1. IntroductionThe target echoes received by torpedoes are a collection of target reflection points, each of which independently reflects the incoming torpedo signal. The reflections from these points are not uniform. There are highly reflective points, usually called “ highlights”, such as a submarine’s bow, hull, and stern [1,2]. These highlights have a relatively stable relative position and can characterize the target endpoint location; therefore, torpedoes usually obtain target scale information by extracting target echo highlight features. The scale of the target is stable and representative. As a stable feature, the scale of the target varies little with the environment, but the scale of different targets varies very significantly. Therefore, active acoustic homing torpedoes use the target highlights to estimate the scale of the target and use it as a criterion for target recognition, which has become the primary method for target recognition by active acoustic homing torpedoes (including various active sonars) [3,4,5,6]. Figure 1 shows the attack posture of the torpedo.Many scholars have made great progress in the research of torpedo true and false target scale recognition. As the target scale is usually proportional to the target echo intensity, Lee D J et al. [7] converted acoustic measurements of echo intensity to fish scale estimates by constructing a database, while obtaining the relationship between target intensity and fish scale. Furthermore, a linear regression analysis was performed for all species to reduce the data to empirical equations, to show the variation of target intensity with fish scale and species. On the other hand, Buerkle, U. [8] showed that the fish scale calculated from the echo intensity needed to be corrected when using the relationship between echo intensity and fish scale. This method did not consider the fish’s orientation, since the active sonar receives the target echo intensity, which is not precisely proportional to the target scale, but to the reflected area of the target acoustic signal. In addition, the target echo strength received by the active sonar is also relative to the target material and structural ocean channel. Therefore, it is difficult for the active sonar to estimate the target scale using the target echo intensity for target recognition.Since it is challenging to recognize targets accurately based on the echo intensity, Wang Y et al. [9] recognized weak targets by target echo pulse broadening in a strong interference background. Moreover, they solved the problem of few echo features and the difficult recognition of weak targets underwater. They obtained the relationship between pulse broadening, target material, pulse power, and target distance of different underwater weak targets using statistical data analysis. The results show that the pulse-broadening characteristics of the echo signal can be used to recognize weak targets in the background of strong water impurity interference. Yu L et al. [10] estimated the echo broadening of the target, and derived the target length as a parameter by expectation maximization to obtain the feature parameters for recognizing the target. The simulation results show that the method has higher target recognition accuracy than other feature recognition methods. Xu Y et al. [11] recognized underwater targets by extracting underwater target orientation heading features. They used underwater target highlighting structure features to obtain underwater target orientation heading features using quadratic least-squares fitting. The experimental simulation results show that the target scale can be recognized by the target orientation heading features. However, when encountering strong interference, such as acoustic decoys with virtual scale, the active sonar makes a significant error in estimating the target scale. It is difficult to accurately identify the target by echo broadening and apparent angle (azimuthal orientation).

In this paper, we first simulate the echo signals received by torpedoes from submarines, suspended acoustic decoys, and mobile acoustic decoys for virtual-scale simulation. Secondly, we estimate the parameter of each target echo signal to obtain their echo broadening and apparent angles, which are converted into apparent scales, respectively. Then, we investigate the correlation between the echo broadening and the apparent angle of different targets. We thus propose a method to recognize the true and false targets based on the correlation between the target’s echo broadening and apparent angle, which solves the problem that torpedoes are facing in recognizing the scale features of acoustic decoys simulating virtual scales. In addition, the method improves the ability of active sonar to perform target scale recognition with strong interference.

4. Simulation VerificationThe echo of any target is composed of several sub-echoes iteratively; each sub-echo can be regarded as emitted from a scattering point, which is the bright spot. Therefore, we can equate any target to a combination of several bright spots. The acoustic decoys are usually modeled as multi-highlight echoes to simulate scale targets [20,21].

