JPH0660841B2 - Reverberation simulation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application] The present invention relates to a reverberation simulation method for generating a signal that simulates underwater reverberation with respect to a monostatic sonar at high speed and high fidelity. By incorporating the underwater reverberation simulation device configured according to the present invention into the underwater sound field simulation device, it becomes possible to more efficiently perform testing, development, and the like of a system using an underwater acoustic sensor.

(Summary of the Invention) The present invention is a reverberation simulation method for a reverberation simulation device that generates a simulated underwater reverberation signal, and is for the REVGEN open loop version ^{3), 4)} performed in the reverberation simulation method ^{1), 2 )} . In addition to the improvements, improvements were made to allow more flexible setting of the usage of random numbers when generating simulated reverberation. These improvements are described in F. O. M. It was obtained by starting from the reverberation equation of theory ⁵⁾ and deriving a reverberation simulation equation suitable for simulating the statistical properties of reverberation, and a signal that simulates underwater reverberation using the reverberation simulation equation. High speed underwater reverberation for monostatic sonar, by creating
It can be simulated with high fidelity.

(Prior Art) In the REVGEN open loop version, the scattering intensity, position, and velocity of a scatterer are simulated using the Monte Carlo method for calculation of the covariance of the Doppler density matrix (DDM). A master DDM is calculated from the DDM covariance thus obtained, and a DDM is created from that and white noise.
It is converted into a matrix and multiplied with the transmitted waveform to generate a simulated reverberation signal. In the case where the motion of the sonar platform where the acoustic sensor is arranged is known in advance, the calculation of the master DDM can be performed in advance, and only the part after the calculation of the master DDM can be executed in the reverberation generation. Since it is sufficient, the reverberation signal can be generated in real time. When doing this precalculation, REVGEN is calculated without calculating the master DDM for all times.
A method called update algorithm ^{6), 7)} is also used to interpolate the DDM of the time between them from the master DDM updated at a longer time interval by the sampling time of the reverberation to be generated.

The reverberation simulation method previously proposed by the present inventor does not need to use Monte Carlo calculation for a scatterer for calculating DDM covariance. Also, when calculating the simulated reverberation, the master DDM
To the B-matrix need not be performed for all DDMs.

References are listed below.

1) Kyoji Sudo: "Reverberation simulation method," Japanese Patent Laid-Open Publication
1-123120. 2) K. Sudo: “On the improvement of the underwater reverberation simulation method,” Defense Agency Technical Research Division, Technical Report 1029, Showa 6
June 3rd. 3) D. W. Princehoues: “Reverberation generator
ocean algorithm, a status report, ”Applied Phisics
Lab., Univ. Washington, APL-UW7806, Feb. 1
5, 1987.4) ---: "REVGEN, Areal-t.
ime reveraberation generator, “in1977 IEEE
International Conference.on Acoustics Speech and
Signal Processings, pp.827-835, 1977. 5) V. V. Ol'shevskii: “Characteristics of S
ea Reverberation, ”English translation by VMA
lbers. New York: Consultants, Bureau, 1967. 6) S. G. Chamberlain and J. C. Galli: "AMode
l for Numerical Simulation of Non-stationary Sonar
Reverberation Using Linear Spectral Prediction, ”
IEEE JOUR. Ocean Engineering, vol.oe8, on.1
pp.21-36, Jan. 1983. 7) J. G. Melville and M.M. E. Stegman: “The E
ffect of Update Randomization on REVGEN Outp
ut: Broadband Energy Detector, ”Naval Ocean system
s Center, NOSC tr292, Aug. 1978. 6) M. E. Stegman and J. G. Melville: “The Eff
ect of Update Randomization on REVGEN Outpu
t: Matched Filter Processor, ”Naval Ocean Systems
Center, NOSCtr451, Aug. 1979. (Problems to be Solved by the Invention) In the conventional REVGEN open-loop version, the reverberation generation itself can be executed in real time by combining it with an update algorithm, but a large amount of time is required for preprocessing to obtain a master DDM.

