Precision Ultrasonic Distance Sensing via Hybrid Optimization: Integrating Time-of-Flight Correction With BFGS and Differential Evolution Algorithms

Signal attenuation and multi-peak distortion pose significant challenges for long-range ultrasonic Time-of-Flight (TOF) estimation. To address this, this paper 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 algorithm (TBDE), for enhanced TOF estimation. This optimization algorithm adopts a segmented search strategy: the fast convergence of the BFGS algorithm is utilized to quickly find the local optimal solution. Then, the powerful global search capability of the DE algorithm is used to find the global optimum, which effectively overcomes the shortcomings of traditional optimization algorithms, such as the tendency to fall into the local optimum and the slow convergence speed. The experimental results show that the proposed method outperforms the mainstream algorithm in terms of convergence speed and accuracy; the root mean square error (RMSE) is reduced to 2.30 × 10-4, and the number of iterations for convergence is shortened to 80 iterations. The average absolute error is 0.11 cm over a measurement range of 250 to 700 cm, which confirms the effectiveness of the method by ensuring high accuracy with fast operation efficiency.