CN117192556A - An accurate estimation method of underwater target distance based on normal wave mode group delay - Google Patents

Abstract

The invention discloses an accurate underwater target distance estimation method based on a simple wave mode group delay, and belongs to the technical field of signal and information processing. According to the method, the characteristic that the time delay difference of the adjacent two-order modes of the time-frequency distribution of the simple wave reaches the hydrophone is equal-difference series is utilized, the time value of each-order mode reaching the hydrophone is obtained through the time-frequency distribution of a received signal, the time delay difference of the last-order mode and the first-order mode is compared with the calculation value of an equal-difference series summation formula, the corresponding condition of the time value and the mode order is determined, and then each parameter is substituted into an underwater target distance calculation formula, so that the accurate estimation of the distance is realized. The method and the device can judge whether the time-frequency distribution of the received signal has the condition of modal missing, determine the specific order of the modes and realize accurate estimation of the underwater target distance by using all the modes.

Description

An accurate estimation method of underwater target distance based on normal wave mode group delay

Technical field

The invention belongs to the technical field of signal and information processing, relates to an accurate estimation method of underwater target distance based on normal wave mode group delay, and is suitable for sonar signal processing.

Background technique

Underwater target distance estimation has always been a key issue in the field of hydroacoustics. According to the normal wave theory of underwater sound propagation, the sound source will excite multi-order modes underwater. The sound pressure at the receiving point is the superposition of various modes, and the distance information of the sound source is included in the received signal.

Since the normal wave is a dispersive waveguide, each order of normal waves will produce inter-mode dispersion and intra-mode dispersion during the propagation process. This phenomenon can be observed by expressing the received signal on the time-frequency distribution diagram. The degree of dispersion is related to the sound source. Directly related to the relative distance of the receiving end. For time-frequency distribution technology, please refer to the document "Source depth estimation using modaldecomposition and time-frequency representations", which contains related theories about normal wave theory and time-frequency analysis. In a passive ranging method of shallow sea underwater sound sources based on a single hydrophone, Li Xiaoman et al. aimed at the passive ranging problem of broadband pulse sound sources in shallow sea waveguides and used any two-order normal wave mode based on the group delay theory. The relationship between the time delay difference of the state arriving at the hydrophone and its group velocity is used to estimate the distance of underwater targets.

When performing time-frequency processing on the received signal, due to the correlation between the normal wave mode energy, the sound source and the depth of the hydrophone, the energy of some modes of the sound source signal reaching the hydrophone may be close to zero. The modal dispersion curve obtained by frequency processing will also have corresponding missing situations. At this time, the modal order corresponding to the group velocity obtained by the acoustic calculation software will not be judged, which directly affects the accuracy of underwater target distance calculation.

Contents of the invention

In order to solve the above-mentioned problems in the prior art, the present invention provides an accurate estimation method of underwater target distance based on the normal wave mode group delay. This method uses the time-frequency distribution of the received data to determine whether there is a missing mode and determine The specific order of the modes, using all modes to achieve accurate estimation of underwater target distance.

The technical solution of the present invention is:

Utilizing the normal wave time-frequency distribution, the time delay difference between two adjacent modes arriving at the hydrophone is an arithmetic sequence characteristic. The time value of each mode arriving at the hydrophone is obtained through the time-frequency distribution of the received signal, and the last mode is Compare the time delay difference of the first-order mode and the calculated value of the arithmetic sequence summation formula to determine the correspondence between the time value and the mode order, and then substitute each parameter into the underwater target distance calculation formula to realize the distance calculation. Accurate estimate.

According to the normal wave theory, when the sound field propagates, the group velocity of each mode is different. The arrival time t _n (ω) of the n-th mode signal propagating to a distance r satisfies the following relationship:

t _n (ω)=r/c _gn (ω)

where c _gn (ω) is the group velocity of the n-th mode with frequency ω, so the time delay difference ΔT _mn (ω) between the n-th mode and the m-th mode can be expressed as:

In the above formula, c _gm (ω) is the group velocity of the m-th mode with frequency ω, so when the signal frequency is ω ₀ , the underwater sound source distance is calculated using the m-th and n-th mode group velocities. r _mn (ω ₀ ) can be expressed as:

