AU2021102410A4

AU2021102410A4 - A ranging and speed measurement method by jointing hyperbolic frequency modulation and linear frequency modulation

Info

Publication number: AU2021102410A4
Application number: AU2021102410A
Authority: AU
Inventors: Caixia SONG
Original assignee: Qingdao Agricultural University
Current assignee: Qingdao Agricultural University
Priority date: 2021-04-23
Filing date: 2021-05-07
Publication date: 2021-09-23
Anticipated expiration: 2029-05-07
Also published as: CN113253280B; CN113253280A; LU500118B1

Abstract

OF THE DISCLOSURE The invention relates to a ranging speed method by jointing hyperbolic frequency modulation (HFM) and linear frequency modulation (LFM), mainly including the following steps: 1) a target moving toward a sonar direction; 2) first transmitting an HFM signal, and then transmitting an LFM signal, start-stop frequencies for transmitting HFM and LFM respectively being not restricted by a magnitude relationship, and band pulse widths of the two signals being independently configured; 3) finding time when matched filtering maximum values of the two signals appear, respectively; and 4) calculating a distance and a target speed between the target and the sonar system by using a delay relationship between the HFM signal and the LFM signal. This method using HFM + LFM combined signals for speed measurement and ranging eliminates ranging errors when ranging with a single HFM signal and a single LFM signal, and improves the speed measurement and ranging accuracies. HFM and LFM parameters can be independently configured, so that the method has a more flexible signal combination mode, reduces operation cost, and can support engineering applications. 1/14 DRAWINGS: Design function model and calculate Get the arrival time ti of HFM Signal processing Get the arrival time t2 of LFM Matched filtering Received echo -- -Calculate the target speed and distance Source 0- Transmit HM and LFM signal Target Fig. 1 3.2 3.15 3.1 3.05 2.9 ?1 2.85 -3w -20 -10 0 10 21 3w Speednm/s Fig. 2

Description

1/14

DRAWINGS:

Design function model and calculate

Get the arrival time ti of HFM

Signal processing Get the arrival time t2 of LFM

Matched filtering

Received echo -- -Calculate the target speed and distance

Source

0- TransmitHM and LFM signal Target

Fig. 1

3.2

3.15

3.1

3.05

?1 2.9

2.85 -3w -20 -10 0 10 21 3w

Speednm/s

Fig. 2

A RANGING AND SPEED MEASUREMENT METHOD BY JOINTING HYPERBOLIC FREQUENCY MODULATION AND LINEAR FREQUENCY MODULATION BACKGROUND OF THE INVENTION

[0001] 1. Technical Field

[0002] The invention relates to the field of signal processing technology, in particular to a ranging and speed measurement method by jointing hyperbolic frequency modulation and linear frequency modulation.

[0003] 2. Description of Related Art

[0004] Prior to pulse compression, detection distance and resolution are a pair of incompatible contradictions in waveform design, the two has to be compromised, and the emergence of pulse compression well solves this problem. In a large number of pulse compression signals, Linear Frequency Modulation (LFM) signals are very popular among signal designers with unique advantages and good pulse compression performance.

[0005] The advantages of LFM include:

[0006] 1) LFM has certain Doppler's tolerance, which is conducive to low-speed target detection;

[0007] 2) LFM is an equal-amplitude signal, which is conducive to improving the emission efficiency of a peak power limited system;

[0008] 3) High distance resolution can be obtained by increasing the bandwidth of LFM;

[0009] 4) In addition, the generation and processing technologies of LFM are relatively mature.

[0010] With the above advantages, LFM has been widely used in radar and sonar. However, since the fuzzy function of linear frequency modulation signals is of a diagonal blade type, Doppler mismatch is easily caused when the target speed is too high. This not only affects the detection performance, but also causes matched filtering delay. Generally, the distance of a target is determined according to the time of occurrence of a peak in the output of a detector. As a result, the measurement accuracy will be reduced, and a ranging error will be present.

[0011] Hyperbolic Frequency Modulation (HFM) signals are insensitive to Doppler, which just can make up the shortcomings of LFM. The traditional speed measurement method depends on a narrow-band filter bank to calculate a speed according to the radial speed of a target relative to sonar, and if the accuracy requirement of speed measurement is higher, Doppler filter banks required are increased in multiples, so the cost of this method is too high.

