Prony's method applied to estimate noise source locations and their sound powers

An application of Prony's method for evaluating the acoustic power and location of sound sources from spatially sampled data is described. A sound source considered as a point source has an intensity proportional to the inverse square of the distance between source and observation point. The Fourier transform of this intensity function is an exponential function with a real exponent. The shift property of the Fourier transform results in a spectral change in the phase angle, which is expressed in the transform domain by a multiplicative exponential function of pure imaginary exponent. In this paper the usual time axis of the Fourier pair of time and frequency is treated as a variable denoting the location of the sound source. Accordingly, each spectral component of spatially sampled sound intensity generated by n point sources can be expressed as a linear combination of n complex exponentials. By applying Prony's method to the spectral data, these unknown exponents can be calculated numerically. This paper deals with an estimation procedure to find the location and power of a noise source. The estimation is done by minimizing the sum of the squares of the errors between the model and measured data. The proposed method has general applicability to problems where the so-called inverse square law for intensity can be assumed to be valid.