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A semi-analytical geometrical acoustics method for numerical simulation of ultrasound based motion sensing

Vamshi Krishna Chillara, Wontak Kim

Abstract

We present a semi-analytical geometrical acoustics method to numerically simulate ultrasonic signal characteristics pertinent to motion sensing applications in indoor environments. The proposed methodology treats motion sensing from the first-principles in the sense that the expressions for acoustic field from the source, that scattered by the target and then received at the receiver are all derived from a kinematic standpoint incorporating target motion into consideration. A series of examples are presented throughout to demonstrate the effect of source directivity, wall reflections, and motion trajectories on the Doppler signal strength and frequency characteristics observed for motion sensing applications. Finally, we present a comparison of simulated results with experimental results on data acquired with a human target moving in an environment with an ultrasonic source and receiver. We specifically compare the baseband signal characteristics and their corresponding Short-time Fourier Transforms that depict Doppler frequency characteristics and show them to be in good qualitative agreement.

A semi-analytical geometrical acoustics method for numerical simulation of ultrasound based motion sensing

Abstract

We present a semi-analytical geometrical acoustics method to numerically simulate ultrasonic signal characteristics pertinent to motion sensing applications in indoor environments. The proposed methodology treats motion sensing from the first-principles in the sense that the expressions for acoustic field from the source, that scattered by the target and then received at the receiver are all derived from a kinematic standpoint incorporating target motion into consideration. A series of examples are presented throughout to demonstrate the effect of source directivity, wall reflections, and motion trajectories on the Doppler signal strength and frequency characteristics observed for motion sensing applications. Finally, we present a comparison of simulated results with experimental results on data acquired with a human target moving in an environment with an ultrasonic source and receiver. We specifically compare the baseband signal characteristics and their corresponding Short-time Fourier Transforms that depict Doppler frequency characteristics and show them to be in good qualitative agreement.
Paper Structure (21 sections, 39 equations, 11 figures, 2 tables)

This paper contains 21 sections, 39 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Receiver moving in the pressure field of a stationary source
  3. Receiver moving in a planewave field
  4. Receiver moving in the pressure field of an isotropic point source
  5. Stationary receiver in a pressure field generated by a moving point source
  6. Doppler effect for a few simple cases
  7. Point scatterer moving in the pressure field of a source and reflecting ultrasound towards receiver
  8. Some interesting observations
  9. Point Scatterer moving in multi-reflection environment with a non-uniform source directivity: Integration with Image Source Method
  10. Source directivity
  11. Moving target motion representation
  12. Temporal sampling and Baseband signal representation
  13. Image Source Method
  14. Results
  15. Point target in motion
  16. ...and 6 more sections

Figures (11)

  • Figure 1: Piston source beam directivites for $n_s=(\theta=0^{\circ}, \phi=90^{\circ})$)
  • Figure 2: Piston source beam directivites for $n_s=(\theta=0^{\circ}, \phi=30^{\circ})$
  • Figure 3: (a) On-axis Motion Trajectory (b) Source in-plane directivity (c) Stepping velocity Profile (d) Baseband signal and Doppler characteristics for stepping velocity profile (e) Constant velocity profile (f) Baseband signal and Doppler characteristics for a constant velocity profile
  • Figure 4: (a) Transverse motion velocity profile(b) Diagonal motion velocity profile (c) Transverse motion trajectory (d) Diagonal motion trajectory (e) Baseband signal and Doppler characteristics for transverse motion trajectory (f) Baseband signal and Doppler characteristics for diagonal motion trajectory
  • Figure 5: (a) Motion Trajectory (b) In-plane directivity (c) Beam-plane directivity (c) Stepping velocity profile (e) Baseband signal and Doppler characteristics for stepping velocity profile (f) Constant velocity profile (g) Baseband signal and Doppler characteristics for constant velocity profile
  • ...and 6 more figures