Although the reverberation simulation method proposed by the present inventor has improved the above points, the hardware used for the reverberation simulation apparatus has a sufficient computing capacity, and the reverberation due to the motion of the scatterer is large. However, the handling is not defined when the randomness for generating the randomness and the generation of the random number that generates the inter-beam correlation can be performed multiple times during the reverberation simulation for one ping (transmission of one sound wave).

The present invention has been made to solve the above problems, and simplifies the scatterer simulation for obtaining the master DDM, and the motion of the scatterer and the inter-beam correlation required to generate the DDM can be obtained. The random number to be expressed can be updated in a form that matches the computing capacity of the hardware used in the reverberation simulator, and the reverberation simulation that produces simulated underwater reverberation is also suitable for faster computation. The purpose is to provide a scheme.

[Configuration of the Invention] (Means for Solving the Problems) In order to achieve the above object, the reverberation simulation method according to the present invention is based on the F. O. M. Reverberation formula by theory [However, the subscript n represents an amount relating to each scatterer, and when the number of transmission beams is 1 and the number of reception beams is L, L-column vector with the i-th component being the reverberation observed in the i-th received beam of L, Δf _n : Doppler shift due to the motion of the platform where the acoustic sensor is arranged and the n-th scatterer, θ _n : Phase shift due to the nth scatterer, r _n : relative distance between the platform and the nth scatterer, _St (t): transmission waveform (0 at time t <0), c: speed of sound, Let L-column vector obtained from the scattering intensity of the nth scatterer and the beam pattern. ] The simulation formula of the Doppler density matrix (DDM) of the form suitable for the simulation derived from [However, with the subscript m (m = 1,2, ...), the time axis is (O = t _o
<T ₁ <... <t _m <...) section t _m-1 <t ≤ t _m
Represents the corresponding representative value in L-column vector each having independent complex normal white noise component, ξ _m (t): Unit complex normal white noise, master DDM that is an L × L matrix Is Required from. Where α: absorption coefficient, r _m : ct _m / 2 Ω: solid angle centered on the platform, An L-column vector in which the i-th component is the product of the i-th received beam pattern in the m-th time section and the beam pattern at the time of transmission (both include the phase difference for each beam), a _m (Ω): Amplitude (assuming positive real number) related to scattering intensity of scatterer, ρ _m (f, Ω): Ω, probability density relationship for Doppler shift due to motion of scatterer in the region corresponding to t, F _m ( Ω): Doppler shift due to platform motion in the solid angle Ω direction, Hermitian conjugation. ] And the reverberation simulation formula derived from this Is used to generate a signal that simulates an underwater reverberation.

The above reverberation simulation formula used in the present invention is defined by F. O. M. It is derived from the theory of reverberation. Basically, it is only necessary to reproduce the statistical properties of the reverberation in the reverberation simulation, the statistical properties of the reverberation can be approximated to a quasi-stationary normal stochastic process, and normal random numbers and uniform random numbers are used in the generation of the simulated reverberation signal. This is because the shape is convenient.

F. O. M. According to theory, the reverberation can be approximated as a quasi-stationary normal stochastic process, and is expressed as the superposition of reflections of a transmitted signal by a large number of scatterers existing in water as follows. However, assuming that the bandwidth of the transmission signal is smaller than its center frequency, consider a monostatic sonar in which the transmitting and receiving devices are located at the same position. Further, in order to simplify the expression, the sound velocity c in water is expressed as constant.

However, the number of transmission beams is 1, the number of reception beams is L, and the meanings of the symbols are as follows.

L-column vector with the i-th component being the reverberation observed in the i-th received beam of L (the start of transmission is the origin of time t), Δf _n : platform on which the acoustic sensor is arranged And n
The Doppler shift due to the motion of the th scatterer, θ _n : Phase shift due to the n th scatterer, r _n : Relative distance between the platform and the n th scatterer, _St (t): Transmission waveform (transmission start time Time origin t = 0), c: speed of sound.

Also, the L-column vector Is Can be written. However, And the symbols are as follows.

Ω _n : solid angle representing the orientation of the nth scatterer as seen from the platform, L-column vector with the i-th component as the complex beam pattern of the i-th received beam, b _T (Ω): complex beam pattern of the transmitted beam, α: absorption coefficient, A _n : amplitude related to scattering intensity of scatterer (It should be a positive real number).

