Parameter estimation for ultrasonic echo signals through improved matching pursuit and flower pollination algorithms

Accurate estimations of the time of arrival (TOA) are essential in ultrasonic nondestructive testing. The parameters of ultrasonic pulse echoes are usually estimated by detecting the peak value of the envelope with a Hilbert transformation (HT). However, ultrasonic pulse echoes are likely to be polluted by noise in the propagation process, distorting the envelope signal and preventing the TOA from being accurately estimated. This paper proposes an algorithm for estimating the parameters of ultrasonic echo signals based on joint sparse representation and the flower pollination algorithm (FPA). An improved matching pursuit algorithm is developed to eliminate the noise and improve the envelope extraction of the echo signals. This reduces the superposition of repeated signals and improves the reconstruction accuracy. The signal envelope is then extracted by an HT. Finally, FPA is used to fit the envelope and estimate the parameters. Numerical simulations and experimental results show that the parameters estimated by the proposed method are highly accurate and have a mean square error that is close to the Cramer–Rao lower bound.