A depth discrimination method based on the scintillation of frequency domain

An innovative algorithm of target depth discrimination suitable for passive horizontal array in shallow sea is discussed in this paper. Based on the idea of modal scintillation theory, a new target depth discrimination method of high calculation speed for horizontal array is proposed by analysing the commonness between frequency domain energy of low-frequency broadband signals and modal excitation. This method avoids the mode decomposition of the horizontal array signals, greatly reduces the complexity, improves the stability, has a fast calculation speed and can perform the real-time depth judgment. In this paper, the principle of the algorithm is derived in detail in the theoretical aspect, and then the algorithm is simulated in the shallow sea environment to verify its effectiveness, and the influence of different influencing factors on the performance of the algorithm is explored. At the same time, the algorithm is verified by the actual experimental data and achieves good results, indicating that the algorithm has certain practical application value in the target depth discrimination domain.


Introduction
The complex shallow sea environment and the large number of interference seriously affect the identification and early warning of underwater targets.Real-time target depth discrimination is of great significance for anti-submarine warfare and has to be an urgent problem to be solved.
At present, there are many achievements about depth discrimination, and the typical methods can be divided into three categories.The first type is based on the radiation noise feature extraction [1].This method uses different noise spectra of ships and underwater targets to distinguish them.However, with the upgrading of equipment, the noise level of submarines and ships is getting lower and lower, and the difficulty of obtaining reliable line spectra is greatly increased.The second type is based on matching field [2].In this kind of method, depth identification is carried out by matching the measured sound field with the copy sound field, but the performance of the algorithm will be sharply reduced due to the mismatch of environment and distortion of receiving array.The third type is based on normal mode characteristics.Such methods are flexible and changeable, deriving many achievements with practical application value [3][4][5][6][7][8][9][10][11].According to the series solution of the wave equation in hydroacoustics, the sound field is formed by superposition of several normal modes, and each normal mode have different performances with the change of frequence and the depth of the sound source.Premus [3] found that the undulations caused by internal and surface waves in water were discrepant at different depths for each normal mode, thus the mode scintillation index was proposed to describe such differences and realize classification of surface and underwater targets.However, the performance of this method is greatly affected by the source level of the target-radiated noise and the operating distance.To solve this problem, An L [4] proposed a modified mode scintillation index to eliminate the influence of variables, and achieved good results.Shi J J [5] proposed a target classification method based on fusion scintillation index.
Vertical linear array (VLA) or horizontal linear array (HLA) is usually selected as the information carrier for underwater targets depth discrimination.However, the posture of the VLA is hard to maintain, and it is prone to distortion when the water fluctuates, so it cannot move with the ship in real time.However, the HLA is more flexible and can be towed with the ship for real-time confrontation and avoidance, and it is far away from the ship, avoiding the influence of the ship noise, and also has a better resolution for the horizontal orientation.
The above depth discrimination techniques mostly rely on the spatial sampling advantages of VLA and cannot be directly applied to HLA.For example, several algorithms based on modal scintillation [3][4][5] need to decompose each normal mode, which is easier to realize for VLA.But for HLA, it is necessary to extract modal components by means of copy vector's matching [11], compressed sensing [12] and other methods.However, these decomposition methods are complex and cannot be widely used due to strict applicable conditions.Therefore, this paper draws on the idea of modal scintillation and jumps out of its essence.Under the premise of HLA, a new target depth discrimination algorithm is proposed, without estimating the modal components, greatly improving the calculation speed, and then can provide real-time strategy adjustment basis for water confrontation, so as to make up for the blank of real-time target depth discrimination using HLA.

Algorithm theory
This section provides a theoretical introduction and comparison between the original modal scintillation theory and the proposed new algorithm.

