Ships Matching Based on an Adaptive Acoustic Spectrum Signature Detection Algorithm

In this paper, an acoustic spectrum signature tracks matching algorithm based on the Manhattan distance and the Euclidean distance of signature vectors, and a multi-frame fusion algorithm are proposed for reliable real time detection and matching of boat generated acoustic signal spectrum signatures. The experiments results have shown that the proposed tracks matching algorithm has the ability to discriminate the tracks from different ships and the ability of matching of the tracks from the same ship; and the spectrum signature detection algorithm has captured the critical features of ship generated acoustic signals. In the process of signal spectrum signature detection, the observation of time and frequency space is structured by dividing input digitalized acoustic signal into multiple frames and each frame is transformed into the frequency domain by FFT. Then, a normalization of signal spectrum vector is carried out to make the detection process more robust. After that, an adaptive median Constant False Alarm Rate (AMCFAR) algorithm is used for the detection and extraction of boat generated spectrum signature, in which an extreme low constant false alarm rate is kept with relative high detection rate. Finally, the frame detections are accumulated to build up the track spectrum signatures.


INTRODUCTION
Tracks matching plays an important role at detection and tracking of marine vehicles, including some underwater targets, such as submarine etc. The discrimination of targets is based on the comparison of the given spectra with the reference spectra available as endmembers in a spectral library. The comparison is done using the similarity as a criterion [1][2][3][4]. Stochastic measures such as spectral information divergence consider the spectral band to band variability as a result of uncertainty incurred by randomness. The spectrum can be modelled as a probability distribution so that the spectral properties can be further described by statistical moments of any order [1]. The hybrid approaches of spectral angle mapper and spectral information divergence is found to increase the discriminatory power as against the individual measures [4].
Detection and extraction of underwater acoustic signal play an extremely important role in marine vehicle tracking and is one of the key technologies in underwater source detection, location, tracking, recognition and as well as acoustic communication [5][6][7][8][9][10][11]. Energy detection, feature detection and matched filter detection are commonly used range from high detection performance to low computation complexity, which can usually work well to some extent. Among these researches of the underwater passive detection methods, energy detection is mostly discussed and used in practical for its merits of lowest computational cost and easy to realize, while shows a poor performance under low SNR marine environment. However, over the past several decades, the marine environment has been more complexed in both natural and anthropogenic influences that ambient noise revealed. And as a consequence, the existing underwater passive detection methods are facing serious challenges, for which advanced detection scheme with better performance is still worthy investigating, especially under low signal-to-noise ratio (SNR) region [12][13][14].
This paper is focused on the research of theoretic algorithm development and experiments of tracks matching, and automatic detection ship spectrum signature based on boat generated acoustic signals from hydrophone ( [15][16][17][18]). In this paper, an observation space is created by dividing input acoustic signals into multiple frames, with each frame sampled and transformed into the frequency domain. Then, an Adaptive Median Constant False Alarm Rate algorithm [19] is used for automatic target detection of boat-generated acoustic signals in each frame to provide a low constant false alarm rate with relatively high detection rate. Finally, the track signal spectrum signature is built up by a multi-frame detection vector fusion algorithm, in which the signal-to-noise ratio (SNR) in the observation period has been increased in the detection phase.
The proposed algorithms have been tested on real boat generated acoustic signals obtained from a hydrophone.

MULTI-FRAME SPECTRUM SIGNATURE DETECTION IN TIME FREQUENCY DOMAIN
In this section, the observation is created first. Then, an adaptive signal spectrum components detection algorithm is used for the signature detection.

Multi-Frame Spectrum Observation Space
The observation space for multi-frame spectrum detection and fusion is created by dividing input time domain signal into multiple frames, and each frame in transformed into frequency domain by using FFT, which is shown in Fig. 1, in which x-direction represent number of frequency bins, and the y-direction represent time or number of frames. Electronic copy available at: https://ssrn.com/abstract=3389706