Obviously, this formula is suitable for distance estimation of single-frequency pulse sound sources. For broadband signals with ω ₁ ~ ω ₂ frequency bands, in order to accurately estimate the distance, any two-order modes of each integer frequency point are selected and calculated sequentially. , so the normal wave with Nth order mode can be obtained An estimated distance, that is, the theoretical formula for passive ranging of underwater sound sources can be expressed as:

Since at the same frequency, the sequence {ΔT ₂₁ (ω), ΔT ₃₂ (ω),···,ΔT _N(N-1) (ω)} composed of the time differences of all adjacent two modes is approximately equal to Difference sequence, in the experiment, assuming that the M-order normal wave mode is obtained after short-time Fourier transform, calculate ΔT ₂₁ (ω), ΔT ₃₂ (ω),..., ΔT _M(M-1) (ω) respectively value, at this time, the delay difference U _M between the last mode and the first mode can be expressed as

U _M =t _M (ω)-t ₁ (ω)

where t _M and t ₁ are the time values for the last mode and the first mode to arrive at the hydrophone respectively, and then assume the sequence {ΔT ₂₁ (ω), ΔT ₃₂ (ω),···,ΔT _{M( M-1)} (ω)} is an arithmetic sequence, and the sum of each term S _M is calculated using the arithmetic sequence summation formula.

Compare S _M and U _M. If the two values are similar, it is considered that there is no missing mode at this time. Otherwise, it is judged that there is a missing mode in this calculation.

When it is found that there is a missing mode in the dispersion curve received by the hydrophone, the sub-terms of the original arithmetic sequence are still an arithmetic sequence, and the three consecutive items in the original arithmetic sequence are tested in sequence until the continuous one is found. The S ₄ and U ₄ of the three items are numerically approximate. At this time, the tolerance d of this sub-item can be calculated, and then the relationship between the time value t _n (ω) of each order mode to reach the hydrophone and the order n can be calculated. Each time value received by the hydrophone is substituted into the above relational expression, and its corresponding modal order can be determined. Since this method needs to use three consecutive delay differences that meet the conditions, it needs to be used when the receiving dispersion curve contains the continuous fourth-order mode excited by the signal.

Beneficial effects of the present invention: On the basis of using the normal wave group delay theory to calculate the underwater target distance, the present invention determines whether there is a mode loss in the time-frequency distribution of the received signal, and can accurately calculate the underwater target under the mode loss condition. distance.

Description of the drawings

Figure 1 is a flowchart of the present invention for accurately estimating the distance to an underwater target.

Figure 2 is a shallow sea waveguide environment model used in the present invention.

Figure 3 shows the mode missing situation of the received signal dispersion curve; among them, (a) is the correspondence between the curve and the order when the mode missing is not considered, (b) is the modal order and order after judging the mode missing. Dispersion curve corresponding situation.

Figure 4 is a comparison chart of distance calculation results when modal missing is considered and when missing is not considered.

Detailed ways

The specific embodiments of the present invention will be described in detail below with reference to the technical solutions and drawings.

As shown in Figure 1, the present invention proposes an accurate estimation method of underwater target distance based on normal wave mode group delay, which specifically includes the following steps:

Step 1: Obtain the time-frequency distribution of the signal received by a single hydrophone.

According to the normal wave theory, the signal propagated through the ocean waveguide and received at the hydrophone is expressed as:

Among them, j is an imaginary number, r is the horizontal distance between the receiving point and the sound source, z is the depth of the receiving point, z _s is the depth of the sound source, ξ _n (ω) is the horizontal component of the sound source wave number with frequency ω; Z _n ( z,ω) and Z _n (z _s ,ω) are the nth-order mode amplitude corresponding to the receiving point and the transmitting point respectively, ω ₁ is the minimum sound source frequency, ω ₂ is the maximum sound source frequency, S(ω) is the spectrum of the generated signal.

The received signal is subjected to time-frequency processing to obtain M dispersion curves of each order mode of the normal wave.

Step 2: Calculate the time delay difference ΔT ₂₁ (ω ₀ ), ΔT ₃₂ (ω ₀ ),..., ΔT _M(M-1) for all two adjacent dispersion curves to reach the hydrophone at frequency ω ₀ (ω ₀ ).

