A Robust Self-contained Solution for Inertial Attitude Determination Under External Acceleration

Document Type : Research Article


1 Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran.

2 Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran.


One of the main issues in inertial navigation systems is attitude determination, which means estimating the level angles (i.e., roll and pitch). This paper investigates the attitude estimation problem for an accelerated rigid body using three gyros and three accelerometers. The most critical challenges in attitude determination systems are external accelerations and gyroscope drift errors. Thus, a novel method based on the adaptive filter-Kalman algorithm is proposed to estimate and compensate for these errors. Linearization was performed around a general work point, and the covariance matrix's adaptive values were obtained so that leveling angles were accurately determined despite external accelerations. The simulation results, along with the car test, which was performed in different dynamic conditions with external accelerations, showed that the introduced algorithm has a high capability in accurately estimating leveling angles. This approach can be used for GPS-less navigation Algorithms.


Main Subjects

  1. 2017, Comparison of Complementary and Kalman Filter Based Data fusion for attitude Heading Reference System
  2. 2019, A Robust Complementary Filter Approach for Attitude Estimation of Unmanned Aerial Vehicles using AHRS
  3. A Complementary Filter for Attitude Estimation
  4. 2021, Attitude Adaptive Estimation with Smart Phone Classification for Pedestrian Navigation.
  5. Crassidis, J. L., and Junkins, J. L. Optimal Estimation of Dynamic Systems. Chapman and Hall/CRC, 2011.
  6. Jazwinski, A. H. Stochastic Processes, and Filtering Theory. Courier Corporation, 2007.
  7. Schmidt, S. F. "The Kalman Filter-Its Recognition and Development for Aerospace Applications." Journal of Guidance and Control, Vol. 4, No. 1, 1981, pp. 4–7.
  8. Farrell, J. L. "Attitude Determination by Kalman Filtering." Automatica, Vol. 6, No. 3, 1970, pp. 419–430.
  9. Murrell, J. Precision Attitude Determination for Multimission Spacecraft. 1978.
  10. Lefferts, E. J., Markley, F. L., and Shuster, M. D. “Kalman Filtering for Spacecraft Attitude Estimation.” Journal of Guidance, Control, and Dynamics, Vol. 5, No. 5, 1982, pp. 417–429.
  11. Markley, F. L. "Attitude Error Representations for Kalman Filtering." Journal of guidance, control, and dynamics, Vol. 26, No. 2, 2003, pp. 311–317.
  12. Bar-Itzhack, I. Y., and Oshman, Y. "Attitude Determination from Vector Observations: Quaternion Estimation." IEEE Transactions on Aerospace and Electronic Systems, No. 1, 1985, pp. 128–136.
  13. Bar-Itzhack, I., Deutschmann, J., and Markley, F. Quaternion Normalization in Additive EKF for Spacecraft Attitude Determination. 1991.
  14. Deutschmann, J., Bar-Itzhack, I., and Galal, K. Quaternion Normalization in Spacecraft Attitude Determination. 1992.
  15. Psiaki, M. L., Theiler, J., Bloch, J., Ryan, S., Dill, R. W., and Warner, R. E. “ALEXIS Spacecraft Attitude Reconstruction with Thermal/Flexible Motions Due to Launch Damage.” Journal of Guidance, Control, and Dynamics, Vol. 20, No. 5, 1997, pp. 1033–1041.
  16. Psiaki, M. L., Klatt, E. M., Kintner Jr, P. M., and Powell, S. P. “Attitude Estimation for a Flexible Spacecraft in an Unstable Spin.” Journal of Guidance, Control, and Dynamics, Vol. 25, No. 1, 2002, pp. 88–95.
  17. Choukroun, D., Bar-Itzhack, I. Y., and Oshman, Y. “Novel Quaternion Kalman Filter.” IEEE Transactions on Aerospace and Electronic Systems, Vol. 42, No. 1, 2006, pp. 174–190.
  18. Psiaki, M. L. "Backward-Smoothing Extended Kalman Filter." Journal of guidance, control, and dynamics, Vol. 28, No. 5, 2005, pp. 885–894.
  19. Landis Markley, F., Berman, N., and Shaked, U. "H -Type Filter for Spacecraft Attitude Estimation." ADVANCES IN THE ASTRONAUTICAL SCIENCES, Vol. 84, 1994, p. 697.
  20. Markley, F. L., Berman, N., and Shaked, U. Deterministic EKF-like Estimator for Spacecraft Attitude Estimation. No. 1, 1994, pp. 247–251.
  21. Smith, R. H. "An H1-Type Filter for GPS-Based Attitude Estimation." AAS Paper, 1995, pp. 95–134.
  22. Haupt, G. T., Kasdin, N. J., Keiser, G. M., and Parkinson, B. W. "Optimal Recursive Iterative Algorithm for Discrete Nonlinear Least-Squares Estimation." Journal of guidance, control, and dynamics, Vol. 19, No. 3, 1996, pp. 643–649.
  23. Mehra, R. "On the Identification of Variances and Adaptive Kalman Filtering." IEEE Transactions on automatic control, Vol. 15, No. 2, 1970, pp. 175–184.
  24. Ma, Z., and Ng, A. Spacecraft Attitude Determination by Adaptive Kalman Filtering. 2002.
