Innovative Analysis for Parameter Estimation Quality
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Innovative Analysis for Parameter Estimation Quality Marina B. A. Souza*, Leonardo de Mello Honório, and Edimar José de Oliveira Abstract: This paper performs an analysis of the solution space influence of a nonlinear dynamic system on the parameter estimation quality. For parameters estimation, the proposed approach uses an Optimal Input Design (OID) as the Suboptimal Excitation Signal Generation and Optimal Parameter Estimation (SOESGOPE). Based on the studies of a small mobile robot that is represented by a parametric mathematical model indicate that the model reliability level maximizes using the shortest set of parameters. Applications, qualities, and limitations of the method are analyzed considering the solution space. Through an in-depth analysis of the identification process of a differential mobile robot, the paper becomes a reference for a review of a nonlinear dynamic system, aiming to select the most suitable model for the identification process. Keywords: Nonlinear systems, optimal parameter design, parameter identification, solution space influence
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INTRODUCTION
Modeling approaches are critical in dynamic systems, providing new ways towards the analysis of data from the structure, and assisting in making control decisions. Generally, system identification methods deal with the development of mathematical models from input/output data [1–4]. In this field, concerning a parametric model, an indispensable stage is the parametric estimation. A proper estimation of a parameter set related to the model guarantees a suitable reproduction of the real system. Identification methods based on experimental tests compare the output states using an error function, that may be treated by techniques based on Artificial Neural Networks (ANN), filtering, and iterative optimization processes [5]. For simplicity of implementation, several works approach the architecture based on neural networks [6, 7]. A significant advantage of ANN is the possibility of using it in both linear and nonlinear systems. Although the ANN is applicable in identification systems, this type of method uses a black-box model that does not consider the involved parameters. Filtering methods do not present the identification as the main objective, however it is possible to apply the Extended Kalman Filter (EKF) as a parallel estimator [8]. The computational complexity of an EKF is around the cube of the state vector dimension [9]. In the case of adding parameters to be estimated, the complexity also involves the parameter vector. In situations that do not
require a high sampling rate, it is possible to apply the parameter estimation tool. [10] applied the EKF to estimate states and parameters related to a patrol ship. Along with the possibility of not having a high-speed estimation system, the authors considered only hydrodynamic derivatives as variables to be estimated, in this case, eight parameters. On the other hand, quadrotors require a higher sampling rate, in which case, on
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