The problem of classification of marine vessels based on passive sonar data is very challenging because of the requirement of high reliability of such an application. In this work the classification of the marine vessel has been considered post-detection for a single target in the beam- formed output at the receiver. The acoustic energy radiated from a marine vessel and coupled into the ocean medium does not reach the point of observation intact. This is because the ocean is an extremely complicated acoustic medium, whose main characteristic is inhomogeneity [1-3]. This characteristic, coupled with the time dispersion and time-varying nature of the channel [4] and the ambient noise [5, 6], causes the spectrum of the received acoustic signal to undergo temporal and spatial fluctuations in magnitude and phase. Further, littoral waters typically cause more complicated underwater channel distortions than deep waters [5-8]. The radiated signal of a marine vessel has variability even within the same class of marine vessels because of the different running machinery configurations, called the regimes of operation [8-11].
An important aspect of the problem of marine vessel classification is therefore to design 'effective’ features that can be extracted from the received signals [12]. The effectiveness pertains to the uniqueness of the feature with respect to the designated class in spite of the environmental degradation. Many efforts have been made in the past to classify marine vessels based on their spectral characteristics [12-23] and more recently on the basis of the fractal features [24, 25], chaotic features [26] and eigenmode decomposition [27]. The previously available literature does not explicitly attempt to mitigate the severe underwater channel distortions.
In this work, the proposed cepstrum-domain feature compensation method is motivated by homomorphic techniques for decoupling the channel from the radiated signal of a marine vessel [28-33]. Two techniques have been proposed, namely, the cepstral liftering and the cepstral averaging methods to reduce the distortions because of the underwater channel [32]. Furthermore, the uncorrelatedness of the ambient noise vis-a-vis the source radiated signal, permits the application of spectral averaging techniques to reduce the effect of ambient noise. The processing steps represented by the shaded blocks in Fig. 1 are proposed for improved passive marine vessel classification.
The proposed marine vessel classification method for three classes of propulsion types, namely diesel (D), gas turbine (GT) and steam (S) has been studied in two stages: firstly, using synthetic data and secondly, using recordings of real radiated signals. The synthetic data have been generated for the signal at source with wide variability by incorporating various machinery regimes, different propeller descriptions, coupled frequency combinations etc. The signal at source is then passed through an underwater channel model with varying range, depth, bottom profile, bottom type, sound velocity profile (SVP) etc. [11]. The channel model has been validated against the JASA bench mark problem [34]. The simulated data considered for validation of the proposed algorithms take into account channel cases for depths varying from 60 to 200 m for a range of 4 km. The ambient noise has been taken to be white Gaussian and has been linearly added at the receiver to generate different signal-to-noise ratio (SNR) cases. The real recording of data for six ships, two each from the three propulsion classes was then used as test data, with synthetic data being used for populating the pattern library.
This paper has been organised into seven sections. In Section 2, the spectrum-based features evaluated in the work have been discussed. Section 3 presents the cepstrum-based features. In Section 4, the classifier used for evaluating the effectiveness of the proposed method has been discussed. Section 5 is concerned with the description of the data used for the study, whereas Section 6 presents the classification results and related discussion. The paper is concluded in Section 7. The signal model [35] is described in the Appendix along with a description of the spectral features.
Further description of these features is given in the Appendix.
The multipath distortions are not known a priori and they are typically time varying because of the relative motion of the source and the receiver and the time-varying characteristics of the medium. Thus, it is difficult to estimate the channel
path delays accurately and track their precise changes over time. In the problem of passive marine vessel classification, the received signal can be modelled as a convolution of the radiated source signal and the time-varying impulse response of the channel.
A simulation study on synthetic data has shown that the source signal cepstrum and the channel response cepstrum largely segregate towards the lower and higher cepstrum indices, respectively [32]. It is shown that the signal and the channel appear largely in non-overlapping regions of the cepstrum for shallow underwater channels. Thus, by 'liftering’ the received signal cepstrum, it is possible to enhance the features for marine vessel classification. It is also demonstrated that for a range up to 4000 m and depth of 100 m, cepstral liftering is able to significantly reduce the underwater channel distortions on the radiated noise of marine vessels for this purpose. The mathematical derivation for the channel compensation technique in the cepstrum domain is also presented [32].
The first 512-cepstral coefficients (out of 8192 coefficients present in one frame for a sampling rate of 8192 Hz) corresponding to 62.5 ms, excluding the zeroth index {cym[0]}, which is simply the logarithm of the energy, have been windowed from the N indices (equivalent to one frame length) and then grouped into uniform bands of 16 each to reduce the cepstral dimension to 32 features. The sub-frame length is 1 s and five such sub-frames are averaged during the spectral averaging process to obtain a frame of 1 s compressed from 5 s duration prior to averaging. The average cepstral features are obtained by smoothing ten previous frames corresponding to 50 s. An average cepstral feature vector comprising of 32 features is obtained.
