*Article* **Multibody-Based Input and State Observers Using Adaptive Extended Kalman Filter**

**Antonio J. Rodríguez 1,\*, Emilio Sanjurjo 1, Roland Pastorino <sup>2</sup> and Miguel Á. Naya <sup>1</sup>**


**Abstract:** The aim of this work is to explore the suitability of adaptive methods for state estimators based on multibody dynamics, which present severe non-linearities. The performance of a Kalman filter relies on the knowledge of the noise covariance matrices, which are difficult to obtain. This challenge can be overcome by the use of adaptive techniques. Based on an error-extended Kalman filter with force estimation (errorEKF-FE), the adaptive method known as maximum likelihood is adjusted to fulfill the multibody requirements. This new filter is called adaptive error-extended Kalman filter (AerrorEKF-FE). In order to present a general approach, the method is tested on two different mechanisms in a simulation environment. In addition, different sensor configurations are also studied. Results show that, in spite of the maneuver conditions and initial statistics, the AerrorEKF-FE provides estimations with accuracy and robustness. The AerrorEKF-FE proves that adaptive techniques can be applied to multibody-based state estimators, increasing, therefore, their fields of application.

**Keywords:** adaptive Kalman filter; multibody dynamics; nonlinear models; virtual sensing; multibody based observers