Modal scintillation theory
The modal scintillation index [3] can be used to distinguish surface and underwater targets in ocean waveguides.The method is based on the modal decomposition of the received sound pressure field, which is correlated with the perturbation of the sound source depth at its average position.The fluctuation of sound source depth is caused by the influence of surface wave or internal wave fluctuation on the platform.The variance of the modal excitation function generated by the depth perturbation of the sound source shows some certain characteristics related to the depth, so the modal scintillation index is used to characterize the variance of the modal excitation function.
According to the normal mode theory, the complex sound pressure field of the far-field sound source with depth z can be expressed as the superposition of normal mode: ( 1 ) Among them, s z is the depth of the sound source, s r is the distance between the receiver and the sound source, rm k is the horizontal wave number of the m-th mode, and ( )  m z is the characteristic function of the m-th mode.For narrowband random signals, a is a random complex variable with zero mean and the variance is described as 2   a .The excitation function of order m can be expressed as: The excitation function is related to the depth of the sound source, and the m-th modal scintillation index is represented by m SI (scintillation index): var ( ) As shown in Figure 1, with the fluctuation of water, for the target of surface, the modal excitation functions of all modes are near the zero-crossing point, and the derivative is the largest.Therefore, the modal excitation function value changes drastically, the variance is the largest, and the modal scintillation index is relatively large.However, when the target is underwater, there is always one or more orders of which the modal excitation function obtains the extreme value at the depth of the target sound source.At this time, the derivative is the smallest, the modal excitation function changes slightly, and the modal scintillation index of the corresponding mode is relatively small.Therefore, the binary target depth discrimination can be carried out according to the variance of the target modal excitation function.However, this method needs to separate normal modes to calculate the modal scintillation index of each order.Although the signal received by vertical array can be decomposed by simple generalized inverse calculation, it is complex and difficult to achieve for the horizontal array signal.

Frequency domain energy scintillation theory
For a receiving point with a fixed receiving depth r z , it is assumed that the receiving sound pressure is separated into the sound pressure components corresponding to each mode, the m-th sound pressure component m p can be expressed as: There is only a constant coefficient ( )  m r z different from the m-th modal excitation function ( ) m s h z .Therefore, the sound pressure component m p and the modal excitation function m h of the corresponding modal have the same fluctuation characteristics, as shown in Figure 2.
For low-frequency broadband signals, the modal order numbers is small and the superposition complexity is low.When the frequency changes, the horizontal and vertical wave numbers of each order change accordingly, and the modal sound pressure m p of each order also changes.The total sound pressure p is the superposition of multiple modal sound pressure component m p , which will form complex fluctuations at the underwater depth.However, at the surface of the water, the superposition result is always zero, and the change trend of m p is similar at the sound source depth close to the surface.Therefore, the superimposed sound pressure p also conforms to the characteristics of the largest derivative and the largest variance at the source depth near the water surface.At the source depth of underwater, there is always a certain frequency point of the superposition of sound pressure in a certain frequency band to obtain the extreme value at the underwater depth, and the variance is minimum at this time.Following the modified modal scintillation index, the energy fluctuation index at a certain frequency point is defined as: By comparing the value of ( , ) i s ESI f z , the depth attribute of the target can be judged.In this method, the modal scintillation minimum screening in the modal domain is converted to the energy scintillation minimum screening in the frequency domain, the modal dimension is extended to the frequency dimension, and the modal energy is reduced to into the total energy, avoiding the problem of horizontal array signal's mode decomposition.When the acoustic signal is a low-frequency broadband signal and the frequency sampling is sufficient, the surface and underwater target classification can be realized.

Simulation analysis
In this section, the feasibility of the algorithm is verified by simulation, and the influence of hydrological environment, receiving depth, horizontal distance and signal-to-noise ratio on the robustness of the algorithm is analysed.

Simulation verification of depth discrimination method
The feasibility of using frequency domain energy scintillation index to classify underwater targets is verified by simulation.In the shallow sea pekeris waveguide environment, the sea depth is set to 80m, the receiving depth is 20 m, and the distance between the receiver and the sound source is 10 km.The fluctuation of the sound source position is assumed to follow the standard normal distribution affected by seawater fluctuations.The lower frequency limit is set at 200 Hz, the upper frequency limit at 2000 Hz, and the frequency interval at 3 Hz.The average depth of the sound source varies from 2 to 75 m, and the step length is 0.5 m.For each s z , 100 fluctuation sequences with a mean of s z and a variance of 2 are generated.The kraken model is used to calculate the received sound pressure values corresponding to different sound source depths at different frequency points, and the equation( 5) is used to calculate the ( , )  It can be seen that in this shallow sea environment, when the sound source depth is less than 10 m, the ESI-min value is larger, and when the sound source depth is greater than 10 m, the ESI-min is very small.Therefore, the ESI-min value screened in the frequency domain can better distinguish the surface and underwater sound source targets with a boundary of 10 m, which proves the feasibility of the algorithm.