Conduct time-frequency analysis on the actually received time domain signal obtained in step ₁ , and obtain the time values t ₁ (ω ₀ ), t ₂ (ω ₀ ),·· ·, t _M (ω ₀ ); then, use the formula ΔT _{M (M-1)} (ω ₀ ) = t _M (ω ₀ )-t _M-1 (ω ₀ ) to calculate all two adjacent dispersion curves The time delay difference to reach the hydrophone is ΔT ₂₁ (ω ₀ ), ΔT ₃₂ (ω ₀ ),···,ΔT _M(M-1) (ω ₀ ).

Step 3: Use the sound field calculation software to obtain the group velocities c _g1 (ω ₀ ), c _g2 (ω ₀ ),..., c _gN (ω ₀ ) of all N-order modes of the received signal at this time.

Step 4: Calculate the difference U _M between the last time-frequency curve and the first time-frequency curve of the received signal time-frequency distribution to reach the hydrophone, and the delay difference sequence calculated using the arithmetic sequence summation formula {ΔT ₂₁ ( ω ₀ ),ΔT ₃₂ (ω ₀ ),…,ΔT _M(M-1) (ω ₀ )} and S _M :

U _M =t _M (ω ₀ )-t ₁ (ω ₀ )

Step 5: Calculate the relative deviation p=| _{SM -UM} |/ _UM between U _M and _SM .

Step 6: Judgment of termination conditions. test factor Assignment, judgment/> is established.

Step 7: If the termination conditions are met At this time, the sequence {ΔT ₂₁ (ω ₀ ), ΔT ₃₂ (ω ₀ ),…, ΔT _M(M-1) (ω ₀ )} is an approximate arithmetic sequence, and there is no modal missing in the time-frequency distribution of the received signal. If so, go to step 8; otherwise, it is concluded that there is a missing mode in the time-frequency distribution of the received signal, and go to step 10.

Step 8: Repeat steps 2 and 3 within the range of ω ₁ ~ ω ₂ , and then calculate the estimated distance r _mn (ω) using the m-th and n-th modes at different integer frequency points, where m is in {1,2 ,···,M-1}, n satisfies m<n≤M.

Step 9: Calculate the average of all r _mn (ω) in step 8

r is the final target distance estimate, and the algorithm terminates.

Step 10: Extract three consecutive terms of the initial delay difference sequence {ΔT ₂₁ (ω ₀ ), ΔT ₃₂ (ω ₀ ), ΔT ₄₃ (ω ₀ )}, {ΔT ₃₂ (ω ₀ ), ΔT ₄₃ (ω ₀ ),ΔT ₅₄ (ω ₀ )},…,{ΔT _(M-2)(M-3) (ω ₀ ),ΔT _(M-1)(M-2) (ω ₀ ),ΔT _{M(M- 1)} (ω ₀ )}, M-3 new delay difference sequences are obtained.

Step 11: Let X=4.

Step 12: Calculate the delay difference sequence {ΔT _(X-2)(X-3) (ω ₀ ),ΔT _(X-1)(X-2) (ω ₀ ),ΔT _X(X-1) (ω ₀ )} U ₄ , S ₄ .

U ₄ =t _X (ω ₀ )-t _X-3 (ω ₀ )

Step 13: Calculate the relative deviation p=|S ₄ -U ₄ |/U ₄ between U ₄ and S ₄ .

Step 14: Judgment of termination conditions. judge is established.

Step 15: If the termination conditions are not met Let X=X+1 and repeat steps 12 to 14. If the termination condition is met, use the searched {ΔT _(X-2)(X-3) (ω ₀ ),ΔT _(X-1)(X-2) (ω ₀ ),ΔT _X(X-1) (ω ₀ )}, calculate the tolerance d that satisfies this arithmetic sequence, and record the S ₄ obtained at this time.

Step 16: Substitute S ₄ , d, ΔT _X(X-1) (ω ₀ ) into the following formula:

ΔT _X(X-1) (ω ₀ )＝a ₁ +(x-1)d

Find the values of a ₁ and x, then ΔT _X(X-1) (ω ₀ ) is {ΔT ₂₁ (ω ₀ ),ΔT ₃₂ (ω ₀ ),···, The x-th _term of ΔT _{N(N-1) ( ω 0} )} is used to calculate _{the actual t} The above are the time t _x+1 (ω ₀ ) and t _x (ω ₀ ) for the x+1th and xth order modes of the signal to arrive at the hydrophone, respectively.