When the echo simulation is performed by suspended acoustic decoys, the virtual-scale target simulation is achieved by simulating the echoes of the bright spots of the suspended acoustic decoys at both ends of the torpedo course plumb line; in addition, the time delay simulation amount of the rest of the acoustic decoys is determined according to their distance from the bright spots of their corresponding virtual-scale targets. When the echo simulation is performed by the mobile acoustic decoy line array, each array element performs delay superposition and echo time broadening on the torpedo-seeking signal, according to the incoming torpedo posture, respectively, to realize the virtual-scale simulation of the submarine target.

Among them, the bright spot echo model of a single suspended acoustic decoy and a single array element of a homing acoustic decoy array can be determined based on the three parameters of amplitude factor, time delay, and phase jump. The transfer function can be expressed as:

Hi(r,θ,ψ,ω)=Ai(r,θ,ψ)ejω(v)τiejφ

(10)

where r is the distance from the torpedo to the target bright spot; Ai(r,θ,Ψ) is the amplitude of the echo of this bright spot, which is related to the distance r of the target and the direction of acoustic wave incidence, i.e., the incidence angle θ and the pitch angle Ψ. τi denotes the time delay of this bright spot, determined by the acoustic range of the equivalent acoustic center concerning some reference point, and is a function of θ. ω(v) denotes the difference between the echo’s center frequency and the incident wave’s center frequency, due to the target’s relative motion by a Doppler frequency shift; φ is the phase jump of the return wave.Therefore, the total transfer function of the target is:

Hi(r,θ,ψ,ω)=∑i=1NAi(r,θ,ψ)ejω(v)τiejφ

(11)

where N is the number of target highlights.As the plate element analysis method is capable of accurate prediction of underwater complex target geometry backscattering, we built a benchmark submarine scattering model by plate element method [22,23]. Based on the high-frequency approximation of Kirchhoff’s integral formula, we can divide the target surface into plate elements, calculate the scattered sound field for each plate element separately, and obtain the whole scattered sound field after superposition.The Kirchhoff formula for the acoustic scattering problem is [24]:

φsr2=14π∬S[φs∂∂nejkr2r2−∂φs∂nejkr2r2]ds

(12)

where s is the scatterer surface, n is the surface outer normal, r2 is the scattering point vector diameter, φs is the scattering potential function, and k is the wave vector.

The Kirchhoff approximation is a high-frequency approximation that typically assumes that:

The contribution of the geometric shadow region to the scattered field is neglected.

The object surface satisfies the rigid boundary conditions. Specifically, the scattering potential function under rigid boundary conditions is equal in size to the incident potential function, and the angle is symmetric about the target:

φs=φi∂φs+φi∂n=0

(13)

where the incident wave potential function φi = (A/r1)exp(ikr1) (omitting the time factor e−jωt), and A is the amplitude constant. In the case of transceiver co-location, the surface boundary conditions lead to:

φs=−ik0A2π∫S0ei2k0rr2cosθds

(14)

where r is the scattering point vector diameter and θ is the angle of incidence. We extend the above results to non-rigid surfaces. When the surface radius of curvature R is large (the product of the radius of curvature and wavelength is much larger than 1), the local plane wave approximation can be applied by setting the surface reflection coefficient to V(θ), and the surface acoustic impedance to Zn:

φs=V(θ)⋅φiiωρ(φs+φi)∂φs+φi∂n=−Zn

(15)

where ω is the incident wave angular frequency and ρ is the target surface density. The following equation relates the plane wave reflection coefficient to the total surface acoustic impedance of any complex interface at an infinitely large plane interface:

ρccosθZn=1−V(θ)1+V(θ)

(16)

where the underwater sound speed is c, usually 1500 m/s. Equation (15) can be substituted for Equation (16). In the case of transceiver co-location, the surface boundary conditions lead to:

φs=−ik0A2π∫S0ei2k0rr2V(θ)cosθds

(17)

We can obtain the target intensity in the far-field condition according to Equation (17):Among them:

I=∫s0e2ik0ρ→⋅r0→(n0→⋅r0→)V(θ)ds

(19)

