Fixed-Wing UAV Integrated Navigation with Low-Cost IMU/GPS

Abstract

Today, there is an increase in the use of Unmanned Aerial Vehicles (UAV's), for applications that can be considered dull, dirty or dangerous when compared to those applications of conventional aircraft or helicopters. To further increase the use of UAV's, their navigation filters must be robust and reliable. The trend in current autopilot development is defined by the ever decreasing size of vehicles leading to the creation of miniature Inertial Navigation Systems (INS) with low cost, low grade sensors. Small flying vehicles have fast dynamics requiring higher control rates and higher dynamic ranges with minimal available onboard computational capacities. Sensor and processing limitations have consequences for the achievable navigation performance. This in turn poses limits on the minimal vehicle stability, weather conditions and trajectory smoothness. The most important aspect and thesis goal is to guarantee the navigation filter solution robustness during all flight maneuvers. A navigation filter is an integration algorithm that provides a navigation solution on the vehicle's state vector from sensor data. This thesis focuses on one UAV platform in particular, namely small fixed-wing UAV's. One of the main challenges with designed navigation filters is that they can be theoretically stable but the outcome can sometimes not be used. In practice, the navigation filter outcome can give a diverging solution while theoretically stable. The goal of this thesis is to define the minimal requirements of sensors and other hardware for an INS such that the stabilization requirements posed by the vehicle dynamics and size can be satisfied. With the requirements stated, smaller and more dynamic fixed-wing UAV's can be stabilized based on the integrated navigation solution. The developed observability analysis tool is able to provide a quantitative analysis on the state observability that can be used to analyze different systems or sensor configurations. The observability matrix is composed of the system and observer dynamics. The system dynamics is based on the Inertial Measuring Unit (IMU) prediction of the system states, the observer equations correspond to the observer dynamics. A non-linear local observability analysis has been performed to calculate the observability matrix. The traditional Singular-Values Decomposition (SVD) algorithm provides the singular values of an observability matrix in a decreasing order and indicates the rank of the system. The rank of the observability matrix corresponds to the number of observable system states, the SVD can however not directly link the singular values to the system states. To overcome this problem a different matrix decomposition is used that is able to directly couple the singular values to the system states. This developed matrix decomposition algorithm is based on the QR factorization, called QRsvd. With this algorithm it is possible to quantitatively indicate the observability (degree) of each system state. An analysis into the physical properties of fixed-wing aircraft kinematics resulted in new insight into the movement of flying vehicles. Based on the derived kinematics together with the coupling of an IMU, GPS receiver and fixed-wing aircraft kinematics this resulted in new physical insight. This resulted in three angle correction (AC) equations that can be used as additional attitude/heading angle observers to the conventional IMU/GPS integration. With these three additional observers, the three orientation angles become instantaneously observable. Without the AC equations, a rotational rate constraint is always present to integrate the IMU with GPS. GPS receivers and IMU are separate, self-contained subsystems with different updating frequencies and processing times. Resulting clock differences are called time synchronization errors and result in filter estimation problems. A time synchronization requirement is derived, which is a function of changes in vehicle accelerations and filter innovation. The time synchronization requirement is proportional to the magnitude of the change in vehicle accelerations a and negatively proportional to the magnitude of the identification filter innovation. Vehicles with fast dynamics, like fixed-wing UAV's, can have larger changes in vehicle accelerations magnitude, resulting in a more stringent time synchronization requirement. Based on performed simulations and verification with flight test data, it can be concluded that the improved IMU/GPS filter with AC equations can provide a stable long-term navigation solution with accurate short-term performance, by using (Iterated) Extended Kalman filters. During the performed simulations the position states give the largest source of error, due to the large GPS position uncertainty. For the three orientation angles, the heading angle has a larger identification error compared to the pitch and roll angle. For the orientation angles, the influence of atmospheric wind on the identification performance is minimal except for the heading angle due to the presence of a side-slip angle beta. Coordinate transformations between the Earth, North-East-Down (NED) reference frame F_E and the body-fixed reference frame F_B can be performed using a rotational transformation matrix R_BE. The antisymmetric matrix R_BE holds special properties that can be utilized and fits in the category of Special Orthogonal Lie groups with a dimension of three, called SO(3). Based on SO(3) group properties, a non-linear complementary filter can be constructed that uses this matrix as a single state. The non-linear complementary filter on the SO(3) group, can be used as an alternative to conventional Kalman state identification filters. For (I)EKF the heading angle is the largest source of error of the attitude/heading angles, this is also the case for the SO(3) filter. Differences between the SO(3) filter and (I)EKF are due to two aspects. The SO(3) filter uses constant proportional and integrator gains, where Kalman gain matrices include process and observer uncertainties. The other source of differences can be found in the strong coupling between the individual attitude/heading angles for the non-linear SO(3) filter compared to (I)EKF.