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Precision Ultrasonic Distance Sensing via Hybrid Optimization: Integrating Time-of-Flight Correction With BFGS and Differential Evolution Algorithms
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DOI：10.1109/tim.2026.3718104.png)
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Abstract
En 中文
Signal attenuation and multipeak distortion pose significant challenges for long-range ultrasonic time-of-flight (TOF) estimation. To address this, this article proposes an envelope gradient-front polynomial fitting model and introduces a hybrid method combining the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm with differential evolution (DE), termed the TOF-based BFGS–DE (TBDE) algorithm, for enhanced TOF estimation. The core innovation leverages the gradient signal’s sensitivity to rising edges, approximating the envelope gradient front with a third-order polynomial that explicitly parameterizes TOF as the shift term, thereby enhancing robustness against waveform deformation. This front-focused model is synergistically coupled with a three-stage hybrid optimization framework: coarse TOF initialization via local polynomial fitting, rapid BFGS convergence exploiting high-quality initial solutions, and refined DE search with dynamic boundary contraction guided by physical TOF constraints, achieving a well-balanced tradeoff between convergence speed and accuracy. Compared to standard BFGS, TBDE reduces RMSE by 98.69 % while improving convergence time by 88.24 % over conventional DE, attaining a 93.8 % convergence rate. Comparative evaluation against the envelope cross correlation (ECC) method demonstrates that TBDE has a runtime of 277.93 ms and maintains robust performance under noise and multipath interference. Long-range ranging experiments within 250–700 cm confirm sub-centimeter precision, with the maximum standard deviation of 0.52 cm across the entire measurement range.
Keywords:
Envelope gradient-front polynomial fitting model
long-range ultrasonic distance measurement
TOF-based BFGS-DE (TBDE)
ultrasonic time of flight (TOF)
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1.9W
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