PSI - Issue 38

A. Débarbouillé et al. / Procedia Structural Integrity 38 (2022) 342–351 A. De´barbouille´ / Fatigue Design (2022) 1– ??

351

10

with a system of only one body.

The figure 3 represents the evolution of acceleration of the body car center of gravity. The acceleration estimated by Kalman filter is less noised than the accelerometers measurement. The estimation of Kalman filter follows the dynamic of the model. The figure 4 represents the vertical forces on the wheels center. The estimated forces are close to the simulation forces. The mean relative error is 1.476%. 5. Perspectives and conclusion We have implemented an Augmented and Constrained Extended Kalman Filter adapted to a multi-body 2D model of vehicle. Even if we deal here with 2D, the implementation choices are oriented to easily adapt the approach to a 3D model of vehicle. This approach takes into account constraint equations and non linearities due to the prediction and measurement models. This ACEKF is designed to estimate the wheel center load when the vehicle is rolling on a real road. The road profile is unknown but the Kalman estimator is augmented by road parameters and then can identify it. The wheel center load is well estimated. The combination of measurement from accelerometers, gyrometer tachometer and GPS was identified as a set of sensors su ffi cient to estimate the attitude of a car body and this study confirm the feasibility to identify wheel center loads with the same set. References Kalman, R. E., A New Approach to Linear Filtering and Prediction Problems , Transaction of the ASME—Journal of Basic Engineering, pp. 35-45, March 1960. Maria Isabel Ribeiro, Kalman and Extended Kalman Filters: Concept, Derivation and Properties , Institute for Systems and Robotics, Lisboa, Portugal, 2004. Philippe Martin, Erwan Salau¨n, Generalized Multiplicative Extended Kalman Filter for Aided Atti-tude and Heading Reference System , AIAA Guidance, Navigation, and Control Conference, Toronto, Canada, August 2010. Simon J. Julier and Je ff rey K. Uhlmann, New extension of the Kalman filter to nonlinear systems , Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, July 1997. Yuanxi Yang, Robust Kalman filtering with constraints: A case study for integrated navigation , Journal of Geodesy, June 2010. D.Simon, Kalman filtering with state constraints: a survey of linear and nonlinear algorthms , IET Control Theory Appl., pp. 1–16, 2010. Bruno Ota´vio Soares Teixeira, Jaganath Chandrasekar, Harish J. Palanthandalam-Madapusi, Gain-Constrained Kalman Filtering for Linear and Nonlinear Systems , IEEE transactions on signal processing, Vol. 56, no. 9, pp. 4113-4123, September 2008. Chun Yang, Erik Blasch, Kalman Filtering with Nonlinear State Constraints , IEEE Transactions on Aerospace and Electronic Systems, Volume: 45, Issue: 1, pp 70-84, January 2009. Liyu Xie, Zhenwei Zhou, Lei Zhao, Chunfeng Wan, Hesheng Tang and Songtao Xue, Parameter Identification for Structural Health Monitoring with Extended Kalman Filter Considering Integration and Noise E ff ect , Applied Sciences, 2018. E j Le ff ens, F.L. Markley, M.D. Shuster, Kalman Filtering for Spacecraft Attitude Estimation , AIAA 20th Aerospace Science Meeting, january 1982. E. Risaliti, T. Tamarozzi, B. Cornelis, W. Desmet, Virtual sensing of wheel center loads on a McPherson suspension , International Conference on Noise and Vibration Engineering, 2018. Cyril Joly, David Bre´taille, Franc¸ois Peyret, Comparative study of non-linear filtering techniques applied to real time 2D , traitement du signal, Volume 25 No. 3, 2008. Aida Makni., Fusion de donne´es inertielles et magne´tiques pour l’estimation de l’attitude sous contrainte e´nerge´tique d’un corps rigide acce´le´re´. Traitement du signal et de l’image , Thesis, Universite´ Grenoble Alpes, 2016. Jack C. K. Chou, Quaternion Kinematic and Dynamic Di ff erential Equations , IEEE transaction on robotics and automation, Vol.8, no 1, February 1992. Nachi Gupta, Raphael Hauser, Kalman Filtering with Equality and Inequality State Constraints , ArXiv [math.OC], 2007. Mark L. Psiaki, Backward-Smoothing Extended Kalman Filter , Journal of Guidance, Control, and Dynamics, Vol. 28, No. 5, 2005. Paulo Flores, Margarida Machado, Eurico Seabra, Miguel Tavares da Silva, A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multi-body Systems , Journal of Computational and Nonlinear Dynamics, Vol. 6, January 2011.