Step 17: Substitute a ₁ , d and t _x (ω ₀ ) Where C is a constant, the relationship between the time value t _n (ω ₀ ) and the order n of the n-th order mode of the normal wave arriving at the hydrophone is obtained.

Step 18: Substitute the time values t ₁ (ω ₀ ), t ₂ (ω ₀ ),..., t _M (ω ₀ ) of the initial dispersion curve into the relationship between t _n (ω ₀ ) and the order n respectively. , the corresponding real modal orders are obtained. At this time, the missing modal order can also be determined.

Step 19: Repeat steps 2 and 3 within the range of ω ₁ ~ ω ₂ , and then use the formula in step 8 to calculate the estimated distance r _mn (ω) using the m-th and n-th modes at different integer frequency points, where m Taking values in the range of {1, 2,···,N-1}, n satisfies m<n≤N. It should be noted that neither m nor n can take the missing modal order.

Step 20: Assuming that the number of missing modes is order k, calculate the average r of all r _mn (ω) in step 19:

That is the final target distance estimate.

Claims (3)

1. The accurate underwater target distance estimation method based on the normal wave mode group delay is characterized by comprising the following steps of:

step 1: acquiring time-frequency distribution of single hydrophone received signals

According to Jian Zhengbo theory, propagating through a marine waveguide at a hydrophone receives a signal expressed as:

wherein j is an imaginary number, r is a horizontal distance between the receiving point and the sound source, z is a depth of the receiving point, z _s Is the sound source depth, ζ _n (ω) is a horizontal component of the wave number of the sound source having a frequency ω; z is Z _n (Z, ω) and Z _n (z _s ω) are the corresponding n-th order modal amplitudes at the receiving and transmitting points, ω ₁ For minimum sound source frequency omega ₂ S (ω) is the occurrence signal spectrum for the maximum sound source frequency;

performing time-frequency processing on the received signal to obtain M dispersion curves of each order mode of the simple wave;

step 2: calculate at frequency omega ₀ The time delay difference delta T of reaching hydrophone of all adjacent two dispersion curves ₂₁ (ω ₀ )、ΔT ₃₂ (ω ₀ )、···、ΔT _M(M-1) (ω ₀ )；

Step 3: acquiring group velocity c of all N-order modes of the received signal at the moment _g1 (ω ₀ )、c _g2 (ω ₀ )、···、c _gN (ω ₀ )；

Step 4: respectively calculating the time value of the last time-frequency curve and the first time-frequency curve of the time-frequency distribution of the received signal reaching the hydrophoneDifference U _M And a delay-difference sequence { DeltaT ] calculated using an arithmetic-sequence summation formula ₂₁ (ω ₀ ),ΔT ₃₂ (ω ₀ ),…,ΔT _M(M-1) (ω ₀ ) Sum S of _M ：

U _M ＝t _M (ω ₀ )-t ₁ (ω ₀ )

Step 5: calculation U _M And S is equal to _M Relative deviation p= |s between _M -U _M |/U _M ；

Step 6: termination condition judgment, checking factor according to conditionsAssignment, judgment->Whether or not to establish;

step 7: if the termination condition is satisfiedThen the sequence { DeltaT } ₂₁ (ω ₀ ),ΔT ₃₂ (ω ₀ ),…,ΔT _M(M-1) (ω ₀ ) The time-frequency distribution of the received signals does not have modal missing condition, and the step 8 is carried out; otherwise, the mode loss exists in the time-frequency distribution of the received signal, and the step 10 is carried out;

step 8: at omega ₁ ~ω ₂ Repeating the steps 2 and 3 in a range, and then calculating estimated distances r of different integer frequency points by using the m-th order and the n-th order modes _mn (ω), where M is in the range {1,2, & gtM-1 } and n satisfies M < n.ltoreq.M:

step 9: calculate all r of step 8 _mn Mean value of (ω)

