Nonlinear Multiple Integrator and Application to Aircraft Navigation

In this paper, a nonlinear robust multiple integrator algorithm is presented based on finite-time stability. The nonlinear integrator can obtain the multiple integrals of signal. Conditions are given ensuring finite-time stability for the presented integrator. The stability and robustness are analysed. The merits of the presented integrator include its multiple-integral estimation, finite-time stability, selecting parameters easily, restraining stochastic noise sufficiently, and almost no drift phenomenon. The theoretical results are confirmed by computer simulations and two aircraft navigation experiments on a quadrotor aircraft: 1) the estimation of flying trajectory and velocity from the measurements of accelerations; 2) the estimation of attitude angle and angular rate from the measurements of angular accelerations.