Single-object localization using multiple ultrasonic sensors and constrained weighted least-squares method

Chung Wei Juan*, Jwu Sheng Hu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, an active single-object localization system with U-shaped ultrasonic module array is presented. The proposed algorithm in this system has two stages. The first stage is time-of-flight (TOF) estimation of reflected ultrasonic signals. We analyze several distortion cases of reflection signals and provide solutions to improve the performance of TOF estimation. The second stage is TOF-based object localization. A good localization algorithm can suppress the problems caused by inaccurate TOF estimation and improve the accuracy of target positioning. We propose two object-localization algorithms to estimate the object location. One is the unconstrained least-squares method, and the other is the constrained weighted least-squares method based on the eigenvalues-analyzing technique. The simulation results suggest that the performance of the proposed constrained weighted method is better than that of the unconstrained method. In addition, the median smoother and the outlier exclusion scheme are implemented in the overall system to make the object location estimation more stable. The performance of the proposed system is confirmed by the experiment results, which show that the single-object localization has a considerable degree of accuracy and stability.

Original languageEnglish
Pages (from-to)1171-1184
Number of pages14
JournalAsian Journal of Control
Issue number3
StatePublished - May 2021


  • constrained least squares
  • object localization
  • sensors array
  • time of flight (TOF)
  • TOF estimation
  • ultrasonic range measurement


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