Among them, ρ→=xi→+yj→ is the vector from the point where the face element is located to the reference point, n0→=k→ is the unit normal vector of the face element, r0→=ui→+vj→+wk→ is the unit vector from the receiving point to the reference point, and n0→⋅r0→=cosθ=w. Suppose that the reflection coefficient V(θ) is constant within a plate element; then, the integral of a plate element is:

IΔs=∫Δse2ik0(ux+vy)V(θ)dxdy=V(θ)w∑n=1Ke2ik0(xnu+ynv)(pn−1−pn)(2k0u+2k0pn−1v)(2k0u+2k0pnv)

(20)

where K is the number of polygon vertices and (xn,yn) is the coordinate of the polygon vertex and set p0=y1−yKx1−xK.The target intensity of a complex target can be calculated by the following slab metric method. The target surface is first divided into a grid of many small slabs. The scattered sound field of all the plate elements in the bright area is summed to obtain the approximate value of the scattered sound field of the target, and the plate elements with different orientations are transformed uniformly to some determined plane by coordinate transformation; consequently, we can ascertain:

I=∑i=1N∑j=1MV(θij′)w′∑n=1Ke2ik0(xn′uij′+yn′vij′)(pn−1−pn)(uij′+pn−1vij′)(uij′+pnvij′)sij

(21)

where xn’,yn’ is the coordinate of the vertex of the (i,j)th plate after transformation to the 2D plane, V(θij’) is the local surface reflection coefficient of the (i,j)th plate, and θij’ is the angle between the normal and incident sound lines of the (i,j)th plate. In the later specific calculations, the triangular plate element is adopted; therefore, K = 3 after a simulated Doppler frequency shift.Figure 9 shows the benchmark submarine target echo. We can see the relationship between the target intensity of each part of the submarine (transom, enclosure, and bow), obtained by matching the filtering gain with the angle. The target intensity of the submarine is more significant when the angle is 0°–90°, because the frontal scattering area of the submarine is large, and the structure is simple; the phase cancellation is less. If the angle is closer to 90°, the time delay difference of the target echoes in each part of the submarine are smaller.Figure 10 shows the torpedo and target movement posture. As the fixed advance angle guidance method is less difficult in engineering practice, and can make the torpedo attack end effective, it is an ideal guidance method for an active acoustic homing torpedo. The attack posture of the torpedo can be set using the fixed advance angle guidance method; O point is the active acoustic homing torpedo initial position, A0 point is the target initial position, the distance r0 between the torpedo and the target is 500 m, the orientation θ of the target initially located in the torpedo is 45°, the torpedo speed vt is 50 kn, and the torpedo fixed advance angle α is 5°. Since the torpedo usually attacks from a certain angle behind the side of the target, we can set the initial enemy side angle Φ to 135°. When the target is a submarine or a homing acoustic decoy, the target velocity vm is 15 kn, the submarine is 60 m, and the homing acoustic decoy line array is 40 m. Ten suspended acoustic decoys are deployed at point O; when the targets are suspended acoustic decoys, the deployment scatter error is 40 m [25].

The operating frequency of the torpedo transmitting signal was set to be 30 kHz and bandwidth to be 0.8 kHz. The signal period was 1 s, the time width was 62.5 ms, the sound source level 220 dB, the noise level 60 dB, the receiving directivity index 17 dB, and the detection index 12 dB.