Simulation research on influencing factors 3.2.1. Mismatched hydrologic parameters.
The simulation conditions remain unchanged, the algorithm is simulated in the moderate and harsh hydrological environment of shallow sea respectively, and the performance changes of the algorithm are discussed.The control group is the results under good hydrological environment in section 3.1.The curves of the moderate and severe sound velocity profiles and the corresponding ESI-min versus depth are shown in Figure 4 respectively.environment and simulation results.In the moderate hydrological environment with weak negative gradient, the slight fluctuation caused by the target depth of 58m ~ 72m makes the decision boundary shallow to 7m, but it is still within the safe range of water surface target decision (≥6m).In addition to the probability of misjudgment when there are a few super large cruise ships with deep draft, the algorithm can maintain good stability in most cases.In the harsh hydrological environment, the depth of the underwater sound source ESI-min fluctuates greatly, and the judgment boundary becomes shallower to 4m.When there is a surface target with relatively deep draft, there is a probability of misjudgment.

Different receiving depth.
The receiving array may be deployed at different depths depending on the experimental requirements, so it is necessary to explore the influence of the receiving depth on the algorithm.The simulation conditions still remain unchanged, only the receiving depth is changed, and the receiving depth is set to 10 m, 40 m, and 70 m respectively.The simulation results are shown in Figure 5.  3, that is, the results when the receiving depth is 20 m, it can be seen that as the receiving depth changes, the decision boundary fluctuates between 7~9 m, which has almost no influence on the performance of the algorithm.

Different receiving distance.
The horizontal distance between the target and the receiver changes with time, so it is necessary to explore the relationship between algorithm performance and horizontal distance.The simulation conditions remain unchanged and only the horizontal receiving distance is changed.The horizontal receiving distance is set to 1km, 3km, 5km and 7km respectively.The simulation results are shown in Figure 6.Comparing the above results with Figure 3(receiving horizontal distance of 10 km), it is found that with the increase of horizontal distance, the algorithm effect is getting better, and tends to be stable.As the distance decreases, the decision boundary becomes shallow and the probability of misjudgement increases.3 km can be identified as the effective distance of the algorithm.This is because the sound field tends to be stable in the far field with increasing distance, and is less affected by other factors, while the sound field at close distance is susceptible to interference by various factors.

The influence of signal-to-noise ratio.
In the case of passive reception, different targets have different signal-to-noise ratios(SNR) under different background interference, so the variable of SNR is simulated to fit the actual application scenario.The simulation conditions remain unchanged, and the SNR is assumed to be 0dB, 5dB, 10dB, 15dB, 20dB respectively.The passive received signal is simulated, and the simulated original signal is convoluted with the channel function corresponding to the depth of each sound source to obtain the received signal after channel transmission, and the received signal is superimposed with noise according to different SNR.Then the ESI-min values corresponding to the received signals with different SNR are then calculated.
From the perspective of channel estimation, the transmitted signal ( , , ) x p t f is equivalent to the input signal of the channel, and the underwater acoustic channel is regarded as a filter whose impulse response function is defined as ( , , ) h p t f , and the received signal ( , , ) y p t f is equivalent to the output signal of the channel.Here, p represents spatial position, t represents time and f represents frequency.The input and output of the channel can be combined by convolution operation, namely: By configuring the environmental parameters of the seawater channel, the impulse response function of the underwater acoustic channel is calculated using the acoustic field calculation model, so that the received signal can be obtained by convolution of ( , , ) x p t f and ( , , ) h p t f .The control group is the signal without superimposed noise, and the ESI-min curves obtained by calculating the simulated received signals with different signal-to-noise ratios are shown in Figure 7.
From the above results, it can be seen that the ESI-min value calculated by the actual simulated signal is raised as a whole.This is because in the ocean, the transmitted signal propagates through the water medium.Due to the attenuation, phase shift, dispersion, and multipath effects of the channel, the signal undergoes distortion such as broadening and deformation when it reaches the receiver.When the sound source fluctuates up and down around a certain depth, the corresponding channel will also change.After aliasing of signals from different channels, there will be a deviation between the calculation results and the theoretical calculation results under ideal conditions, and the overall ESImin value will be raised.
The simulation shows that with the increase of signal-to-noise ratio, the effect of the algorithm is getting better.When the signal-to-noise ratio is greater than 10 dB, the discrimination boundary is within the safe range (≥6m).When the signal-to-noise ratio is less than 10 dB, the water surface target with deeper draft may be misjudged.

Real data verification
In this section, the effectiveness of the algorithm is verified again by the processing of real data.In practical signal processing, if the processing object is the tracking beam signal of a target, firstly the signal needs to be divided into multiple snapshots, and each snapshot is an ESI calculation cycle.Then a cycle is divided into several segments to calculate the variance values.In the expected frequency band, the energy distribution in the frequency domain is obtained first, and then the ESI value at each frequency point is calculated.Finally, the minimum value of ESI at all frequency points is screened.The time-varying ESI-min value can be obtained through multiple continuous calculation cycles, and the depth information judgment of the tracking target can be realized by comparing it with the threshold.If it is a comprehensive omnibearing depth attribute discrimination, then the above process needs to be repeated once in each prefabricated orientation.