Adaptive Spectrum Signature Detection Algorithm
An adaptive CFAR spectrum signature detection algorithm used in this paper are structured based on the idea of median CFAR thresholding, and the normalization operation based Neyman-Pearson (NP) criterion ([19-22]), which is widely adopted for signal detection application in either radar or sonar systems.
The basic idea of the Neyman-Pearson detector is to reduce the false alarm rate and maximize the probability of detection. It has been proven that under the Neyman-Pearson criterion, the acoustic signal in the frequency domain needs to be normalized by the average noise power in the optimum detector [23].
The whole multi-frame acoustic signal processing and detection algorithms employed in the paper is shown in Fig. 2. In which, the acoustic signals from hydrophone are sampled and converted into digital signals based on the Nyquist Sampling Theorem (Criterion) ( [24][25][26][27]). In our experiments, the signals are originally sampled at 44.1kHz, then resampled to 2048 Hz, so the maximum frequency range in our scope is 1024 Hz. After that, the digital signal is divided into multiple frames with T=0.5 seconds for each frame, and the data processing period in digital format is N = 1024. Electronic copy available at: https://ssrn.com/abstract=3389706 The digital signals are then transformed into the frequency domain by using FFT (Fast Fourier Transform). Since the data processing period is 1024, we chose the same length, i.e. 1024 points as FFT length.
Normally DC is the strongest component in the boat generated acoustic signals, which does not carry any useful information, but will affect the later processing, so it is necessary to remove DC component first.
We assume that the boat generated acoustic signals are stable random process during the observation period, such as 15 to 20 seconds.
In order to deal with various input signal strength and make the automatic target spectrum signature detection more robust, the normalization is performed in the frequency domain for the multi-frame spectrum fused vector by its magnitude. At this stage, each element in the multiframe fusion vector is divided by the magnitude of the vector (geometric length). After normalization, a magnitude scaling factor of 40 dB (100 times) is used to give the signal a more practical range.
The multi-frame spectrum fusion vector normalization is described as follows in which L is the number of frequency bins in the fusion vector and kf is the scaling factor.
In traditional sonar systems, signal detection is realized by a constant thresholding. Instead, in our approach, a floating threshold vector for the multi-frame fusion vector is calculated based on an Adaptive Median CFAR algorithm, in which the threshold for each frequency bin is adapted by the median value over a sliding window. This is performed in two steps: in the first step, the median threshold of the normalized spectrum vector is subtracted from the original normalized spectrum vector. In the second step, the difference calculated in the first step is compared with a constant CFAR threshold (∆), and if the difference is big enough to cross the constant threshold, the bin is reported as the target frequency, otherwise, it is reported as noise component. The parameter is called sensitivity, as the bigger the ∆ is, the less sensitive our detection system is on weak signals. Since the CFAR threshold in each bin is adapted to its neighbourhood background noise, it will keep our automatic spectrum signature detection system at a very low and constant false alarm rate. In the following, the AMCFAR algorithm is described in details.
The Median Constant False Alarm Rate (Median CFAR) threshold vector, is calculated by feeding into a Median filter (whose properties and size will be discussed in the next section) as follows: The Median filter size is The i j y values are either equal to 1 or 0, which are the detected frequencies based on the multiframe fusion detection. As boat-generated signals typically last at least 20 to 30 minutes, it is reasonable to treat the signal stable random process in the observation period of 15 to 20 seconds, and it has been proven that the proposed algorithm can significantly improve the detection rate.
In order to increase the signal-to-noise ratio in frequency domain, a multi-frame detection vector fusion is used in the paper as shown in Equation Where M is the number of frames in the observation period, and L is the number of frequency bins in each frame.

SIGNATURE TRACKS MATCHING
The discrimination of targets is based on the comparison of the detected signature spectrum with the reference spectra stored in our spectral database, and the comparison is carried out by using the similarity or distance between spectrum signature vectors. The tracks matching algorithm is shown in Fig. 3, in which we can see that the final decision of whether the two signature tracks are from different ships or from the same ship is based on blocks matching and final fusion, and each block consisted of 15 frames, and each frame is a 1024 point spectrum vector.
The blocks matching is based on the similarity or distance measurements between two spectrum signature vectors, which include Manhattan and Euclidean distance distances in our proposed tracking algorithms. Manhattan distance: Manhattan distance is also called taxicab distance. A taxicab geometry is a form of geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates. The taxicab metric is also known as rectilinear distance, L1 distance, L1 distance or 1 l norm (see p L space), snake distance, city block distance, Manhattan distance or Manhattan length, with corresponding variations in the name of the geometry. The latter names allude to the grid layout of most streets on the island of Manhattan, which causes the shortest path a car could take between two intersections in the borough to have length equal to the intersections' distance in taxicab geometry.
Formal definition: The taxicab distance, d(Sig 1 , Sig 2 ), between two vectors Sig 1 and Sig 2 in an N dimensional real vector space with fixed Cartesian coordinate system, is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. More formally, where Sig 1 and Sig 2 are vectors Sig 1 = (Sig 11 , Sig 12 ,..., Sig 1N ), and Sig 2 = (Sig 21 , Sig 22 ,..., Sig 2N ).
For example, in the plane, the taxicab distance between 1 Si g and 2 Si g is Euclidean distance: In similarity measurement, we also use the Euclidean distance or Euclidean metric, which is the "ordinary" straight-line distance between two points in Euclidean space. With this distance, Euclidean space becomes a metric space. The associated norm is called the Euclidean norm, or a generalized term for the Euclidean norm is the L 2 norm or L 2 distance.
The Euclidean distance between signature points Sig1 and Sig2 is the length of the line segment connecting them .In Cartesian coordinates, if the two spectrum signatures Sig 1 = (Sig 11 , Sig 12 ,..., Sig 1N ) and Sig 2 = (Sig 21 , Sig 22 ,..., Sig 2N ) are two points in Euclidean Nspace, then the distance (d) from Sig 1 to Sig 2 , or from Sig 1 to Sig 2 is given by the Pythagorean formula: Stochastic measures such as spectral information divergence consider the spectral band to band variability as a result of uncertainty incurred by randomness. The spectrum can be modelled as a probability distribution so that the spectral properties can be further described by statistical moments of any order. The hybrid approaches of spectral angle mapper and spectral information divergence is found to increase the discriminatory power as against the individual measures.