We represent the M classes of marine vessels as ω1, ω2, …, ωM, and each class is characterised by 2Q feature vectors. Let Ti = {Ui,1, Ui,2, …, Ui,Q} and Si = {Vi,1, Vi,2, …, Vi,Q}, respectively, denote Q training and testing samples, respectively, that are randomly selected from ωi, where Ti ∩ Si = Φ and Ti ∪ Si = ωi. Bayes's method for classification is a fundamental parametric method and is optimal if the parameters have been estimated accurately. Bayesian decision making refers to choosing the most likely class, given the value of the feature or features [40].
Gaussian mixture model (GMM) is known for its robustness as a parametric model and its ability to form smooth estimates of rather arbitrary and multi-modal underlying densities [41]. The number of components of the GMM is data-dependent and needs to be determined after simulation. For our application, we have initially taken four-component GMM assuming each mixture component to represent one of the four speed-dependent regimes of operation of the marine vessels considered. Fig. 2 represents a typical GMM mapping of the probability density function: the title represents the class of the data as D for diesel, S for steam and G for gas turbine, Rx represents the data at receiver, (3) component GMM indicates the three- component representation of the GMM mapping, feature (3) represents the particular feature vector and (7) represents the index of the feature in the feature vector. It has been observed that the three-component and four-component GMM mapping show similar results and since three- component mapping is computationally more efficient, all GMM mappings have finally been carried out with three-component GMM.
GMM mapping of the probability density function
Top panel - histogram; middle panel - normalised histogram; bottom panel - GMM pdf; D - diesel propelled vessel
The top panel in Fig. 2 represents the histogram, the middle panel represents the normalised histogram plot and the bottom panel represents the GMM mapping of the probability density function. In the middle panel the amplitude values on the vertical scale have been normalised to make it comparable with the GMM pdf. The error value in the figure represents the point-to-point rms error between the normalised histogram shown in the middle panel and the GMM plot shown in the bottom panel, and shows a close match between the two.
The study of the proposed method has been carried out in two stages. Firstly, synthetic data were used that have been perceptually audited by trained sonar operators. The synthetic data [11] have incorporated a detailed regime description of each class to incorporate substantial variation (32 variations for each class) in the data at source. The data at source have been passed through the channel model with variations in the parameters such as depth, range, bottom type, bottom profile, SVP etc. [11]. The channel model has been validated against the JASA bench mark problem [34]. At the receiver, ambient noise has been linearly combined at varying SNR.
The performance of the cepstrum-based method has been studied for real recordings in a shallow water channel. The recording sensor is placed at the bottom of a shallow water channel of 30 m depth and the vessel repeated the same course transect with different machinery regimes. The data are acquired using an omni-directional hydrophone (ITC 8264 with sensitivity —175 dB, 1 µPa and bandwidth 10 Hz-100 kHz), filtered (anti-alias pass band dc to 100 kHz) and digitised by a 16-bit ADC at 256 kHz. A Hann window is used with a data update rate of 5 Hz for the broadband spectrum at a frequency resolution of 1 Hz. A 2048-point fast Fourier transform has been used for computation of the spectrum. The vessels made several runs of varying speeds between 8 and 20 knots. Each run also corresponded to a particular machinery regime. The recordings were considered for the bow aspect at a distance of one ship length from the sensor for six vessels, two each for D, S and GT with varying machinery configuration and vessel-passing overhead for a run of 400 -600 m in range.
The synthetic data set have been used to compare the performance of the features mentioned in Sections 2 and 3 using Bayes classification method for marine vessel classification. The synthetic database presented in [11] has been used for simulation with a sampling frequency of 8192 Hz. We have considered four-component GMM that maps the data distribution as discussed in Section 5. In Table 1, we have presented the Bayes classification results for the synthetic data. The results represent the average classification performance for three classes, namely D, GT and S. The averaging pertains to variations in the data at source, related to the different regimes of operations, coupled machinery tonal lines, propeller types etc. and channel variations related to bottom type, bottom profile, SVP, source and receiver depth, range etc. The data have been segmented into stationary frames of 5-s duration assuming the channel to be stationary for 5 s as presented in Section 6. Each of these frames has been further segmented into 1 s sub-frames for sub-frame spectral averaging. The features have been extracted from these frames of 5-s duration reduced to one sub-frame postaveraging except for the tonal features. Thus, decisions are updated every 5 s.
| Feature vector | Correct classification performance, % |
|---|---|
| Spectral | 85.90 |
| Cepstrum | 92.50 |
| average cepstrum | 96.38 |
Table 1 presents the classification results for the Bayesian classification method for no noise synthetic data. As seen from Table 1, the average cepstral features have performed the best with the cepstral features performing marginally below, followed by the spectral features. These results confirm with the analytical discussion presented in Section 4.
