Review on Time Delay Estimate Subsample Interpolation in Frequency Domain

• Published in: IEEE transactions on ultrasonics, ferroelectrics, and frequency control Vol. 66; no. 11; pp. 1691 - 1698
• Main Author: Svilainis, Linas
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.11.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation error; Bandwidth; Bias; Computer simulation; Correlation; Estimation; estimation error; Frequency domain analysis; Frequency response; Inclination angle; Interpolation; Lower bounds; Matlab; Multiplication; Parameter estimation; Random errors; Regression analysis; Signal to noise ratio; Time lag; time-of-arrival estimation; ultrasonic variables measurement
• ISSN: 0885-3010; 1525-8955; 1525-8955
• DOI: 10.1109/TUFFC.2019.2930661

Time delay or the time-of-flight is a most frequently used parameter in many ultrasonic applications. Delay estimation is based on the sampled signal, so the resolution is limited by the sampling grid. Higher accuracy is available if the signal-to-noise ratio is high, then the subsample estimate is desired. Techniques used for subsample interpolation suffer from bias error. Time-of-flight estimation that is free from bias errors is required. The proposed subsample estimation works in the frequency domain; it is based on the cross-correlation peak temporal position. The phase of the cross-correlation frequency response becomes linear thanks to multiplication by the complex conjugate, and its inclination angle is proportional to the delay. Then, subsample interpolation becomes free from the bias error. Twelve algorithmic implementations of this technique have been proposed in this paper. All algorithmic implementations have been analyzed for bias and random errors using simulation and MATLAB codes are given as supplementary material. Comparison with best-performing interpolation techniques (spline approximation, cosine interpolation, carrier phase) is given for both bias and random errors. It was demonstrated that frequency domain interpolation has no bias errors, and noise performance is better or comparable to other subsample estimation techniques. Weighted regression using L2 norm minimization has the best performance: total errors (bias and random) are within 3% of theoretical lower bound.