The previous work for the filter design considers uncorrelated white measurement noise disturbance. For more complex correlated noise disturbance, the conventional adaptive filter results in biased estimates. To overcome this problem, we introduce a linear prefilter to whiten the correlated noise (i.e., colored noise) for obtaining the unbiased estimate of the filter weight. Moreover, the design of some adaptive filters mainly focuses on the integer-order optimization methods. However, compared with the integer-order-based adaptive algorithms, the fractional-order-based algorithms show better performance. Thus, this letter develops a new gradient approach for the adaptive filter design based on the fractional-order derivative and a linear filter. Finally, the simulation results are provided from the system identification perspective for demonstrating the performance analysis of the proposed algorithms.

In this article, a sliding mode dual-channel disturbance rejection control based on an extended state observer is proposed for the attitude control of a quadrotor under unknown disturbances. There exist an inner disturbance rejection channel (IDRC) and an outer disturbance rejection channel (ODRC) in this control scheme. In the IDRC, a low-frequency disturbance compensator is proposed to obtain the disturbance compensation value and to compensate the low-frequency component of the lumped disturbance. In the ODRC, a novel sliding mode controller with a variable-gain switching term and a constant-gain switching term is designed, and the switching terms are used to compensate the virtual disturbance estimation error and the high-frequency component of the lumped disturbance. The low-frequency and high-frequency components of the lumped disturbance can be estimated and the influence of the virtual disturbance estimation error is reduced by using the proposed control scheme. The stability of the system is proved by using the Lyapunov theory. Finally, the effectiveness of the proposed scheme is tested by numerical simulations and platform experiments.