Regarding the beam pattern, the phase difference due to the difference in the acoustic center of each beam is considered in advance.

When the velocities of the platform and the scatterer are smaller than the speed of sound, it can be approximated to the form of Δf _n = F (Ω _n ) + f _n and the Doppler shift due to the motion of the platform and the Doppler shift due to the motion of the scatterer. Where F (Ω)
Is the Doppler shift due to the movement of the platform in the solid angle Ω direction, and f _n is the Doppler shift due to the movement of the n-th scatterer. Using these things, equation (1) can be written in the form of using the integral about the solid angle.

[However, δ: Dirac delta function] Furthermore, the equation (4) is If you put it Can be written. This formula, as pointed out in the reverberation simulation formula,
It is a continuous-time B matrix. Corresponding continuous time D
DM is to B I put it. The inverse transformation is Becomes From equations (5) and (7), Can be written. The covariance of DDM can be calculated by F.S. O. M. It is guided by the assumption of a random phase for the theoretical phase shift. At this time, the radius r
Considering the unit solid angle region of the spherical shell having a thickness of (ct / 2), c × unit time / 2 in the Ω direction, the Doppler shift probability density function due to the motion of the scatterer in this region is given by ρ _t ( f, Ω). This is because, in actual observation, the Doppler shift probability density function of the entire scatterer, not the Doppler shift probability density function of each scatterer, is known. Then, Can be written. here, I said.

Thus, the covariance of the DDM can be written in a form that can be calculated from only the observed amount, and thus the DDM can be expressed in a form suitable for simulation calculation. In the case of the present invention, in order to more positively incorporate the quasi-stationarity of reverberation than the conventional method,
From the quasi-stationarity of reverberation, the time axis is divided into sections in which the average amount can be regarded as almost constant. With the transmission start time as the origin of time, O = t ₀ <t ₁ <t ₂ ... And the m-th section (t _m-1
The subscript m is used to indicate the representative value of the average amount in <t ≦ t _m ). This, and the equation (10), t, f
Being diagonal with respect to, the DDM can be expressed in the following form.

here, Are L-column vectors each having an independent unit complex normal white noise as a component, and ξ _m (t) is a unit complex normal white noise. They have a mean of 0, are independent of each other, and for covariance And Here, δ (tt ′) and the like are Dirac delta functions. It is assumed that h _{m, m} ′ has a value of 1 when m = m ′ and 1 or 0 otherwise. δ _{m, m} ′ is Kronecker δ.

Is an L × L identity matrix. _m is the representative value of the average amount in the mth section, Are tied together. As the method to solve this matrix equation, the right side is Hermitian matrix The diagonal element is a real lower triangular matrix, and each element can be sequentially obtained from the above equation. In general, it is known that the average amount of reverberation can be regarded as substantially constant when the width of the transmission signal is approximately equal to the width of the section.

From equation (13) and equations (6) and (8), To get

The formula (11) is a DDM calculation formula in the present invention.
(14) is the basic equation for reverberation simulation.

(Effect) Using these formulas derived above, it can be understood that the present invention is an improvement over the conventional method. Master D
The reverberation covariance required to calculate DM is given by equation (13)
As can be seen, it is possible to directly calculate based on the observed amount without simulating the scatterer. Therefore, the simulation of the scatterer at the time of calculating the master DDM is greatly simplified. Also, by considering the quasi-stationarity of reverberation, the DDM that reproduces the statistical properties of reverberation can be represented by the master DDM and complex normal white noise without calculating the master DDM for all times. Accordingly, the calculation of the master DDM may be performed in a cycle of about the duration τ of the transmission signal from the above description of the time width. This point is also a feature that leads to a reduction in the amount of calculation.
The use of random numbers appearing in equation (14) also leads to a reduction in the amount of calculation when generating simulated reverberation. In the case of REVGEN, it is necessary to convert each DDM into a B matrix, but by using the combination of the present invention, when reverberation is calculated,
After calculating the Doppler part [the first half including the frequency in formula (14)] and the range part [the latter half including t ′ in formula (14)] for each term of the sum of formula (14), , Their product gives the reverberation contribution from the m th term.