RELATED WORKS AND DISCUSSION
In this paper, a ships matching algorithm based on Manhattan distance and Euclidean distance, a multi-frame detection fusion and an adaptive signal spectrum detection algorithms are proposed, in which the tracks from different ships can be easily discriminated by both Manhattan distance and Euclidean distance; the spectrum signature detection algorithm captured the critical features, with a low false alarm and relative high detection rates in the frequency domain; and the signalto-noise ratio in each frequency bin is increased by a multi-frame fusion algorithm. The input acoustic signal is sampled and divided into multiple frames. Then each frame is transformed into the frequency domain by using FFT. After that, the target generated frequency spectrum will be detected based on accumulated and normalized spectrum vector by the proposed adaptive algorithm, in which the basic idea of the detection algorithm is that of using, for each frequency bin, different, adaptive CFAR (Constant False Alarm Rate) thresholds [8] rather than a single, constant threshold (which is often the case in acoustic systems), which is described below. Then, a multi-frame fusion on is carried out by accumulating single frame detection result vectors in the observation period, for example, in 15 seconds, equivalent of 30 frames in our experiments. Finally, the tracks matching is carried out based on the given Manhattan distance and Euclidean distance measurements.
The basic idea of CFAR thresholding is that every single threshold of each frequency bin is computed based on the surrounding background noise. The higher the background noise, the higher the threshold is set. Moreover, our algorithm uses a median filter window centered at each frequency bin to adapt the threshold value. To the best of our knowledge, while this idea is often used in radar system to obtain lower false alarm rate with relatively higher target detection rate, it is applied here for the first time to sonar-generated acoustic signals.
Since the Median Filter is good at removing high frequency spot noise, it is a very effective way to calculate the threshold vector, which is independent of specific signals. As such, the Adaptive Median CFAR algorithm proves superior to other common approaches such as constant thresholds or average-based thresholds. The major advantage of the Median filter is in its ability to remove interferences such as strong signal or noise spikes without affecting the sharpness of edges (retaining sharp edges after filtering). Conversely, with an Averaging Low Pass Filter, which is equivalent to the Average CFAR algorithm, sharp edges will be blurred after filtering. Moreover, every bin in the averaging window will affect the threshold value, especially when the signal or a noise spike is strong. Evidence of the superiority of the median filter with respect to average filters for signal detection can also be found in [15]. . From our experiments, a window size of 5 has been proved to be the most appropriate.
The combination of multi-frame spectrum fusion and adaptive CFAR detection makes the whole detection system extremely robust and reliable. As boat-generated signals have relatively long duration, we have used a multi-frame spectrum fusion, i.e. time-integration over multiple frames which significantly improves the SNR. Although this step introduces a delay in early detection of incoming boats in the order of 15 seconds, this is completely negligible with respect to the typical travelling speeds of monitored boats. The Adaptive Median Filter Constant False Alarm Rate (AMCFAR) algorithm is used to detect boat signature with relatively high detection rate while maintaining a low and constant false alarm rate.

EXPERIMENTAL RESULTS OF TRACKS MATCHING AND ADAPTIVE SIGNATURE DETECTION ALGORITHM BASED ON THE MULTI-FRAME FUSION
The test signals are provided by Soncom PTY LTD from "C-Buoy/Off-Buoy Processor Sea Trials' at Low Islets, Australia (16.3833° S, 145.5667° E) on 17 June 2002. The proposed tracks matching, multi-frame spectrum fusion and adaptive signature detection algorithms have been successfully tested on several real ship generated signals in the following, which include the signals called "Naiad1" and "SF6" for reference.

