Error Analysis of Optimization Algorithms in Ultrasonic Parameter Estimation

The back scattered ultrasonic echo carries several valuable information in its amplitude, bandwidth, delay in time, phase and time of flight. This information is capable of characterizing properties of the material from which it is reflected. In order to model the reverberations, white Gaussian noise is added to Gaussian echo. The required set of parameters are estimated from the noise altered echo using Maximum Likelihood Estimation. This reduces to least square curve fitting, due to additive white gaussian noise. For optimizing the estimated parameters from the back-scattered signal, different algorithms such as Levenberg-Marquardt, Trust-Region Reflective, Active Set, Quasi Newton and Sequential quadratic programming are used. The proposed work aims at the error analysis of estimated signals using the above-mentioned optimization algorithms for different SNR values viz. 0-20dB. Further the noise added signals are subjected to wavelet denoising, prior to parameter estimation. The experimental result shows that the lowest mean square error is obtained for the echo parameters optimized using Levenberg-Marquardt algorithm, for both noisy and de-noised cases.