BRIEF SUMMARY OF THE INVENTION

[0012] In signal processing, a single LFM is coupled due to distance and speed, and the single LFM fails in accurate ranging and speed measurement due to the movement of a target, so a ranging error is present. HFM signals are insensitive to Doppler, which just can make up the shortcomings of LFM. However, a single HFM cannot achieve speed measurement, and also cannot achieve accurate ranging when the target moves.

[0013] Aiming at the above shortcomings of the existing single LFM and single HFM technologies, the invention proposes a ranging and speed measurement method (RSHL) by jointing hyperbolic frequency modulation and linear frequency modulation. The RSHL method using LFM + HFM combined signals for speed measurement and ranging can well estimate the distance and speed of a moving target, and can also eliminate a ranging error caused when ranging with a single HFM signal or LFM signal. On the other hand, combined LFM and HFM parameters can be independently configured, and pulse width and frequency band can be independently controlled and no longer depend on each other, which optimizes the form of transmitted signals, reduces operation cost, improves measurement accuracy, fully utilizes frequency band resources or pulse width resources, achieves a more flexible signal combination mode and can support engineering applications.

[0014] In order to achieve the above objective, the invention is achieved by the following technical solution.

[0015] A ranging and speed measurement method byjointing hyperbolic frequency modulation and linear frequency modulation, including the following steps:

[0016] Si) assuming that a target moves toward a sonar system, its movement speed v being positive;

[0017] S2) first transmitting an HFM signal, and then transmitting an LFM signal, start-stop frequencies for transmitting the HFM signal and the LFM signal respectively being not restricted by a magnitude relationship, and band pulse widths of the two signals being independently configured;

[0018] S3) finding time ti and t 2 when matched filtering maximum values of the HFM signal and the LFM signal appear, respectively; and

[0019] S4) calculating a distance R and a target speed v between the target and the sonar system by using a delay relationship between the HFM signal and the LFM signal.

[0020] Further, the start-stop frequencies for transmitting the HFM signal and the LFM signal

respectively being not restricted by a magnitude relationship in step S2) indicates that fho and

fi are not restricted by a magnitude relationship, that is, fho > fhi and fhl >= fho, where fho

and fi represent a start frequency and a stop frequency of the HFM signal, respectively; fo and are also not restricted by a magnitude relationship, that is, flo >= fl and fl >= fo, where fo and f1 represent a start frequency and a stop frequency of the LFM signal, respectively.

[0021] Further, the band pulse widths of the two signals being independently configured in step

S2) indicates that T, and T are not restricted by a magnitude relationship, that is, T, >= T and

T,>= T, where T, and T, represent the band pulse widths of the HFM signal and the LFM

signal, respectively.

[0022] Further, the delay relationship between the HFM signal and the LFM signal in step S4)

fh1 xT

indicates= -fhl , where Th and T, represent a delay when a peak of the HFM i fio + f 'T, 2 f, - fio signal appears and a delay when a peak of the LFM signal appears, respectively.

[0023] Further, the distance between the target and the sonar system in step S4) is

R c R 2 K=f- 1 Al hlIh h40 Xfllfl0 ihflO'h 1i -2I , where c=1500m/s represents the speed of

f11 _ fl0 _hl__ h0 sound in water.

(tl - t 2) c

[0024] Further, the target speed in step S4) is v = 2

fl h _I 2 1 fll - 4h0 fi1 - 0l

[0025] The present disclosure has the following advantages:

[0026] 1) The fuzzy function for frequency modulation signals has a coupling of distance and speed, resulting in a ranging deviation. The invention solves the problem of ranging error caused by delays by using different delays of LFM and HFM at different frequency bands and pulse widths.

[0027] 2) The speed is the best way to determine whether the target is present. Since a single frequency modulation signal cannot be used for obtaining an accurate time start and calculating a delay, combined LFM and HFM signals are used herein to jointly calculate the time start, thereby solving the problem of speed measurement.

[0028] 3) The advantages of the LFM and HFM signals are combined to solve the problem of speed measurement and achieve accurate ranging.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0029] In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the accompanying drawings required in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention, and a person of ordinary skill in the art can still derive other drawings according to these accompanying drawings without creative efforts.