As described above, the calculation of the master DDM may be updated in a cycle longer than the sampling time of the reverberation to be generated, so that the method of the present invention reduces the amount of calculation at the time of reverberation generation. Also, for updating the random number, Equation (12)
Can be freely set depending on how to determine the value of h _{m, m} 'of m ≠ m'. For example, if the random number generation unit of the reverberation simulator has a surplus capacity, μ can be updated at the same cycle as the master DDM update cycle. This means that when m ≠ m ',
This corresponds to setting h _{m, m} ′ = 0. As described above, in the reverberation simulation method previously proposed by the present inventor, the random number updating method has been improved to be more flexible in the present invention.

In this way, the method introduced above reduces the amount of calculation compared to the conventional method, increases the flexibility in reverberation generation, and can reproduce exactly the required statistical properties of the reverberation generated. In addition, a high-fidelity reverberation simulator can be constructed.

(Example) An example of the reverberation simulation method of the present invention will be described below.

Here, first, in order to show the relationship with the observed amount, we derive equation (14) when the water is divided into volume reverberation, sea surface reverberation, and sea bottom reverberation as shown in Fig. 1. After that, the relationship with the conventional method is shown, and the flexibility of random number setting is described.

As shown in Reference 2), using the backscattering intensity S _v per unit volume in volume reverberation, the backscattering intensity S _S per unit area in sea surface reverberation, and the backscattering intensity S _B per unit area in seafloor reverberation Becomes In general, since S _S and S _B change depending on the grazing angle with respect to the sea surface and the seabed of the sonar platform on which the acoustic sensor is arranged, the subscript m is added. When t is larger than the duration of the transmitted signal to some extent, the solid angle element with respect to the sea surface portion in the spherical shell having radius r and thickness c × (unit time) / 2 is azimuth angle φ and sea surface grazing angle θ _S. Using Because it can approximate (expressed in the same manner using the grazing angle theta _B also submarine), the scatterer Doppler shift probability density for each _{region, ρ V (f), ρ} S (f)
Assuming that there is no scatterer motion on the bottom of the sea,
Ignoring these Ω dependences, equation (13) becomes However, Can be written. Where * indicates the convolution for f, Is. ∫ _vm dΩ indicates that it is a solid angle integral only for the volume reverberation part in the section m. The same can be done when the water is further divided into several areas.

When actually constructing the underwater acoustic simulator, it seems that a digital computer is often used. that time,
The integral for f appearing in equation (13) can be calculated using FFT. The size of the FFT at this time is F. O. M. Correlation of reverberation according to theory However, when t ′ is stopped and considered, the value differs from 0 only within the range of t′−τ ≦ t ≦ t ′ + τ. Therefore, in order to avoid the influence of aliasing, a value obtained by dividing 2τ by the sampling time may be used.

The reverberation simulation method in this case has a configuration as shown in FIGS. 2 and 3.

FIG. 2 is a block diagram of the reverberation simulation method according to the present invention. This is for the case where reverberation can be expressed as contributions from three regions as shown in FIG. In FIG. 2, the case of discretization is kept in mind, and for the sake of simplicity, a value obtained by dividing the duration τ of the transmission signal by the sampling period (N
Is represented by 4). * In the figure is a linear convolution. Of course, this convolution may be calculated as a circular convolution of a period sequence having a length of 2N by adding an element of 0 to each sequence of the transmission signal and the normal random number. Master DDM
And the product of the normal random numbers indicate that the matrix-vector product relating to the beam component is executed for each frequency component, and the product below it indicates the product for each time component. On the right side, the sum for each time component is shown.

FIG. 3 shows the case where the reverberation can be represented as the sum of contributions from three parts as shown in FIG.
6 is a block diagram showing a method of calculating DM.
Indicates that each frequency component in the sequence in parentheses on the right is multiplied by the effects of propagation loss and backscattering intensity. * In parentheses
Represents a convolution on frequency components. Where γ in equation (17)
_Since the spread of _m and ρ _{vm in} the frequency direction is not normally spread over the entire frequency direction, this convolution can be calculated as a circular convolution.

