Common sound velocity profile target depth estimation method based on frequency dispersion elimination transformation

Abstract

The invention belongs to the technical field of signal and information processing, relates to a common sound velocity profile target depth estimation method based on frequency dispersion elimination transformation, and is suitable for sonar signal processing. In order to overcome the influence of parameter estimation precision reduction caused by sound velocity profile change, on the basis of traditional frequency dispersion elimination transformation, depth estimation under a general sound velocity profile condition is realized by optimizing global waveguide invariants, fitting a sound velocity profile, calculating an equivalent propagation distance and redesigning a frequency dispersion elimination kernel function and an energy matching function.

Description

Technical Field

[0001] The invention belongs to the technical field of signal and information processing, and relates to a general sound velocity profile target depth estimation method based on de-dispersion transformation, which is suitable for sonar signal processing. Background Art

[0002] Underwater sound source localization is particularly important in a variety of underwater acoustic technologies, including resource exploration, underwater search and rescue, and target identification. As a widely used high-tech technology, improving and developing techniques for estimating the depth and distance parameters of underwater targets has become a key tool and a pressing need in the marine sector. Passive estimation methods are particularly popular due to their superior concealment and low ecological disturbance.

[0003] Due to the Heisenberg-Gabor uncertainty principle of traditional time-frequency analysis methods, simple short-time Fourier transforms, wavelet transforms, and Hilbert-Huang transforms all have limitations. While introducing superior time-frequency analysis methods such as the Warping transform effectively addresses these limitations, they also reduce estimation accuracy under typical sound velocity profile conditions. Existing methods are all derived from the Pekeris waveguide acoustic field formula. When processing transient acoustic signals under typical sound velocity profile conditions, variations in the sound velocity profile can cause the group phase velocities of various modes to deviate from the theoretical curve, resulting in inseparable aliasing and distortion of the modes. Extracting modal energy according to the theoretical curve can result in significant energy leakage, impacting depth estimation accuracy.

[0004] Therefore, a depth estimation method for a general sound velocity profile is needed that can overcome the influence of the decrease in parameter estimation accuracy caused by the change of the sound velocity profile. Summary of the Invention

[0005] To address these issues, this paper proposes a target depth estimation method based on a general sound velocity profile using the traditional dispersive transform. By optimizing the global waveguide invariant, fitting the sound velocity profile, estimating the equivalent propagation distance, and redesigning the dispersive kernel function and energy matching function, depth estimation is achieved under general sound velocity profile conditions.

[0006] The technical solution of the present invention is:

[0007] All waveguides have dispersion characteristics, which are determined by the waveguide's characteristics. The dispersion characteristics of underwater acoustic channels are characterized by the fact that the horizontal wave number of the simple normal wave varies with frequency. By using the dispersion characteristics of the simple normal wave, it is possible to obtain relevant information about the ocean environment and signals contained in the waveguide. However, the uncertainty of the underwater acoustic channel increases the difficulty of analyzing its dispersion characteristics. In shallow water waveguides, the sound field can be represented as the superposition of a series of simple normal waves:

[0008] According to the simple normal wave theory, the sound field of the continuous acoustic signal in the ocean waveguide can be expressed as the superposition of simple normal wave modes of various orders:

[0009]

[0010] Where P(r,ω) is the sound pressure, ω is the signal frequency, ρ is the seawater density, is the eigenfunction of the mth mode, k rm (ω) is the horizontal wave number of the mth mode of the signal with frequency ω, z s is the sound source depth, z r is the receiving depth, r is the horizontal distance from the sound source to the receiving point, and S(ω) is the sound source spectrum.

[0011] The phase velocity v of the mode pm and group velocity v gm They can be defined as:

[0012]

[0013] The traditional dispersion-eliminating transform is more suitable for marine environments with constant sound speed. When generalizing the Pekeris waveguide acoustic field to a general sound speed profile, the sound speed is no longer constant. Therefore, both the waveguide invariant β and the determination of the two dispersion-eliminating parameters—the dispersion-eliminating distance r′ and the dispersion parameter γ′—are affected by the general sound speed profile, thus compromising the dispersion-eliminating effect and reducing the accuracy of parameter estimation. Therefore, to generalize the method to general sound speed profiles, improvements are required. The general sound speed profile condition is used to fit the sound speed profile using cubic spline interpolation.

