A non-linear observer for attitude estimation of a fixed-wing unmanned aerial vehicle without GPS measurements

Abstract

In this paper we propose a simple non-linear observer for attitude estimation based only on output from a typical inertial measurement unit (IMU) and dynamic pressure sensor embarked on a low-cost unmanned aerial vehicle. In particular, we aim to provide a good quality attitude estimate in the absence of global positioning system (GPS) ground truth and with potential low-frequency bias and high-frequency noise in the IMU sensor measurements. In addition, the case where the IMU only provides gyrometer and accelerometer outputs is considered; that is, there is no magnetometer output or it cannot be used due to local magnetic disturbances such as are common on a vehicle with electric motors. The proposed observer uses a simple centripetal force model (based on gyrometer and dynamic pressure measurements), augmented by a first-order dynamic model for angle of attack, to estimate non-inertial components of the acceleration. This estimate is used to correct the accelerometer output to provide a low-frequency estimate of the gravitational direction. This inertial direction, along with the gyrometer output, is then used to drive a fully non-linear attitude observer posed on the orthogonal group of rotation matrices SO(3). The observer is augmented with an integral state that ensures compensation of gyrometer bias. The resulting observer is simple to implement and fully non-linear. Experimental results are provided on a real-world data set and the performance of the filter is evaluated against the output from a full GPS/inertial navigation system (INS) that was available for the data set.

Keywords

non-linear observer attitude estimates special orthogonal group unmanned aerial vehicle.

Get full access to this article

View all access options for this article.

References

Baerveldt, A.-J. and Klang, R. 1997: A low-cost and low-weight attitude estimation system for an autonomous helicopter. Proceedings 1997 IEEE International Conference on Intelligent Engineering Systems, Budapest, Hungary, 391-5.

Bonnabel, S. , Martin, P. and Rouchon, P. 2006: A nonlinear symmetry-preserving observer for velocity-aided inertial navigation. Proceedings of the American Control Conference, June 2006, Minneapolis , Minnesota, USA, 2910-14.

Bonnabel, S. , Martin, P. and Rouchon, P. 2009: Non-linear symmetry-preserving observers on lie groups. IEEE Transactions on Automatic Control 54, 1709-13.

Bonnabel, S. , Martin, P. and Rouchon, P. 2008: Non-linear observer on lie groups for left-invariant dynamics with right-left equivariant output. Proceedings of the 17th World Congress the International Federation of Automatic Control (IFAC2008) July 2008, Seoul, Korea, 8594-8.

Choukroun, D. , Bar-Itzhack, I.Y. and Oshman, Y. 2006: Novel quaternion Kalman filter. IEEE Transactions on Aerospace and Electronic Systems 42, 174-90.

Corke, P. 2004: An inertial and visual sensing system for a small autonomous helicopter. Journal of Robotic Systems 21, 43-51. Crassidis, J.L. , Markley, F.L. and Cheng, Y. 2007: Nonlinear attitude filtering methods. Journal of Guidance, Control, and Dynamics 30, 12-28.

Gebre-Egziabher, D. , Hayward, R.C. and Powell, J.D. 2004: Design of multi-sensor attitude determination systems . IEEE Transactions on Aerospace and Electronic Systems 40, 627-49.

Hamel, T. and Mahony, R. 2006: Attitude estimation on SO(3) based on direct inertial measurements. Proceedings 2006 IEEE International Conference on Robotics and Automation (ICRA2006), May 2006, Orlando, Florida, USA, 2170-5.

Jun, M. , Roumeliotis, S. and Sukhatme, G. 1999: State estimation of an autonomous helicopter using Kalman filtering. Proceedings 1999 IEEE/RSJ International Conference on Robots and Systems (IROS’99), October 1999 , Kyongju, South Korea, 1346- 53.

10.

Kim, J. 2004: Autonomous Navigation for Airborne Applications. PhD thesis, Australian Centre for Field Robotics, The University of Sydney.

11.

Lageman, C. , Trumpf, J. and Mahony, R. 2010: Gradient-like observers for invariant dynamics on a lie group. IEEE Transactions on Automatic Control 55, 367-77.

12.

Mahony, R. , Hamel, T. and Pflimlin, Jean-Michel. 2005: Complementary filter design on the special orthogonal group SO(3). Proceedings of the IEEE Conference on Decision and Control, CDC05. Seville, Spain, December.

13.

Mahony, R. and Hamel, T. 2007: Robust nonlinear observers for attitude estimation of mini UAVs. In Advances in Unmanned Aerial Vehicles: State of the Art and the Road to Autonomy. (Intelligent Systems, Control and Automation : Science and Engineering, Vol. 33. Springer, Berlin, 343-376.

14.

Mahony, R. , Hamel, T. and Pflimlin, J.-M. 2008: Non-linear complementary filters on the special orthogonal group. IEEE Transactions on Automatic Control 53, 1203-18, DOI: 10.1109/TAC.2008.923738.

15.

Martin, P. and Salaün, E. 2007: Invariant observers for attitude and heading estimation from low-cost inertial and magnetic sensors. Proceedings of the 46th IEEE Conference on Decision and Control, December 2007, New Orleans, USA, 1039-45.

16.

Martin, P. and Salaün, E. 2008: An invariant observer for Earth-velocity-aided attitude heading reference systems. Proceedings of the 17th World Congress the International Federation of Automatic Control (IFAC2008), 6-11 July, Seoul, Korea, 9857-64.

17.

Roberts, J.M. , Corke, P.I. and Buskey, G. 2002: Low-cost flight control system for small autonomous helicopter . Australian Conference on Robotics and Automation, Auckland, 27-29 November, 71-6.

18.

Salcudean, S. 1991: A globally convergent angular velocity observer for rigid body motion. IEEE Transactions on Automatic Control 46, 1493-7.

19.

Saripalli, S. , Roberts, J.M. , Corke, P.I. , Buskey, G. and Sukhatme, G.S. 2003: A tale of two helicopters. Proceedings of the IEEE/RSJ Intertnational Conference on Intelligent Robots and Systems, October 2003, Las Vegas, USA, 805-10.

20.

Stevens, B.L. and Lewis, F.L. 2003: Aircraft Control and Simulation. 2nd edn. John Wiley and Sons.

21.

Thienel, J. and Sanner, R.M. 2003: A coupled nonlinear spacecraft attitude controller and observer with an unknow constant gyro bias and gyro noise. IEEE Transactions on Automatic Control 48, 2011-15.

22.

Wang, M. , Yang, Y. , Hatch, R.R. and Zhang, Y. 2004: Adaptive filter for a miniature MEMS based attitude and heading reference system. Position Location and Navigation Symposium, July 2004, Monterey , California, 193-200.