# Combined Identification of Vehicle Parameters and Road Surface Roughness Using Vehicle Responses
###### Abstract
There are fewer existing studies on the combined identification of the vehicle parameters and the road roughness. [PERSON] et al. [27] minimized the difference in roughness at the identified front and rear axles and used GA to optimize the optimal vehicle parameters. Subsequently, the road profile was estimated by combining the AKF, Robbins-Monro (RM), and Rauch-Tung-Striebel (RTS) methods. In this method, the roughness required by the objective function of GA was estimated by AKF, that is, the objective function of each iteration of GA needs a complete Kalman filter recursion. [PERSON] et al. [28] divided the measured vehicle acceleration and displacement responses data into two parts. In the first part, vehicle parameters were optimized by minimizing the residual difference between the measured vehicle responses and those estimated by minimum variance unbiased estimation (MVE); in the second part, unknown roughness and vehicle responses were identified by MVE. The estimated responses in the step of vehicle parameter identification are identified by MVE, and the calculation of the system matrix in MVE is inseparable from the vehicle parameters, so the identification of the vehicle parameters and roughness is a mutual iterative process. [PERSON] et al. [29] calculated the residual difference between the unsprung responses predicted by AKF and the sprung responses predicted by DKF-UI and the measured responses, respectively, optimized the best vehicle parameters through GA, and then identified the road roughness through AKF and DKF-UI. These methods embed the iterative interaction process of filter recursion in the framework of the optimization algorithm, which overcame the difficulty of vehicle parameter identification requiring additional experiments. In the context of multi-degree-of-freedom vehicle models with a large number of parameters, an optimization algorithm with a multi-index objective function is often used. However, the fusion filtering recursion in the framework of the optimization algorithm is a complex iterative process. Therefore, it is necessary to develop a method to decouple roughness and unknown parameters, and efficiently identify roughness and unknown vehicle parameters. To overcome the above shortcomings of the existing methods, this paper proposes a new method to simultaneously identify vehicle parameters and road roughness based on the extended Kalman filter with unknown input (EKF-UI), considering the idea that the front and rear axles of a moving vehicle pass through the same road roughness. The measured moving vehicle is modeled as a four-degree-of-freedom semi-vehicle model with front and rear wheels. In view of the coupling effect between axle stiffness and road roughness, which cannot be identified simultaneously, other unknown vehicle parameters except tire stiffness are extended to the state vectors, and the unknown force on the vehicle is defined as the product of the relative displacement between tire and road roughness and tire stiffness. The vehicle physical parameters and the unknown force on the front and rear axles of the vehicle are identified by EKF-UI. Then, the simultaneous equation of front axle position roughness and delayed rear axle position roughness is established, and the axle stiffness is estimated by the nonlinear least squares method. Finally, the roughness surface profile at the front and rear axle positions can be estimated and the roughness of the whole road section can be obtained. The effectiveness of the proposed method is verified by numerical verifications of different roughness grades, different noise levels, and different vehicle speeds. Proposed Method for Simultaneous Identification of Physical Parameters of Moving Vehicles and Road Roughness