[0030] Fig. 1 is a schematic diagram of a working process of an RSHL method according to an embodiment of the invention;

[0031] Fig. 2 is a schematic diagram of influence of a target speed on echo pulse width according to an embodiment of the invention;

[0032] Fig. 3 is a schematic diagram of influence of the target speed on echo spectrum according to an embodiment of the invention;

[0033] Figs. 4(a) to 4(f) show the output of matched filtering at various v under Simulation Environment 1 according to an embodiment of the invention;

[0034] Figs. 5(a) to 5(f) show the output of matched filtering at various v under Simulation Environment 2 according to an embodiment of the invention;

[0035] Figs. 6(a) to 6(f) show the output of matched filtering at various v under Simulation Environment 3 according to an embodiment of the invention;

[0036] Figs. 7(a) to 7(f) show the output of matched filtering at various v under Simulation Environment 4 according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0037] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0038] A ranging and speed measurement method using positive and negative linear frequency modulation signals, as shown in Fig. 1, includes the following steps:

[0039] S1) A target is assumed to move toward a sonar system, its movement speed v being positive.

[0040] S2) A hyperbolic frequency modulation (HFM) signal is first transmitted, and then a linear frequency modulation (LFM) signal is transmitted, start-stop frequencies for transmitting the HFM signal and the LFM signal respectively being not restricted by a magnitude relationship, and band pulse widths of the two signals being independently configured.

[0041] The start-stop frequencies for transmitting the HFM signal and the LFM signal

respectively being not restricted by a magnitude relationship indicates that fho and flare not

restricted by a magnitude relationship, that is, fho> fhi and fhl > fho, where fho andfill

represent a start frequency and a stop frequency of the HFM signal, respectively; fo and fl are also not restricted by a magnitude relationship, that is, flo >= fli and fli >= fo, where f, and fi represent a start frequency and a stop frequency of the LFM signal, respectively.

[0042] The band pulse widths of the two signals being independently configured indicates that

Th and T are not restricted by a magnitude relationship, that is, Th >Tand 7> h, where

Th and T represent the band pulse widths of the HFM signal and the LFM signal, respectively.

[0043] S3) Time ti and t2 when matched filtering maximum values of the HFM signal and the

LFM signal appear are respectively found.

[0044] S4) A distance R and a target speed v between the target and the sonar system are calculated by using a delay relationship between the HFM signal and the LFM signal.

[0045] (1) Doppler invariance of HFM

[0046] T, fho, fhi and Sh (t) are assumed to represent the pulse width of the HFM signal, the

start frequency of the HFM signal, the stop frequency of the HFM signal and the change of the

HFM signal over time, then sh ()Can be denoted by:

sh' flOin(h (1) L0 otherwise

where t' = fhI T , (0 = 2,efhot. f1 - fhoo

[0047] When fl > fo, the frequency modulation signal is referred to as a positive frequency

modulation signal, denoted by HFM*; and when flo > f, the frequency modulation signal is

referred to as a negative modulation signal, denoted by HFM-.

[0048] According to formula (1), the phase p of the HFM signal can be represented as:

fh1 T -t p=2,7 f 0 In fhoh(2) 41 - fhO fhI T( 41 - fhO

[0049] (q is derived to obtain an instantaneous frequency f(t)of the HFM signal, expressed as: d# £(t)= dt fh0fh1 (3) h1 h ( 1 h 0) Th

[0050] When the target moves at a speed v, the relative movement between the sonar and the target will change the transmitted signal having a pulse width of Th into a signal having a pulse width of at a receiving point after being reflected by the target, so that the pulse width of an echo is linearly compressed or stretched q times, as shown in Fig. 2, where q can be expressed as: C +V (4) c-v

[0051] Then, the received echo signal S,(t) is:

-j~rcff,, x xln I" fI f, 'i fl, e f/,jf,o 17

T s, (t)= t ^ (5)

0 otherwise

[0052] According to formula (2) and formula (3), the instantaneous frequency (t) of the

received echo is calculated as:

f(t)= fhOfhl

hl (fhl -fho) 77 Th

[0053] Since the HFM signal is insensitive to Doppler, the hyperbolic frequency modulation signal has Doppler invariance, the change rule of the instantaneous frequency of the received

signal is constant, and only the instantaneous frequency f(t) of the original signal is translated

by a time rh , as shown in Fig. 3.

