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

Abstract

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.