Application of the continuous wavelet transform to the angular location of jet aircraft
Brian G. Ferguson, Kam W. Lo · The Journal of the Acoustical Society of America · 1999
For a fast moving source and widely spaced sensors, the passive wideband cross-correlation method for time delay estimation requires compensation for the relative time scaling between the received signals, otherwise the time delay estimates will be in error. Passive wideband cross correlation with differential Doppler compensation is equivalent to evaluating the continuous wavelet transform, which is an operation that transforms a function (represented by the output waveform of one sensor) by integrating it with time-scaled and time-delayed versions of some kernel function (represented by the output waveform of the other sensor). When the signal-to-noise ratio is high, the coordinates of the wavelet transformed global maximum provide reliable estimates of both the time delay and the ratio of the time scales of the signals received by the two sensors. The wavelet transform is used to process real acoustic data recorded from an orthogonal configuration of three microphones during the low altitude transit of a jet aircraft. The resulting time delay estimates are used to calculate the variation with time of the azimuth and elevation angles of the aircraft during its transit.