Statistical Evaluation of the Underwater Detection

Statistical evaluation of the passive structure for the vessel detection is considered. The passive detection structure is based on the statistical likelihood ratio test and on the Neyman-Pearson statistical criterion. The assumption is that a vessel is approximately so-called noisy vessel. It means that the underwater acoustic vessel noise is approximately a stationary ergodic stochastic zero mean Gaussian process with finite variance. Then the source of the vessel noise is approximately only phenomenon of the vessel propeller. The interference (ambient deep-sea noise) is a stationary ergodic stochastic zero mean Gaussian process with finite variance too. INTRODUCTION Each vessel is a platform with many acoustic sources. These sources are mutually statistically independent. Their sound emissions through the vessel structure form the acoustic field in the sea mass around the vessel. The sound emission into the sea mass around the vessel is especially interesting because the result of this emission is the vessel underwater acoustic noise or the vessel underwater acoustic signal. The vessel underwater acoustic signal is the fundamental phenomenon to detect the vessel by means of the passive sonar. Therefore the research of the vessel underwater acoustic signal is very important. The research results have to enable the vessel constructors to reduce the power of vessel acoustic sources and so to reduce the intensity of the underwater acoustic field around the vessel. In this way, the range of the vessel detectability decreases too and the vessel becomes acoustically invisible for the longer distances. On the other hand, the passive sonar constructors tend to construct the sonar with maximal sensitivity to detect so weak underwater vessel acoustic noise. The sound sources that are on a vessel we can group in two different groups. In the first group we have the sources of cavitation due to the vessel propellers. In the second group we have the sources of sinusoidal oscillations due to operating machinery, mechanisms and propellers. The cavitation is a Gaussian stochastic process with wide-band spectrum. The sinusoidal oscillations are stable and/or unstable sinusoidal oscillations with the narrow-band spectra [1]. So, the vessel underwater acoustic signal is assumed to be a sum of a stochastic process and a finite number of sinusoidal oscillations. The stochastic process is Gaussian and is due to the cavitation phenomenon of the vessel propellers [1]. The sinusoidal oscillations have random phases, approximately stable amplitudes and are due to vessel operating machinery, mechanisms and propellers. The vessel underwater acoustic noise, far away of the vessel, propagates trough the sea as an acoustic medium. The sea has its own underwater noise (ambient noise) that is of stochastic nature. So, the passive vessel detection is statistical detection. The ambient sea noise, as a stochastic process, in the deep-sea locations has a Gaussian distribution too [2]. We assumed that the underwater acoustic noise, of a noisy vessel, is a sum of a zero mean Gaussian stochastic process with a finite variance due to propellers cavitation and of a finite number of sinusoidal waves with extremely small amplitudes. The deep-sea underwater ambient acoustic noise is supposed to be a zero mean Gaussian stochastic process with a finite variance as well. We considered the probability density function of the instantaneous values of the underwater acoustic noise of the noisy vessel and of the deep-sea underwater ambient acoustic noise. To detect the vessel underwater acoustic noise we chose the algorithm of the optimal statistical detection with the likelihood ratio statistical test and the Neyman-Pearson statistical criterion. To evaluate the algorithm of the optimal statistical detection we can choose two statistical methods: the exact or direct method and the approximate or indirect method. The direct evaluation measure is the value of detection probability versus the value of the false alarm probability with signal-to-noise ratio as a parameter. The indirect evaluation measure is the socalled deflection coefficient that is the function of the difference between statistical expectations of the two possible probability density functions of the receiving signal. UNDERWATER ACOUSTIC SIGNAL Vessel Underwater Acoustic Noise As stated before, the vessel underwater acoustic noise is a sum of the Gaussian stochastic process and a finite number of sinusoidal waves. We assume that the Gaussian stochastic process is a stationary ergodic and zero mean with finite variance, and that the sinusoidal waves have constant amplitudes and random phases uniformly distributed in the interval (0,2π). The mathematical model of such a waveform has the following form