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

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.

Roll Angle Estimation of a Motorcycle through Inertial Measurements

“…Since the characterization of the noise is improved, the statistical characteristics of the innovation sequence would be improved as well, thus allowing to use innovation-based adaptive Kalman filters, which should be able to improve the performance of the method for all the maneuvers that have now the worst estimation results. It was recently shown that innovation-based Kalman filters can work reasonably well even if the statistical properties of the noise are not perfect, and even with nonlinear models [ 24 ].…”

Finite Impulse Response Filtering Algorithm with Adaptive Horizon Size Selection and Its Applications

“…2. As (7), (18) are the standard Riccati equations then the existence of the limits in (16) for any 𝜇 > 0 follows from the conditions theorem (a), (b), (c) and (20).…”

“…In general, the Bayesian approach is computationally intractable due to the numerical integration over a large parameter space. In maximum likelihood estimation [19][20][21][22][23][24], the noise statistics are obtained by maximizing the probability density function of the measurement residuals generated by the filter, which is the likelihood of the noise parameters. Adaptive filters based on maximum likelihood methods require nonlinear optimization and are computationally intractable.…”

Editorial of Special Issue “Combining Sensors and Multibody Models for Applications in Vehicles, Machines, Robots and Humans”

“…The eighth work [ 8 ] looks at the general problem of state and force estimation, considering the automotive field as a clear target of application. The authors apply an adaptive method to estimate the noise covariance matrices of a state and input estimator based on multibody models.…”

“…In summary, it can be seen that the papers gathered in the Special Issue contributed either by proposing solutions to the general problem of state, input and/or parameter estimation [ 4 , 5 , 7 , 8 , 9 ], and/or by suggesting applications of the combined use of sensors and multibody models to different fields, such as automotive [ 6 , 8 , 9 ], railway [ 2 ], naval [ 5 ], spatial [ 10 ], machinery [ 4 , 7 ], robotics [ 3 ], biomechanics [ 1 ] and music [ 6 ] applications, thus showing the theoretical challenges and practical interest of this research topic.…”