To address the instability in extracting key parameters such as time-of-flight (ToF) from ultrasonic echoes due to noise and multi-echo superposition, this paper proposes a robust parameter estimation method based on the secretary bird optimization algorithm (SBOA). The proposed approach adheres to the Gaussian convolution-based echo parameterization and cosine-similarity matching framework, while innovatively introducing SBOA to perform global optimization of model parameters. Consequently, the multi-echo ToF estimation is formulated as a nonlinear optimization problem aimed at maximizing waveform shape consistency. To evaluate the method’s performance, simulations are conducted under multi-echo superposition scenarios. Comparisons are made with representative baseline techniques, including wavelet transform (WT), empirical mode decomposition (EMD), and variational mode decomposition (VMD), using mean squared error (MSE), estimated signal-to-noise ratio (ESNR), and normalized cross-correlation (NCC) as performance metrics. Experimental results demonstrate that, in challenging low-SNR and echo-interference environments, the proposed method achieves overall superiority across all quantitative metrics and exhibits a stronger capability to preserve the main-lobe morphology and structural features of echoes. Validation on semi-synthetic signals further confirms its effectiveness, with practical applicability to be verified by measured datasets in future work. This work provides an effective and robust solution for ultrasonic signal processing in complex field conditions.
Wang et al. (Fri,) studied this question.