Comparação de modelos dinâmicos utilizando filtro IMM aplicado ao problema de rastreamento de VANTs

Abstract

In target tracking problems, two of the main concerns are the choice of suitable mathematical models that represent the dynamics of a certain object’s movements and the choice of suitable stochastic filters used to estimate its trajectory and verify the quality of the models through the performance of such models. The literature has several models proposed to represent such dynamics, but most of these models are two-dimensional. This work aims to implement, propose and compare not only existing models in the literature, but also new three-dimensional dynamic models using the IMM filter, to analyze the performance of the filters based on the verification of the quality of the estimates. In order to do this, three mathematical models were modified in the three-dimensional form - Constant Velocity Model with Polar Velocity, Constant Velocity Model with External Input and Maneuver Centered Constant Velocity Model - outside the study and analysis of four other models. To verify that all models are suitable, these were implemented computationally in three stochastic filters: Kalman filter, Extended Kalman filter and Unscented Kalman filter. First, the models were individually implemented each of the filters, paying attention to their limitations, and then they were aggregated into an IMM filter. As a comparative of performance, it was used mean squared errors. For the trajectory data it was used a modified and updated trajectory simulator, capable of offering measurements closer to reality, that is, measurements with noises. As a result, it was observed that in the application of the filters individually, the combination of Constant Velocity Model with Polar Velocity with Extended Kalman Filter had the best performance. In relation to the results obtained by the IMM filter estimates, one of the combinations is highlighted due to the low MSE, even when compered to the individual filters.