When the acoustic signal propagates in the ocean channel, the surface and bottom reflections produce multipath scattering [26,27,28,29]. Moreover, the sound velocity gradient causes the refraction of acoustic waves, which tend to refract toward the lower sound velocity region, leading to the propagation of the acoustic signal curve. This paper applies Dushaw’s depth-dependent sound velocity profiles derived from summertime temperature, pressure, and salinity data in the North Atlantic off the coasts of Britain and Ireland [30]. Figure 11 shows the sound speed profile data. The refraction and reflection of the acoustic signal cause the acoustic signal to propagate in different channels, causing the attenuation of the single-channel acoustic signal amplitude and the superposition of the different channel acoustic signal time delays. The target echo simulation was performed, using the BELLHOP ray tracing program, to obtain the time delay and amplitude attenuation of the target echo signals of different channels. We superimpose them to obtain the multipath echo signals. The target scattering was simplified to specular scattering in the simulation because the target scattering angle was difficult to simulate. Figure 12 shows the acoustic signal propagation trajectory obtained by simulation using the BELLHOP program. The depth of the ocean is set at 600 m. The depth of the sound source and the receiving point is 200 m, and the distance between them is 500 m. The angle range of the sound source signal emission is −15°–15°, and the sound source emits 20 signals at equal intervals. The receiving point receives signals in the depth range of its depth −10 m–10 m, and the receiving angle range is also −15°–15°. Our simulation of the acoustic signal propagation path can make the echo signal more realistic, which in turn makes the verification of the effect of the proposed target recognition method more reliable.Among them, Figure 13a–d are the estimation process of the target distance, the orientation, the apparent angle, and the echo broadening information, respectively [31]. Then, the apparent angle and echo broadening of each cycle are converted into the apparent scale to analyze the correlation between echo broadening and apparent angle of the submarine, mobile acoustic decoy, and suspended type acoustic decoy.Figure 14 shows the apparent scale of the target converted according to the apparent angle and echo broadening of each cycle. The echo broadening and apparent angle cannot distinguish the scale difference between the real-scale target and the virtual-scale target. Under substantial interference, the target scale cannot be accurately recognized only by the echo broadening and apparent angle alone. Therefore, we recognized the target by correlating the echo broadening and the apparent angle. We also analyzed the difference between the equivalent scales obtained from the target echo broadening and the apparent angle in the following.The apparent scale difference of each target is obtained from the apparent angle and the echo broadening; as shown in Figure 15, it can be observed that the apparent scale difference of each cycle of the submarine target is within the range of [0.2 m, 4.0 m], which is obviously smaller than the apparent scale difference of the mobile acoustic decoy and the suspended acoustic decoy.Figure 16 shows the apparent scale difference of different ship angles. The target porthole angle is set to be 0°–180° in steps of 15°. It can be seen that when the target angle is in the range of 0°–75° and 105°–180°, the apparent scale difference of the submarine target is in the range of [0.5 m, 2.2 m], which is much smaller than the apparent scale difference of the mobile acoustic decoys and suspended acoustic decoys. When the target angle is in the range of 75°–105°, the apparent scale difference of submarine, mobile acoustic decoys and suspended acoustic decoys is about 12 m, so it is impossible to distinguish between the targets. Therefore, the torpedoes in this chord angle range cannot recognize the real and fake targets based on the echo broadening and apparent angle. This is due to the fact that the time delay difference between the echoes at the two ends of the target is very small near the positive transverse chord angle, which corresponds to the small equivalent distance between them. In addition, the echoes have mostly overlapped, and it is difficult to distinguish the bright spots by subframe segmentation, thus causing errors in accurate orientation estimation and making the spatial scale of the simulation smaller than the theoretical spatial scale at this time, resulting in a large error.Figure 17 shows the apparent scale difference at different initial distances. The initial target distance was set from 500 m–2000 m, with 500 m as a step. It can be seen that when the target distance is 500 m, the apparent scale difference between the submarine target is 2.4 m, which is much smaller than the apparent scale difference between the mobile and suspended acoustic decoys. When the target distance is greater than 1000 m, the apparent scale difference between the submarine, mobile and suspended acoustic decoys is very small, and it is impossible to distinguish between the targets; therefore, the torpedo cannot recognize the real and fake targets according to the echo broadening and apparent angle in the chord angle range. When the target is outside the scale recognition range, the echo signal propagation loss is larger and the signal-to-noise ratio of the target echo signal is lower, which leads to the inability of the torpedo to estimate the target parameters accurately. Moreover, the multipath effect exists in the long-range target echo, resulting in an inevitable time overlap of the target echo signals from different channels. As the estimated target echo broadening of the torpedo is larger than the time extension, due to the scale of the target itself, the target echo broadening cannot be estimated accurately, and it cannot recognize the target by the target scale recognition method proposed in this paper.