The final target distance estimated value is obtained;

step 10: extracting successive 3 items { DeltaT of initial delay difference sequence ₂₁ (ω ₀ ),ΔT ₃₂ (ω ₀ ),ΔT ₄₃ (ω ₀ )}、{ΔT ₃₂ (ω ₀ ),ΔT ₄₃ (ω ₀ ),ΔT ₅₄ (ω ₀ )}、…、{ΔT _(M-2)(M-3) (ω ₀ ),ΔT _(M-1)(M-2) (ω ₀ ),ΔT _M(M-1) (ω ₀ ) Obtaining M-3 new delay difference sequences;

step 11: let x=4;

step 12: calculate the delay difference array { DeltaT } _(X-2)(X-3) (ω ₀ ),ΔT _(X-1)(X-2) (ω ₀ ),ΔT _X(X-1) (ω ₀ ) U of } ₄ 、S ₄ ；

U ₄ ＝t _X (ω ₀ )-t _X-3 (ω ₀ )

Step 13: calculation U ₄ And S is equal to ₄ Relative deviation p= |s between ₄ -U ₄ |/U ₄ ；

Step 14: termination condition judgment, judgmentWhether or not to establish;

step 15: if the termination condition is not satisfiedLet x=x+1, repeat steps 12 to 14; if the termination condition is satisfied, the searched { DeltaT is used _(X-2)(X-3) (ω ₀ ),ΔT _(X-1)(X-2) (ω ₀ ),ΔT _X(X-1) (ω ₀ ) Calculating a tolerance d satisfying the series of differences, and recording S obtained at this time ₄ ；

Step 16: will S ₄ 、d、ΔT _X(X-1) (ω ₀ ) Substituted into the following formula:

ΔT _X(X-1) (ω ₀ )＝a ₁ +(x-1)d

obtaining a ₁ The value of x is DeltaT _X(X-1) (ω ₀ ) For { DeltaT in absence of mode of received signal ₂₁ (ω ₀ ),ΔT ₃₂ (ω ₀ ),···,ΔT _N(N-1) (ω ₀ ) The x-th term of }, now used to calculate DeltaT _X(X-1) (ω ₀ ) T of (2) _X (ω ₀ ) And t _X-1 (ω ₀ ) In practice, the time t for the x+1st order and the x order modes of the signal to reach the hydrophone is respectively _x+1 (ω ₀ ) And t _x (ω ₀ )；

Step 17: will a ₁ D and t _x (ω ₀ ) Substitution intoWherein C is a constant, when the n-th order mode of the simple wave reaches the hydrophoneIntermediate value t _n (ω ₀ ) A relation with the order n;

step 18: time value t of initial dispersion curve ₁ (ω ₀ )、t ₂ (ω ₀ )、…、t _M (ω ₀ ) Substituted into t _n (ω ₀ ) In the relation between the order n, the corresponding real mode orders are obtained, and the missing mode order can be determined at the moment;

step 19: at omega ₁ ~ω ₂ Repeating the steps 2 and 3 in a range, and then calculating the estimated distance r of different integer frequency points by using the equation of the step 8 and using the mode of the mth order and the nth order _mn (ω), where m is in the range {1,2, & gtN-1 } and N satisfies m < n.ltoreq.N;

step 20: let the number of missing modes be k-th order, calculate all r in step 19 _mn Average value r of (ω):

and r is the final target distance estimated value.

2. The accurate underwater target distance estimation method based on the reduced wave mode group delay according to claim 1, wherein the specific process of the step 2 is as follows: performing time-frequency analysis on the actually received time domain signal obtained in the step 1 to obtain frequency omega ₀ The time value t of each simple wave dispersion curve reaching the hydrophone ₁ (ω ₀ )、t ₂ (ω ₀ )、···、t _M (ω ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the Then, use the formula DeltaT _M(M-1) (ω ₀ )＝t _M (ω ₀ )-t _M-1 (ω ₀ ) Calculating the time delay difference delta T of all adjacent two dispersion curves reaching the hydrophone ₂₁ (ω ₀ ),ΔT ₃₂ (ω ₀ ),···,ΔT _M(M-1) (ω ₀ )。

3. The method for accurately estimating the distance between underwater targets based on the simple wave mode group delay according to claim 1 or 2, wherein in the step 19, neither m nor n can take the missing mode order.