A Theory and Experiment of Instantaneous Wave Source Localization from a Wave Distribution on a Small Region

We deal with the problem of direction and distance estimate of emission sources in 3-D space. We first introduce a partial differential equation (PDE) what we call the location constraint PDE (LC-PDE), which provides a necessary and sufficient description of wavefield generated by a source at direction n and distance R. To remove differentials, we integrate the LC-PDE in a finite rectangular area with complex sinusoidal weight functions. By using a well-known class of window function to eliminate the integral boundary terms, we show an exact finite set of algebraic equations can be obtained including n, R as the unknown variables and small number of 2-D discrete Fourier transform (DFT) components of wavefield as the measurements.

[1]  N. Ono,et al.  Design and experiments of bio-mimicry sound source localization sensor with gimbal-supported circular diaphragm , 2003, TRANSDUCERS '03. 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers (Cat. No.03TH8664).

[2]  Jont B. Allen,et al.  Image method for efficiently simulating small‐room acoustics , 1976 .

[3]  R. Miles,et al.  Mechanically coupled ears for directional hearing in the parasitoid fly Ormia ochracea. , 1995, The Journal of the Acoustical Society of America.

[4]  Hiroyuki Shinoda,et al.  A Three-Dimensional Sound Localization Sensor System Based on the Spatio-Temporal Gradient Method , 1993 .

[5]  G. Carter,et al.  The generalized correlation method for estimation of time delay , 1976 .

[6]  R. Miles,et al.  Directional hearing by mechanical coupling in the parasitoid fly Ormia ochracea , 2004, Journal of Comparative Physiology A.

[7]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[8]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[9]  Shigeru Ando,et al.  Bio-mimicry Sound Source Localization with Gimbal Diaphragm , 2003 .

[10]  Shigeru Ando,et al.  An Exact Direct Method of Sinusoidal Parameter Estimation Derived From Finite Fourier Integral of Differential Equation , 2009, IEEE Transactions on Signal Processing.

[11]  F.L. Degertekin,et al.  Optical Sensing Inadirectional Memsmicrophone Inspired by the Ears of the Parasitoid Fly, Ormia Ochracea , 2006, 19th IEEE International Conference on Micro Electro Mechanical Systems.

[12]  A direct algebraic method of instantaneous wave source localization , 2008, 2008 SICE Annual Conference.

[13]  S. Ando,et al.  Partial Differential Equation-Based Algorithm of Sound Source Localization with Finest Granularity in Both time and Frequency , 2007, 2007 Fourth International Conference on Networked Sensing Systems.

[14]  N. Ono,et al.  Partial-differential-equation-based sound source localization: Finite Fourier integral approach and its application to multiple source localization , 2006 .

[15]  N. Ono,et al.  Directivity steering principle for biomimicry silicon microphone , 2005, The 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS '05..