[0054] Then, assume:

(t) = f, (t -rTa) (7)

[0055] Formula (3) and formula (6) are combined to solve a matched filtering delay Th caused

by Doppler of the target:

fhl(1-7)h (8)

fhl -fhO

[0056] Since c » v,-1 can be substituted by , and formula (8) can be expressed as:

fh1 x (- )XTh

fh~ Iho

[0057] Doppler characteristics of LFM

[0058] Let I(r,& ),r and6 represent a fuzzy function of Pulse Continuous Wave (PCW), the

delay of the fuzzy function Z(r,8 ) and the frequency shift of the LFM signal, where the PCW is

a single frequency signal, expressed as:

Fje(-)in (Tl-r ) (T-T S((1e) "" |<T, (10) (0 |r|>T

[0059] According to the transformation property of the fuzzy function, the fuzzy function

Z(r,) of the LFM can be expressed as:

e

|(0 r> T,

[0060] Where represents the degree of modulation of the LFM signal. Then, the following formula can be obtained:

sinZT(e -pz)(T -|z) rc(e - pr)(T -|rd) (12)

[0061] The section of e-pr = 0 is expressed as:

XZ1re) = T -r I- (13)

[0062] X (r,C) decreases linearly with the increase of T , and the pulse pressure delay T, caused

by the moving target is:

C (14)

[0063] When the sonar and the target move relatively, the received signal produces a frequency shift. The LFM has certain Doppler tolerance, and the instantaneous frequency of the received signal is only a delay, so a good peak can be obtained by matched filtering. However, the position of the peak has a delay, with a delay amount:

2v fio~fui T, ZI =v -x f+lx T (15) c 2 f(5 f -

[0064] Where fl and f, represent a start frequency and a stop frequency of the LFM signal,

respectively.

[0065] However, due to the delay T, caused by Doppler, the distance of the target is determined

according to the time of occurrence of a peak in the output of a detector. As a result, the measurement accuracy will be reduced, and a ranging error will be present.

[0066] Now, the distance and speed based on HFM + LFM combined signals of any configuration are solved.

[0067] After steps S) and S2), time ti and t2 when matched filtering maximum values of the

HFM signal and the LFM signal appear are respectively found, then: 2R ti = -+ rh (16) C

2R t2 - -R+ T, (17) C

[0068] According to formula (16) and formula (17), the speed v of the target and the distance R between the target and the sonar can be solved:

(tl - t 2) c v= 2

fhlIT1 2 /

fill Jho fi;- f; (18)

2 fihlfo fl +foT 2 fIT f~l flo fill- 40 (19)

[0069] Formula (18) and formula (19) are general forms of v and R, respectively. That is,

Th fhl f1 and fho f 0 are special forms of the RSHL method.

[0070] Four Simulation Environments are configured for performance evaluation of the RSHL method.

[0071] Simulation Environment 1: In the HFM signal, its start frequency, stop frequency and

pulse width are fh =2000Hz, fil=3000Hz, and Th =3s, respectively. In the LFM signal, its start frequency, stop frequency and pulse width are fo=OOOHz, fM=900Hz and T =4s, respectively.

For the HFM signal and the LFM signal, the same sampling frequency f =7000Hz is used, the

Signal to Noise Ratio (SNR) of the echo signal is -20 dB, and the distance between the target and the sonar source is 15 km.

[0072] Simulation Environment 2: In the HFM signal, its start frequency, stop frequency and

pulse width are fh0 =2000Hz, fil=2200Hz, and T, =4s, respectively. In the LFM signal, its start

frequency, stop frequency and pulse width are f o=1700Hz, fM=1100Hzand T=3s,

respectively. For the HFM signal and the LFM signal, the same sampling frequency fa=7000Hz

is used, the SNR of the echo signal is -20 dB, and the distance between the target and the sonar source is 15 km.

[0073] Simulation Environment 3: In the HFM signal, its start frequency, stop frequency and

pulse width are fh0 =2000Hz, fil=3000Hz, and T, =7s, respectively. In the LFM signal, its start

frequency, stop frequency and pulse width are f1100Hz, fM=1300Hz and T =3s,

[0074] Simulation Environment 4: In the HFM signal, its start frequency, stop frequency and

pulse width are fh0 =2100Hz, fil=2200Hz, and T, =1s, respectively. In the LFM signal, its start

frequency, stop frequency and pulse width are f0 =2200Hz, fM=2100Hz and T =1s,

respectively. For the HFM signal and the LFM signal, the same sampling frequency ft=7000Hz is used, the SNR of the echo signal is -20 dB, the gain of the SNR is10log(100*1)-16= 4dB, the SNR is a low SNR, and the distance between the target and the sonar source is 15 km.

[0075] Figs. 4(a) to 4(f) show performance analysis at different speeds based on Simulation

Environment 1. Table 1 gives numerical results of the RSHL method, the HFM signal and the LFM signal.