Tracking beam data verification
The algorithm is verified using the actual data of three sets of tracking beams.The target signal-tonoise ratio, target and interference number, and data duration of each group are shown in the following table (Table 1 Calculated by the above process, the results are shown in Figure 8.It can be seen from the above results that the algorithm has a good processing effect on these three sets of data.The ESI-min value corresponding to the surface ship is large, and the ESI-min value corresponding to the underwater target is small, which can be clearly separated and the performance is stable over time.Moreover, it corresponds to the numerical range of the simulation results in Section 3.2.4,which proves the effectiveness of the algorithm.The omnidirectional depth discrimination verification is performed in an experimental scene with water surface interference.The original omnidirectional course map and the omnidirectional course map screened by the algorithm (retaining the underwater target) are listed respectively.The results are shown in Figure 9.

Omnidirectional data verification
From the processed results, it can be seen that the algorithm can eliminate multiple water surface interference targets well and retain the cooperative sound source trajectory as accurately as possible, even for the sense with numerous and complicated surface interference targets and low signal-to-noise ratio.The practical application effectiveness of the algorithm is proved.

Summary
Based on the idea of modal scintillation, this paper compares the energy fluctuation in the frequency domain with the modal fluctuation characteristics, and derives a new method suitable for passive horizontal array for moving target depth discrimination with strong environmental adaptability, high error tolerance rate, fast calculation speed and low complexity.It is found by stimulation that the algorithm has a large error in harsh environment or when the horizontal distance is less than 3km.In addition, when the signal-to-noise ratio is less than 10dB, the probability of misjudgement will also increase.Except for the above situations, the depth discrimination with high accuracy can be achieved.The algorithm is verified by the actual experimental data, and the results show that the algorithm is feasible and has certain engineering application value.In the future, the surface and underwater depth discrimination under non-ideal conditions can be further studied to improve the tolerance of the algorithm.

Figure 1 .
Figure 1.The fluctuation characteristics of the first four order excitation function.

Figure 2 .
Figure 2. The variation characteristics of each mode with source depth.
values corresponding to different sound source depths at different frequency points, and the minimum ( , ) i s ESI f z value at each sound source depth is taken in frequency.According to the above steps, 100 independent Monte Carlo simulation experiments are repeated to calculate the average value of min ( ) s ESI z .The simulated curve of the average min ( ) s ESI z with the depth of the sound source is shown in Figure 3.

Figure 3 .
Figure 3.The min ( ) s ESI z curve in pekeris environment.

Figure 4 .
Figure 4. (a) Moderate hydrological environment and simulation results.(b) Harsh hydrologicalenvironment and simulation results.In the moderate hydrological environment with weak negative gradient, the slight fluctuation caused by the target depth of 58m ~ 72m makes the decision boundary shallow to 7m, but it is still within the safe range of water surface target decision (≥6m).In addition to the probability of misjudgment when there are a few super large cruise ships with deep draft, the algorithm can maintain good stability in most cases.In the harsh hydrological environment, the depth of the underwater sound source ESI-min fluctuates greatly, and the judgment boundary becomes shallower to 4m.When there is a surface target with relatively deep draft, there is a probability of misjudgment.

Figure 5 .
Figure 5. (a) The result of receiving depth 10m.(b) The result of receiving depth 40m.(c) The result of receiving depth 70m.Combining above simulation results with Figure3, that is, the results when the receiving depth is 20 m, it can be seen that as the receiving depth changes, the decision boundary fluctuates between 7~9 m, which has almost no influence on the performance of the algorithm.

Figure 6 .
Figure 6.(a) The result of receiving distance 1km.(b) The result of receiving distance 3km.(c) The result of receiving distance 5km.(d) The result of receiving distance 7km.

Figure 8 .
Figure 8.(a) The first group result.(b) The second group result.(c) The third group result.It can be seen from the above results that the algorithm has a good processing effect on these three sets of data.The ESI-min value corresponding to the surface ship is large, and the ESI-min value corresponding to the underwater target is small, which can be clearly separated and the performance is stable over time.Moreover, it corresponds to the numerical range of the simulation results in Section 3.2.4,which proves the effectiveness of the algorithm.

Figure 9 .
Figure 9.The original(upper) and the processed(under) omnidirectional course map.

Table 1 .
).Data information of three groups.