[0014] Taking the variable sound velocity profile into consideration, firstly, cubic spline interpolation is used to fit the variable sound velocity profile, and the entire water body is divided into q = n + 1 measurement points, z q is the water depth at the measuring point q, c q is the sound velocity at the measuring point q, so the measuring points are defined as (z0,c0), (z1,c1),…, (z n ,c n ), divide the water body into h segments q =z q+1 -z q , the boundary is the natural boundary M0=M n =0, for each measuring point:

[0015] a q M q-1 +b q M q +d q M q+1 =e q ,q=1,2,...n-1 (4)

[0016] in

[0017] a q =h q-1 (5)

[0018] b q =2h q-1 +h q (6)

[0019] d q =h q (7)

[0020]

[0021] The sound velocity profile of each section is fitted as follows:

[0022] S(z q )=A q +B q (zz q )+C q (zz q ) 2 +D q (zz q ) 3 (9)

[0023] The overall expression of the variable sound velocity profile is:

[0024]

[0025] in:

[0026] A q =c q (11)

[0027]

[0028]

[0029] Substitute the general sound velocity profile c(z) into equation (11) to solve the horizontal wave number k rm (ω), and calculate the phase velocity v according to equations (2) and (3) pm and group velocity v gm :

[0030]

[0031] The waveguide invariant does not change significantly with the sound velocity profile, but it still causes a certain error in the estimation of its value. Therefore, the global waveguide invariant β is redefined using the group velocity and phase velocity calculated above:

[0032]

[0033] Where M is the total modal order, and under the global waveguide invariant β, the modal-related dispersion parameter γ is defined as m :

[0034]

[0035] At this time, the de-dispersion kernel function for the m-th order mode can be defined as:

[0036]

[0037] The reference speed of sound Reference distance At this time, the sound field expression obtained after introducing the kernel function is:

[0038]

[0039] The final sound field expression after the dispersion-free transformation under the general sound velocity profile condition is:

[0040]

[0041] At this time, after the de-dispersion transformation, the energy of each mode is focused at different equivalent distance points instead of being focused at the same distance point as in the Pekeris waveguide. At this time, the various modes of the signal under general sound velocity profile conditions can be clearly separated in both the time domain and the time-frequency domain. Whether setting a binary mask filter in the time-frequency domain or setting a time threshold in the time domain, the energy of each mode of the signal can be accurately extracted. The energy of each mode in the time domain is extracted as shown in formula (14):

[0042]

[0043] in, is the start time of the mth mode, is the end time of the mth mode, and y(t) is the signal obtained by the target receiving signal after the improved dispersion-free transformation. After the water depth is divided into grids with a specified step size, it is assumed that the simulated sound source target signal is excited at different depth points. The simulated sound source target signal at each depth point is transmitted to the receiver and the received target signal is obtained. The energy of each mode is calculated by the improved dispersion-free transformation and matched with the energy of each mode of the actual target receiving signal obtained in the previous sequence. The maximum matching value is output and it can be considered that the depth point of the simulated signal at this time is the actual target signal depth, realizing the depth estimation of the continuous target sound signal. The comparison function is defined as follows:

[0044]

[0045] in, and All are calculated by the method in step 7. The energy of each order actually extracted by the target, The energy of each order calculated by simulation is the maximum point of the energy matching function output, which is the estimated target depth.

[0046] The present invention has the following beneficial effects: Compared with the traditional dispersion-free transform, the proposed method demonstrates superior applicability under general sound velocity profile conditions, resulting in more accurate depth estimation. This method is widely applicable and has better engineering practicality. When the sound velocity profile is that of a Pekeris waveguide, the method can be completely reduced to the traditional dispersion-free transform. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is the shallow sea waveguide environment model used in the present invention.

[0048] Figure 2 It is a de-dispersion aggregation point diagram searched using the method of the present invention.

[0049] Figure 3 is a depth estimation map using the method of the present invention. DETAILED DESCRIPTION

[0050] The specific implementation of the present invention is described in detail below in conjunction with the technical solutions and drawings.

[0051] The present invention provides a general sound velocity profile target depth estimation method based on de-dispersion transformation, comprising the following steps:

[0052] Step 1: Use cubic spline interpolation to fit the variable sound velocity profile, and divide the entire water body into q = n + 1 measurement points, z q is the water depth at the measuring point q, c q is the sound velocity at the measuring point q, so the measuring points are defined as (z0,c0), (z1,c1),…, (z n ,c n ), divide the water body into h segments q =z q+1 -z q , the boundary is the natural boundary M0=M n =0, for each measuring point a q M q-1 +b q M q +d q M q+1 =e q ,q=1,2,...n-1. Among them, a q =h q-1 , b q =2h q-1 +h q , dq =h q , The sound velocity profile of each section is fitted as follows: The overall sound velocity profile is c(z)=a q +b(z- q z)+c(z q -z) 2 +d q (zz) 3 (z q ≤z≤z q+1 ), where: a q =c q ,

[0053] Step 2: Solve for the horizontal wave number k rm (ω):

[0054]

[0055] Among them, k rm (ω) is the horizontal wave number of the mth mode of the signal with frequency ω; ω is the signal frequency, is the eigenfunction of the m-th mode.

[0056] Step 3: Solve for the global waveguide invariant β:

[0057]

[0058] Where M is the total modal order, v pm is the phase velocity, v gm is the group velocity.

[0059] Step 4: Solve for the modal-dependent dispersion parameter γ m :

[0060]

[0061] Step 5: Solve the de-dispersion kernel function of the mth mode

[0062]

[0063] The reference speed of sound Reference distance r is the horizontal distance from the sound source to the receiving point, H is the depth of the water body, and j is an imaginary number.

