Improvement in the accuracy of estimating the time-of-flight in an ultrasonic ranging system using multiple square-root unscented Kalman filters

The square-root unscented Kalman filter (SRUKF) is applied to identify the shape parameters of an ultrasonic echo envelope. The SRUKF has better stability than the normal unscented Kalman filter (UKF) because the square-root of the error covariance matrix used in the SRUKF guarantees positive semidefiniteness. Considering the effect of the initial state on the convergence speed of filters, the multi-SRUKF is used to estimate the time-of-flight (TOF). Each SRUKF has a different initial state. The result estimated in a limited time with minimum mean square error is finally adopted. Simulation experiments for various couples of shape parameters and signal-to-noise ratios validate the improvement in the TOF accuracy. Real experiments using the echo signals of a SensComp 600 ultrasonic transducer show that the relative means and standard deviations of the TOF error obtained using the multi-SRUKF method are less than 0.2% and 0.15%, respectively.