SPECTRUM SIGNATURE DETECTION TEST
The proposed algorithms have been coded in Matlab, and the signature detection results have been shown in Figs. 4 and 5. Fig. 4 (a) shows us that the "Naiad1" boat signal has a pretty wide frequency band with a quite weak strength, which spreads between about 40 to 1k Hz, with the main frequency component at about 200 Hz and the strength of these frequency components between 0.5 to 4 dB. Fig. 4 (b) shows us the binary detections based on the Median CFAR threshold, in which the floating CFAR threshold vector has adapted to its original normalized multiple spectrum fusion vector to avoid any false detections. Fig. 4 (c) shows us the detected spectrum signature of "Naiad1" in the observation period with the normalized multiple frame spectrum vector, in which we can see that the spectrum signature has been reliably detected without any false detections. Figure 4 Experimental results of "Naiad1" with the adaptive median CFAR algorithm with the sliding window size of 5, and proposed multiple frame fusion algorithms (block size: 45; initial frame number: 40).

"SF1" BOAT SIGNAL TEST
The proposed Adaptive Median CFAR detection and Multi-Frame spectrum fusion Algorithms have also been tested on "SF1'" boat signal, and the test results are shown in Fig. 5. Fig. 5 (a) shows us that the "SF1" boat signal has also a pretty wide frequency band, which spreads between about 50 to 380 Hz, and 700 to 900 Hz, with the main frequency component at about 200 Hz 750 Hz, and the strength of these frequency components between 5 to 25 dB. Fig. 5 (b) shows us the binary detections with the Median CFAR threshold, in which the floating CFAR threshold vector has adapted to its original normalized multiple spectrum. accumulated spectrum fusion vector, in which the SNR has been significantly improved, and it also shows us the normalized multiple spectrum fusion vector (blue) vs its fusion vector to avoid any false detections. Fig. 4 (c) shows us the detected spectrum signature of "SF6" in the observation period (red) with the normalized multiple frame spectrum fusion vector (green), in which we can see that the spectrum signature has been reliably detected without any false detections. The overall procedure is computationally light, thus allowing us cost-effective real-time implementation even on systems with limited computational power and size constraints such as on-board embedded computers.

TRACKS MATCHING BASED ON MANHATTAN DISTANCE-"NAIAID1" VERSUS "SF1" SIGNALS
The proposed tracks matching algorithm has been tested on signal "Naiad1" and "SF1". Each track has 9 blocks, and each block is consisted of 15 frames, and the spectrum signature of each block is calculated based on the single fame detection and fusion in the same block. The spectrum signatures of the two tracks are shown in Table 1 (a), (b) and (c).      The detected spectrum signature Frequency (Hz)

Final detections
In Table 1, we can see that the spectrum signatures in two tracks of different ships are quite different, and the similarities of the spectrum signatures from the same ship are much more than that from the different ships, but there are also some variations in the same track.
The calculated Manhattan distances between the two tracks in Table 1 are shown in Table 2.

TRACKS MATCHING BASED ON EUCLIDEAN DISTANCE-"NAIAID1" VERSUS "SF6" SIGNALS
The calculated Euclidean distances between the two tracks in Table 1 are shown in Table 3.  Table 3 shows us that the Manhattan distances between Track 1 (Naiad1) and Track 2 (SF1) are around 140.

TRACKS MATCHING BASED ON MANHATTAN DISTANCE-"NAIAID1" VERSUS "NAIAID1" SIGNALS
The matching of two tracks that are actually from the same target ship is tested by using the data from the same track but shifted by about one block.
The calculated Manhattan distances between the two tracks (Naiad1 and Naiad1 by shifting around 1 block) are shown in Table 4 . Electronic copy available at: https://ssrn.com/abstract=3389706 Table 4 shows us that the Manhattan distances between Track 1 (Naiad1) and Track 2 (Naiad1) with 1 block shift) are around 300.

TRACKS MATCHING BASED ON EUCLIDEAN DISTANCE-"NAIAID1" VERSUS "NAIAID1" SIGNALS
The calculated Euclidean distances between the two tracks (Naiad1 and Naiad1 by shifting around 1 block) are shown in Table 4 .  Table 5 shows us that the Euclidean distances between Track 1 (Naiad1) and Track 2 (Naiad1) with 1 block shift) are around 40.

