acceptable estimation error for the extended Kalman filter.