Applications of cross correlation

Cross correlation• In signal processing, cross-correlation is a measure of similarity of

two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product.

• For continuous functions, f and g, the cross-correlation is defined as:

• where f* denotes the complex conjugate of f.• Similarly, for discrete functions, the cross-correlation is defined as:

Applications of cross correlation

• pattern recognition• Signal detector• Weather forecasting• Security system designing• Water traffic monitoring

Cross-correlation of ship noise for water traffic monitoring

•One of the vessel features that can be remotely measured and used for vessel detectionand classification is the vessel's acoustic signature

Water traffic monitoring

• Any moving vessel radiates an underwater sound whose parameters depend on the vessel hull structure, machinery , propeller, etc.

• Measurements of underwater sound radiated by vessels can provide enough information for vessel identification.

• Underwater sounds can be listen by using the hydrophones.

• A hydrophone is a microphone designed to be used in underwater for recording or listening the underwater sound.

Water traffic monitoring

•We considered a method that enables such tasks as vessel tracking and individual vessel signature extraction in busy environments, using a system with a few hydrophones. This method is based on cross-correlation processing of acoustic signals detected by different hydrophones.

Water traffic monitoring

• The noise radiated by a ship propagates underwater and reaches the hydrophones at different times due to different propagation distances.

• This delay depends on the direction of the ship.

• The core of the cross-correlation method is based on the analysis of the timedelays in the recorded signals.

Water traffic monitoring•An example of the calculated cross-correlation between twohydrophones for two vessels :

•The time variation of the cross-correlation function can be presented in the form of afloating chart similar to a spectrogram. Such graph has two geometric dimensions: thehorizontal axis represents time, the vertical axis is the delay between two hydrophonesignals; a third dimension is shown in color indicating the amplitude of a cross correlation function.

Water traffic monitoring

• We used the cross-correlation function for calculating the spectral density of the vessels’ sound.

• The spectral density of the received signal is directly related to the spectral density of their cross-correlation.

• While contributions of different boats cannot be separated in the time domain, they can be separated in delay in the cross-correlation: the spectrum of the contribution of a vessel in the cross-correlation gives an estimation of the spectra of sound radiated from this vessel.

Water traffic monitoring

• But the problem is that, this method is not suitable for busy areas like big harbours and estuary etc….

• Only the developed cross-correlation method allows vessel’s detection and tracking in busy estuary and harbor environments.

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