TRACKS MATCHING (DISCRIMINATION) BASED ON MANHATTAN AND EUCLIDEAN DISTANCES
The power of discrimination (difference) or matching (similarity) of proposed algorithms are tested by plotting the Manhattan and Euclidean distances of tracks from different target tracks or from the same target tracks on the same space, drawing a line to separate them.

TRACKS MATCHING (DISCRIMINATION) BASED ON MANHATTAN DISTANCE:
The Manhattan distances between Track 1 (Naiad1) and Track 2 (Naiad1) (with 1 block shift) is shown in Figure 6 in red lines, and the Manhattan distances between Track 1 (Naiad1) and Track 2 (SF1) are shown in green lines. Figure 6. The Manhattan distances between Track 1 (Naiad1) and Track 2 (Naiad1) (with 1 block shift), and distances between Track 1 (Naiad1) and Track 2 (SF1). Figure 6 shows us that the tracks distances of different target ships "Naiad1" versus "SF1" are around 1600, but the tracks distances of the same target ship "Naiad1" versus "Naiad1" are around 300. So, by drawing a line around 1000, it is very easy to separate the tracks of the same ship from the tracks from different ships.

TRACKS MATCHING (DISCRIMINATION) BASED ON EUCLIDEAN DISTANCE:
The Euclidean distances between Track 1 (Naiad1) and Track 2 (Naiad1) (with 1 block shift) is shown in Figure 7 in red lines, and the Euclidean distances between Track 1 (Naiad1) and Track 2 (SF1) are shown in green lines. Figure 7. The Euclidean distances between Track 1 (Naiad1) and Track 2 (Naiad1) (with 1 block shift) , and distances between Track 1 (Naiad1) and Track 2 (SF1). Figure 7 shows us that the tracks distances of different target ships "Naiad1" versus "SF1" are around 140, but the tracks distances of the same target ship "Naiad1" versus "Naiad1" are around 40. So, by drawing a line around 90, it is very easy to separate the tracks of the same ship from the tracks from different ships.

CONCLUSION AND FUTURE WORK
In this paper, an acoustic spectrum signature tracks matching algorithm based on the Manhattan distance and the Euclidean distance of signature vectors, and a multi-frame fusion algorithm are proposed for reliable real time detection and matching of boat generated acoustic signal spectrum signatures. In which, an adaptive median constant false alarm rate algorithm has been used for effective spectrum signature detection of boat-generated acoustic signals, in which a low constant false alarm rate is kept with relatively high detection rate. The proposed algorithms have been tested on many real acoustic signals recorded from hydrophone at a site on the Australian coastline, two of them are shown in the paper. The statistical analysis and experimental results showed that the proposed algorithms have increased the SNR significantly in the observation period, and have kept a very low false alarm rate and relatively high detection rate for the whole detection system.
The following conclusions can also be drawn: 1) The experiments results have shown that the proposed tracks matching algorithm has the ability to discriminate the tracks from different ships and the ability of matching of the tracks from the same ship; and the spectrum signature detection algorithm has captured the critical features of ship generated acoustic signals.
2) The proposed multi-frame fusion algorithm has increased the SNR significantly, and made the whole detection more robust.
3) The proposed Adaptive Median CFAR algorithm is used to detect target frequency signature from a multiple frame fusion spectrum vector, keeping our automatic target detection system at low and constant false alarm rate. This algorithm has been proven that it is especially good for detecting LOFAR target frequency components.

4)
A magnitude normalization (in the frequency domain) is used to keep our automatic detector more robust to noise and spurious frequencies.
5) With the default sensitivity value, most target frequency components are correctly detected. Further decreasing the sensitivity value makes the false detection rate (alarm rate) lower, but at the same time less target frequency components will be detected.
6) The boat-generated frequency spectrum signature can be detected with high accuracy. In the experiment reported in this paper, the detected boat-generated frequencies of 'Naiad1' and 'SF1' are very close to the "ground truth".

Future work:
1) Recognition -The detected spectrum signatures can be used for ship recognition and tracking in the future, in which the study of similarity measures between ship spectrum signatures, and the neural network can also be possibly applied for the recognition of detected ships, based on a database of collected spectrum signatures.
2) Tracking-The proposed real time processing and detecting based sonars can be connected into a worldwide undersea network, in which the ships around each sonar can be detected, tracked, and displayed in a control center.
3) Arrays processing -Sonar array processing based on the proposed algorithm as a building block can also be used to increase the SNR of input signal, or detect the direction of incoming ships, [29][30][31][32][33][34][35]