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.

The growing functionalities implemented on vehicles have increased the importance of simulation in the design process. This complexity is mainly driven by the introduction of electrified powertrains, Advanced Driver Assistance Systems (ADAS) and Automated Driving Systems (ADS). Additionally, the automotive industry must reduce development times and cost, while keeping flexible development capabilities and fulfilling demanding regulation standards for safety-critical systems. Existing testing frameworks based on simulation implement typically analytical models to ensure real-time performance, and provide limited flexibility to perform Hardware in the Loop (HiL) setup based tests. In this work a vehicle modelling approach which guarantees high accuracy and real-time capabilities is proposed. Moreover, the proposed approach is validated firstly with real vehicle data, demonstrating that it can fairly reproduce the behaviour of the vehicle tested; and secondly, in a HiL setup to demonstrate the real-time execution capabilities of the approach.

Nowadays, the growing functionalities implemented on vehicles make the simulation phase much more important in the design process. For that purpose, a representative model is required, as it allows to reproduce the exact behaviour of the vehicle, and reduce not only the time required for its setup and testing, but also the cost related to these. Due to this, the development of accurate vehicle models has become one of the main areas of interest for the automotive industry. In this work a 16 DOF (degree of freedom) full vehicle model is presented. This model is based on multibody formulation combined with an appropriate solver for real-time execution. In order to validate this model, data from a real test vehicle has been used, comparing the real dynamic response of the vehicle to the one provided by the developed dynamic model. Results show that the presented approach represents effectively the behaviour of a real vehicle, both in longitudinal and lateral terms.

Lumped-parameter thermal networks (LPTNs) are efficient computational models that can be used to replicate the thermal behavior of eMotors in a way that is compatible with real-time execution. The accuracy of the simulation results delivered by LPTNs relies on the selection of an appropriate topology and the accurate tuning of their parameters, namely resistances, capacities and heat sources. It is difficult, however, to obtain an accurate tuning of the parameters starting from theoretical expressions, and these often need to be adjusted based on experimental calibration. Several methods can be used to this end; among these, finite differences are a popular option. This paper presents a methodology for the analytical determination of the sensitivity of LPTN dynamics with respect to its lumped parameters. The obtained analytical sensitivities provide information about the effect of the circuit parameters on the thermal dynamics of the overall system, and can be used to enable the use of gradient-based optimization methods to adjust the LPTN parameters. The proposed method overcomes several limitations of finite difference approaches, like the computational load incurred when the number of parameters to be adjusted is large, and the variability of the results with the increment used to define the finite differences. The analytical sensitivities were tested in the analysis and optimization of a benchmark thermal model and the LPTN representation of a permanent-magnet synchronous motor.