The Bayes classification algorithm results are presented in Table 2 across varied SNR values. The data used for testing both the algorithms are identical. We will discuss each feature set separately in the succeeding sub-sections.
| Feature vector | —10 dB SNR, % | Zero dB SNR, % | 10 dB SNR, % | 20 dB SNR, % | 30 dB SNR, % | No noise, % |
|---|---|---|---|---|---|---|
| Spectral | 44.58 | 53.82 | 60.97 | 72.98 | 78.26 | 85.90 |
| Cepstrum | 33.33 | 31.88 | 41.04 | 77.84 | 90.42 | 92.50 |
| average cepstrum | 60.69 | 70.34 | 76.79 | 80.13 | 90.62 | 96.38 |
The effect of ambient noise is considerably higher as seen from Table 2, the classification performance degrades drastically with SNR. The spectrum of the signal gets distorted in terms of amplitude and phase, because of the channel and the ambient noise. This causes smearing of the classes in the feature space, as discussed in Section 4. The random fluctuation because of ambient noise causes the spread of the features in the feature space, and thus reduces the inter-class distance and increases the intra-class distance. Bayes method as presented in Table 2 shows a gradual degradation of classification performance with SNR.
Classification results presented in row 1 of Table 2 demonstrate that the spectral features are sensitive to the underwater channel distortions and the randomness of the ambient noise, as concluded because of the degradation in the classification performance as SNR is reduced. The spectral features comprise of narrowband and broadband features thus making them vulnerable to the channel as well as the ambient noise distortions.
The classification performance with cepstral features improves compared to that of spectral features given in Table 2. Cepstral liftering method [32] reduces the channel- induced time-dispersive distortions, which explains the performance enhancement of cepstral features over spectral features.
The broadband spectrum manifests in the lower frequency indices in the cepstral domain, whereas the narrowband tonals with harmonic structure appear as impulses at the corresponding delays. As discussed in the previous section, the broadband spectrum is sensitive to the wideband ambient noise distortions and the effect is even more prominent in the cepstral domain. In Table 2, it is observed that the cepstral features are unable to discriminate the classes below about 20 dB SNR. Thus, there is a drastic degradation of the classification performance across SNR in the cepstral features.
Classification results presented in row 2 of Table 2 reveal that the cepstral features are sensitive to the ambient noise similar to the spectral features at lower SNR. At lower SNRs, the classification results demonstrate poor performance for the cepstral features as seen in columns 1 -3 in row 2 of Table 2.
In our simulations, ten frames have been averaged for the cepstral averaging to reduce the non-stationary channel distortions. This causes a further delay in the decision updates, presenting a trade-off to the designer between delayed decisions and better smoothing of the channel distortions. Table 2 demonstrates further enhancement in the classification performance for averaged cepstral features vis-a-vis cepstral features.
The averaging causes smoothening of the randomness because of ambient noise as well, thereby reducing the sensitivity of the average cepstral features to ambient noise distortions. In Table 2, we observe that using averaged cepstral features we are able to classify the three classes even at low SNR values compared to cepstral features. Thus, we may conclude that average cepstral features are able to effectively classify the marine vessels based on their propulsion types, under channel-induced distortions and at low SNR values of ambient noise.
The classification results obtained by using real ship data for testing and synthesised data for training are presented in Table 3. The synthesised signals as presented in [11] for D, GT and S vessels at various regimes of operation are used to populate the pattern library. Six real data recordings (two each of D, GT and S) at varying regimes of operations are used for evaluating the proposed features using Bayes classification result. The pattern library used for testing synthetic data is used here as well for testing the real recorded data. The data having been recorded at close range, the SNR is expected to be reasonably high ( ∼ 30 dB). The classification results presented in Table 3 demonstrate the effectiveness of the proposed cepstrum- based features for marine vessel classification.
| Feature vector | Correct classification performance, % |
|---|---|
| Spectral | 65.93 |
| Cepstrum | 78.93 |
| average cepstrum | 80.38 |
This work presents signal processing methods of the cepstrum-based features that are effective against the channel distortions and the ambient noise. These are used to reduce three types of distortions of the acoustic radiated noise of marine vessels. The sub-frame spectral averaging method reduces the ambient noise present at the receiver, the cepstral liftering method reduces the time-dispersive effect of the shallow water channel and the cepstral averaging method smoothens out the degradations because of the time-varying nature of the underwater channel. The comparison with spectral features shows the advantage of using cepstrum-based features in a shallow underwater channel.
A marine vessel radiated signal x[n], propagating through an underwater channel undergoes distortion characterised by the channel impulse response h[n], and degradation because of additive ambient noise w[n]. In this work, the underwater channel is assumed to be quasi-stationary. Thus, the channel is characterised mathematically as a linear time- invariant filter in a given frame, as the channel impulse response varies across the stationary frames denoted by the index m, to map the linear time-varying channel model as shown in Fig. 3 [28].
The noise spectrum is Gaussian with zero mean and variance equal to
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