Convergence analysis of the extended Kalman filter used in the ultrasonic time-of-flight estimation

The ultrasonic Time-of-Flight (ToF) estimation may be achieved using different algorithms, such as signal processing techniques, artificial intelligence and, statistical estimators, among others. These algorithms have a highlight point, which is the guarantee of the estimation reliability through the convergence of the results and low estimation uncertainty. Hence, this work aims to perform the convergence analysis of the Extended Kalman Filter (EKF) algorithm to ToF estimation, with application in wind speed measurement. Therefore, a state space model of a delayed sine wave was constructed. The modeling used shows the influence of time-varying parameters, which determine the convergence of the states. By analyzing the convergence of the algorithm, it was possible to determine the range of variation of the model parameters to guarantee the final estimation results. Through the construction of a computational model using Matlab@Simulink are presented the simulation results to wind speed measurement.