Aircraft stability derivative estimation provides a framework for flight control systems design and improvement from their implementation to their operation lifetime. Estimating such parameters on-line has a special interest in establishing the accuracy of airborne simulations and enhancing the adaptive flight control systems. The present paper proposes an on-line estimation method based on a nonlinear flight model. The temporal axis is subdivided according to equidistant temporal landmarks, and the parameter estimation is done at the end of such subintervals with the measurements performed on the system during the corresponding subinterval. The optimization approach underlying the estimation method is based on a cyclical optimization along coordinate axes, a derivative-free technique that has shown to outperform standard derivative-free optimization algorithms. Simulations related to a modern transport aircraft demonstrate that the proposed method is an accurate stability derivative estimator for nonlinear flight models.