The word “decomposition” means that it is written after the equation (13). The contribution of the sea surface reverberation part and the seabed reverberation part can be calculated in the same manner.

Now, to see the relationship with the reverberation simulation method previously proposed by the present inventor, it is sufficient to set h _{m, m} ′ = 1 for all m in equation (12). That is, It can be seen that the update of is performed for each ping, and that a set of values set once is used as it is in a single ping, which corresponds to the conventional reverberation simulation method.

To see the relationship with traditional update algorithms,
For the expression (12), the following form is used as the expression of ξ.

_{ξ m (t) = k m} δ (t-τ m) ^{_{where, <k m k m '*}} > = δ m, m' | t m -t m-1 | a is the distribution function of tau _m is , In the interval t _m-1 <t ≦ t _m , 1
/ (T _m -t _m-1 ), otherwise 0. This expression is Equation 1
It is easy to understand that 3) is satisfied. Using this equation, the reverberation equation (14) becomes:

Looking at this equation, in addition to updating by Doppler component randomization, which is equivalent to the idea of conventional updating algorithms, the effect of τ _m corresponding to the randomness of the relative distance between the scatterer and the platform is considered. I understand.

Thus, it can be seen that the reverberation simulation method of the present invention enables more flexible updating of the random number than the conventional method.

[Effects of the Invention] As described above, in the reverberation simulation method of the present invention, the labor required for the processing for calculating the master DDM is significantly reduced. Further, the calculation amount for the calculation at the time of generating the simulated reverberation signal is also reduced, and the updating method of the random number can be flexibly set. Despite these features, the reverberant signal produced meets the required statistical properties.

In addition, when the movement of the platform is predetermined, as in the REVGEN open loop, the calculation of the master DDM is performed in advance, and only the reverberation generation part using random numbers is executed in real time. It is possible. Also in this case,
According to the method of the present invention, the random number generation is not required for the calculation of the master DDM, so that the calculation labor is greatly reduced.

[Brief description of drawings]

FIG. 1 is a schematic diagram of three regions in the sea considered in the embodiment of the reverberation simulation method according to the present invention, FIG. 2 is a block diagram in the case of the embodiment, and FIG. 3 shows a master DDM appearing in FIG. It is a block diagram showing a calculation method.

Claims (1)

[Claims] 1. F. O. M. Reverberation formula by theory [However, the subscript n represents an amount relating to each scatterer, and when the number of transmission beams is 1 and the number of reception beams is L, L-column vector with the i-th component being the reverberation observed in the i-th received beam of L, Δf _n : Doppler shift due to the motion of the platform where the acoustic sensor is arranged and the n-th scatterer, θ _n : Phase shift due to the nth scatterer, r _n : relative distance between the platform and the nth scatterer, _St (t): transmission waveform (0 at time t <0), c: speed of sound, Let L-column vector obtained from the scattering intensity of the nth scatterer and the beam pattern. ], The simulation formula of the Doppler density matrix (DDM) of the form suitable for the simulation [However, with the subscript m (m = 1,2, ...), the time axis is (0 = t _o
<T _l <... <t _m <...) section t _m-1 <t ≤ t _m
Represents the corresponding representative value in L-column vector each having independent complex normal white noise as a component, ξ _m (t): unit complex normal white noise, master DDM that is an L × L matrix Is Required from. Where α: absorption coefficient, r _m : ct _m / 2 Ω: solid angle centered on the platform, An L-column vector in which the i-th component is the product of the i-th received beam pattern in the m-th time section and the beam pattern at the time of transmission (both include the phase difference for each beam), a _m (Ω): Amplitude related to the scattering intensity of the scatterer (assuming a positive real number), ρ _m (f, Ω): Ω, probability density function for Doppler shift due to motion of the scatterer in the region corresponding to t, F _m ( Ω): Doppler shift due to platform motion in the solid angle Ω direction, Hermitian conjugation. ] And the reverberation simulation formula derived from this A reverberation simulation method characterized by generating a signal simulating underwater reverberation using.