  25. Lam, Q. M., and Wu, A. Enhanced Precision Attitude Determination Algorithms. No. 1, 1998, pp. 61–68.
  26. Mehra, R., Seereeram, S., Bayard, D., and Hadaegh, F. Adaptive Kalman Filtering, Failure Detection and Identification for Spacecraft Attitude Estimation. 1995.
  27. Rapoport, I., and Oshman, Y. Optimal Filtering in the Presence of Faulty Measurement Biases. No. 2, 2002, pp. 2236–2241.
  28. Carter, M., Vadali, S., Chamitoff, G., Carter, M., Vadali, S., and Chamitoff, G. Parameter Identification for the International Space Station Using Nonlinear Momentum Management Control. 1997.
  29. Kim, J.-W., Crassidis, J. L., Vadali, S. R., and Dershowitz, A. L. International Space Station Leak Localization Using Vent Torque Estimation. 2004.
  30. Psiaki, M. L. Estimation of the Parameters of a Spacecrafts Attitude Dynamics Model Using Flight Data. 2003.
  31. Kim, I., Kim, J., and Kim, Y. Angular Rate Estimator Using Disturbance Accommodation Technique. 2002.
  32. Schaub, H., Akella, M. R., and Junkins, J. L. "Adaptive Control of Non-linear Attitude Motions Realizing Linear Closed Loop Dynamics." Journal of Guidance, Control, and Dynamics, Vol. 24, No. 1, 2001, pp. 95–100.
  33. Costic, B. T., Dawson, D. M., De Queiroz, M. S., and Kapila, V. "Quaternion-Based Adaptive Attitude Tracking Controller without Velocity Measurements." Journal of Guidance, Control, and Dynamics, Vol. 24, No. 6, 2001, pp. 1214–1222.
  34. 1997, Inertially Aided GPS Based Attitude Heading Refrence system AHRS for general aviation aircraft
  35. Ncørguard, N. K. Poulsen, O. Ravn, New developments in state estimation for non-linear systems, Journal of Automatica, Vol. 36, No. 11, pp. 1627-1638, 2000.
  36. Lefferts, E. J., Markley, F. L., and Shuster, M. D., “Kalman Filtering for Spacecraft Attitude Estimation”, Journal of Guidance, Control, and Dynamics, Vol. 5, No. 5, 1982, pp. 417–429.
  37. Markley, F. L., "Attitude Error Representations for Kalman Filtering," Journal of Guidance, Control, and Dynamics, Vol. 63, No. 2, 2003, pp. 311–317.
  38. Yan, Z., Li, B., & Zhu, S. (2020). "Improved AHRS Algorithm for Unmanned Aerial Vehicles Based on Particle Filter. " Sensors, 20(21), 6253.
  39. Zhang, R., Wei, X., & Ma, J. (2020). "A Novel Inertial Navigation System Using a Low-Cost MEMS AHRS." Sensors, 20(24), 7256.
  40. Zhou, H., Wang, F., & Zhang, Z. (2021). "Adaptive Unscented Kalman Filter for Improving Attitude Estimation Accuracy of MEMS-Based AHRS." Sensors, 21(2), 503.
  41. Delgado-Mata, C., De Sousa, R. A., & Fu, W. (2021). "Novel Adaptive Unscented Kalman Filter with Fading Memory for Robust AHRS." IEEE Sensors Journal, 21(14), 15262-15273.
  42. Liu, X., Zhang, T., & Lv, P. (2021). "Attitude Estimation for AHRS Based on Mahony Filter and Adaptive Notch Filter." In 2021 7th International Conference on Control, Automation and Robotics (ICCAR) (pp. 692-697). IEEE.
  43. Hovland, G., Børhaug, T. E., & Johansen, T. A. (2021). "Nonlinear Optimization of the Attitude and Heading Reference System Problem." Journal of Guidance, Control, and Dynamics, 44(11), 2236-2249.
  44. Zeng, J., Liu, Y., & Han, C. (2022). "AHRS Correction Algorithm Based on RBF Neural Network for Underwater AUVs." IEEE Access, 10, 36399-36411.
  45. Shu, X., Li, H., & Zhu, L. (2022). "Quaternion-Based Adaptive Unscented Kalman Filter for AHRS with Biased Rate Gyro." IEEE Transactions on Instrumentation and Measurement, 71, 1-12.
  46. Li, T., & Liu, H. (2022). "A Robust AHRS Attitude Complementary Filter Algorithm Based on a Nonlinear Parameter Fading Extended Kalman Filter." IEEE Access, 10, 72988-72998.
  47. Wu, J., Gao, Y., & Liu, H. (2022). "Adaptive Unscented Kalman Filter Algorithm for Attitude and Heading Reference System." IEEE Access, 10, 23157-23165.
  48. 2007, Calibration and data fusion solution for the miniature attitude and heading reference system
  49. 2020, Attitude heading reference algorithm based on transformed cubature Kalman filter
  50. 2020, Attitude determination improvement in accelerated motions for maneuvering underwater vehicles
  51. 2014, Accurate orientation estimation using AHRS under conditions of magnetic distortion
  52. Adaptive filter for a miniature MEMS based attitude and heading reference system, 2004.
  53. 2020, Fuzzy Adaptive Attitude Estimation for a Fixed-Wing UAV with a Virtual SSA Sensor During a GPS Outage
  54. 2021, A novel adaptive Kalman filter for Euler-angle-based MEMS IMU/magnetometer attitude estimation
  55. 2018, Kalman filter for mobile-robot attitude estimation: Novel optimized and adaptive solutions
  56. Peter H. Zipfel, Modeling and Simulation of Aerospace  Vehicle Dynamics, 2000
  57. Simon