High resolution parameter estimation of ultrasonic echoes for NDE applications

Ultrasonic backscattered echoes represent not only the impulse response of the transducer, but they also contain information pertaining to the inhomogeneity of the propogation path, the effect of frequency dependent absorption and scattering, the dispersion effect, and the geometric shape, size and orientation of reflectors. Therefore, a well-defined modeling of the backscattered echo leading to a high resolution parameter estimation of the echo amplitude, arrival time. Echo skewness, center frequency and bandwidth is highly desirable for nondestructive evaluation of materials, target detection, object classification, velocity measurement and/or the ranging system. In this paper, a maximum likelihood (ML) model of the backscattered echoes is developed, assuming that all parameters describing the shape of the echo are unknown. The unknown parameters can be estimated by minimizing the mean square error using iterative techniques. Iterative parameter estimation has suffered has suffered from the problem of convergence and/or inaccurate results due to the local minima of the error function. In this investigation, a two-stage iterative estimation process known as the "Expectation/Maximization algorithm" is developed for the optimal parameter estimation of the echoes with low signal-to-noise ratio. In the first stage of the algorithm, we estimate the expected signal, and in the second stage the maximum likelihood criterion is used to estimate parameters. It has been observed that the EM algorithm is less dependent on the initial guess, is computationally efficient and performs well in resolving interfering multiple echoes.