The Kalman filter (KF) is the optimal estimator that minimizes the mean square error when the state and measurement dynamics are linear in nature, provided the process and measurement noise processes are modeled as white Gaussian. However, in the real world, one encounters a large number of scenarios where either the process or measurement model (or both) are nonlinear. In such cases a class of suboptimal Kalman filter implementations called extended Kalman filters (EKF) are used. EKFs operate by linearizing the nonlinear model around the current reference trajectory and then designing the Kalman filter gain for the linearized model. Recently, an alternative approach has emerged for a certain class of problems where the error in the states is estimated using a Kalman filter, rather than the state itself. This error state KF (ErKF) approach, by deriving the error state dynamics, via the perturbation of the nonlinear plant, lends itself to optimal updates in the error states and optimal prediction and updates in the error state covariance. This is because the error state dynamics are linear, thereby satisfying a condition for optimal Kalman filtering. This paper offers a comparison between the EKF and ErKF via simulations and shows that the ErKF performance is robust to a variety of aircraft maneuvers performed. Furthermore, this paper shows that the ErKF, unlike the EKF, need not be repeatedly tuned with respect to the noise covariances in order to obtain acceptable estimation performance.

In this work we show an application of L1 Adaptive control theory for attitude control of UAVs. We implement the flight control system on a multirotor to show robustness and precise attitude tracking in the presence of modeling uncertainties and environmental disturbances. We choose backstepping control architecture, since the kinematics and dynamics of multirotors in most cases can be written in strict feedback form. We further exploit the fact that the kinematics of the plant, while free of uncertainties, is nonlinear, which makes it highly suitable for dynamic inversion control at each level of backstepping. On the other hand, plant dynamics is uncertain and is affected by environmental disturbances such as wind gusts, unmodeled dynamics etc. Therefore, we consider 3 variants of the control architecture. The first method uses backstepping to determine the moment demand and augments it with the L1 adaptive controller to account for uncertainties and provide robustness with guaranteed transient performance. The second architecture apply the concept of L1 adaptive backstepping to the same problem; and the third architecture uses L1 backstepping for quaternion representation of the system dynamics, which helps to avoid the singularities associated with Euler angles.

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