[0064] Step 6: Solve the sound field P(r ref ,ω;γ′,r′):

[0065]

[0066] Among them, ρ(z s ) is the water density at the sound source depth, z s is the sound source depth, z r is the receiving depth, r is the horizontal distance from the sound source to the receiving point, and S(ω) is the sound source spectrum.

[0067] Step 7: Extract the energy of each mode in the time domain in, is the start time of the mth mode, is the end time of the m-th mode, and y(t) is the signal obtained by the target received signal after the modified de-dispersion transformation in step 6.

[0068] Step 8: After normalizing the modal energies of the target continuous sound signal extracted in step 6, construct the energy matching function in, and All are calculated by the method in step 7. is the energy of each order actually extracted according to the target, The energy of each order calculated by simulation.

[0069] After the water depth is divided into grids with a specified step size, assuming that the simulated target signal is excited at different depth points, the target receiving signal at each depth point traverses steps 2 to 7, calculates the modal energy of the simulated signal at the current depth point and matches it with the modal energy of the actual target signal, and outputs the maximum matching value. It can be considered that the depth point of the simulated signal at this time is the actual target signal depth, thus realizing the depth estimation of the continuous target acoustic signal.

[0070] In this embodiment, a shallow sea area in summer is taken as an example, the water depth is 63m, and the water density is 1.023kg / cm 3 , the sound velocity profile is as follows Figure 1 As shown, the density of the seabed sediment is 1.8 kg / cm 3 The velocity of sound in the sediment layer is 1600 m / s, with an attenuation of 0.2 dB / λ. The ocean is vacuum above the top. The signal frequency is 600-800 Hz, the source depth is 25 m, the hydrophone depth is 40 m, the hydrophone is 20 km from the source, and the search step size is 0.1 m. In shallow waters, higher-order modes contribute less to the acoustic field, so the first four modes were used for the experiment. Figure 2 Using the dispersion parameter and distance parameter of the present invention to search the plane, Figure 3This figure shows the depth estimation results obtained using the method of the present invention. Experimental verification shows that the proposed method, compared to the traditional dispersion-free transform, demonstrates superior applicability and more accurate depth estimation results under general sound velocity profile conditions. The method is widely applicable and has better engineering practicality. When the sound velocity profile is a Pekeris waveguide, the method can be completely reduced to the traditional dispersion-free transform.

Claims

1. A general sound velocity profile target depth estimation method based on de-dispersion transform, characterized in that: The following steps are involved: Step 1: Use cubic spline interpolation to fit the variable sound velocity profile, and divide the entire water body into q = n + 1 measurement points, z q is the water depth at the measuring point q, c q is the sound velocity at the measuring point q, so the measuring points are defined as (z0,c0), (z1,c1),…, (z n ,c n ), divide the water body into h segments q =z q+1 -z q , the boundary is the natural boundary M0=M n =0, for each measuring point a q M q-1 +b q M q +d q M q+1 =e q ,q=1,2,...n-1; Among them, a q =h q-1 , b q =2h q-1 +h q , d q =h q , The sound velocity profile of each section is fitted as follows: The overall sound velocity profile is c(z)=a q +b(z- q z)+c(z q -z) 2 +d q (zz) 3 (z q ≤z≤z q+1 ), where: a q =c q , Step 2: Solve for the horizontal wave number k rm (ω): Among them, k rm (ω) is the horizontal wave number of the mth mode of the signal with frequency ω; ω is the signal frequency, is the eigenfunction of the mth mode; Step 3: Solve for the global waveguide invariant β: Where M is the total modal order, v pm is the phase velocity, v gm is the group velocity; Step 4: Solve for the mode-dependent dispersion parameter γ m : Step 5: Solve the de-dispersion kernel function of the mth mode The reference speed of sound Reference distance r is the horizontal distance from the sound source to the receiving point, H is the depth of the water body, and j is an imaginary number; Step 6: Solve the sound field P(r ref ,ω;γ′,r′): Among them, ρ(z s ) is the water density at the sound source depth, z s is the sound source depth, z r is the receiving depth, r is the horizontal distance from the sound source to the receiving point, and S(ω) is the sound source spectrum; Step 7: Extract the energy of each mode in the time domain in, is the start time of the mth mode, is the end time of the mth-order mode, and y(t) is the target received signal obtained after the modified de-dispersion transformation in step 6; Step 8: After normalizing the modal energies of the target continuous acoustic signal extracted in step 6, an energy matching function is constructed. After dividing the water body depth into a grid according to the specified step size, assuming that the simulated target signal is excited at different depth points, the target receiving signal at each depth point traverses steps 2 to 7, and the modal energies of the simulated signal at the current depth point are calculated and matched with the modal energies of the actual target signal. The maximum matching value is output, and it can be considered that the depth point of the simulated signal at this time is the actual target signal depth, thereby realizing the depth estimation of the continuous target acoustic signal.

2. The method for estimating target depth using a general sound velocity profile based on de-dispersion transform according to claim 1, wherein: The energy matching function in step 8 is: in, and All are calculated by the method in step 7. is the energy of each order actually extracted according to the target, The energy of each order calculated by simulation.

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