Kalman filters based on multibody models: linking simulation and real world. A comprehensive review

Abstract

The Kalman filter algorithm estimates variables of linear systems combining information from real sensors and a mathematical model of the system. It may be applied to observe nonlinear systems by means of a linearization of the system model. Multibody system dynamics constitutes a methodology for the analysis and design of mechanical systems. During the last twenty years, many ways of employing a multibody model as the Kalman filter model have been explored. This paper gathers up diverse algorithms, from the first ones based on the continuous expressions of the filter, to the indirect methods that enable real-time implementations of the observation of mechanical systems with a large number of variables. A detailed explanation of the methods and a description of the strengths and weaknesses of each one is presented along this paper, including a benchmark evaluating the performance of the methods. An important aspect of the Kalman filter is the characterization of the system uncertainty by means of white Gaussian noise. Sometimes, the statistical properties of the noise are unknown. Several methods to determine these properties are described, and a new methodology to model systems perturbed by colored noise (time-correlated noise) is presented. In Kalman filters based on multibody models, the information from a real mechanical system can be employed to keep the model behaving like the actual system with a great level of accuracy, linking the simulation to the real behavior of the system.