Time delay estimation via third-order cumulant

Time-delay is a very significant measurement in the field of non-destructive test. The accuracy of time-delay estimation (TDE) directly influences the precision and reliability of the relative measurement method used in non-destructive testing, such as leak location in underground pipeline leak test, ultrasonic blood velocity measurement, ultrasonic material stress measurement etc. In this paper, methods based on third-order cumulant are applied, including Cross Third-order Cumulant Method and Bispectrum Method, to ultrasonic time delay estimation. Higher-order cumulant can effectively suppress big noise interference. According to the principle that the third moment sequence of a zero-mean Gaussian process is identical to zero, we can use third-order cumulant to estimate time delay. Comparing with Generalized Cross-correlation Method, these methods can suppress the effect of correlated Gaussian noise sources and can be used as the substitution of Generalized Cross-correlation Method.