[0076] Taking Fig. 4(a) as an example, the performance of the RSHL method at different speeds v is analyzed. As can be seen from Fig. 4(a), after matched filtering in the RSHL method, the

maximum points respectively appear at ti=20.1834 and t2 = 19.2644. According to formula (19),

R=15.0056 km. According to formula (18), the value of v is 14.6649 m/s. The speed measurement error of RSHL is 2.234%, and the ranging error is 0.0373%. The ranging errors of HFM and LFM are respectively 0.917% and 3.678%. As can be seen from Table 1, compared to HFM and LFM, the ranging accuracies of RSHL are increased by 95.92875% and 98.98496%, respectively.

0 0 0 0 0 C) 0 0 00 0

Cd 00 ' 00 cl m cl 00 '.C 00 00 cl 6 0)- oR oR oR oR 06

00 000 00 0

cl It ' m0 f 00

0 000 00 0

00r- 00 0 od to mf 00 k

C)

;J00000

Cd Cl 00

0 0 0

00

C)

00 0l 0 C)~~~O ~ cj ),

[0078] Figs. 5(a) to 5(f) show performance analysis at different speeds based on Simulation Environment 2. Table 2 gives numerical results of the RSHL method, the HFM signal and the LFM signal.

[0079] Taking Fig. 5(a) as an example, the performance of the RSHL method at different speeds v is analyzed. As can be seen from Fig. 5(a), after matched filtering in the RSHL method, the

maximum points respectively appear at t1 =20.8983 and t 2 =19.8434. According to formula (19),

R=14.9912 km. According to formula (18), the value of v is 15.5126 m/s. The speed measurement error of RSHL is 3.4173%, and the ranging error is 0.0586%. The ranging errors of HFM and LFM are respectively 4.4915% and 0.783%. As can be seen from Table 2, compared to HFM and LFM, the ranging accuracies of RSHL are increased by 98.69383% and 92.50745%, respectively.

0 0 0 c/ C0 0 LC) 0 06

00 00tl l -0 cc

00) '.0 \

Cd tol Cl% It m~ 00 0

00 0 00 00 00

efD Cl kn~

Cd~ ~ccc ~ ~c CA

0- 0 0 * 00 0000

od 'f) C/) \~t ' :

00

0 0

0m

[0081] Figs. 6(a) to 6(f) show performance analysis at different speeds based on Simulation Environment 3. Table 3 gives numerical results of the RSHL method, the HFM signal and the LFM signal.

[0082] Taking Fig. 6(a) as an example, the performance of the RSHL method at different speeds v is analyzed. As can be seen from Fig. 6(a), after matched filtering in the RSHL method, the

maximum points respectively appear at t1 =20.4286 and t 2 = 20.2249. According to formula (19), R=14.9837 km. According to formula (18), the value of v is 16.0827 m/s. The speed measurement error of RSHL is 7.218%, and the ranging error is 0.1086%. The ranging errors of HFM and LFM are respectively 2.143% and 1.1245%. As can be seen from Table 3, compared to HFM and LFM, the ranging accuracies of RSHL are increased by 94.92923% and 90.33645%, respectively.

0 C 00 0- 0 0C

c/i ~cl 0 ooo

Ct \ elC I) \

0 00 00 00 00 0

~ Wf I) 00 Cl

0 0

00 0 00 0

00) C', 0N C cd ;:If C Clk c C=;

0 0 0 0 0' 0'

0 0 0 00 0m

00 00

000 00 0 (~0

[0084] Figs. 7(a) to 7(f) show performance analysis at different speeds based on Simulation

Environment 4. Table 4 gives numerical results of the RSHL method, the HFM signal and the LFM

signal.

[0085] Taking Fig. 7(a) as an example, the performance of the RSHL method at different speeds

v is analyzed. As can be seen from Fig. 7(a), after matched filtering in the RSHL method, the

maximum points respectively appear at ti=20.44 and t,=19.57. According to formula (19),

R=15.004 km. According to formula (18), the value of v is 14.9655 m/s. The speed measurement

error of RSHL is 0.23%, and the ranging error is 0.0273%. The ranging errors of HFM and LFM

are respectively 2.222% and 2.118%. As can be seen from Table 4, compared to HFM and LFM,

the ranging accuracies of RSHL are increased by 98.76988% and 98.70947%, respectively.

0 0 0 0 0 -~ ~ C) ~0 0 m t 0 00 - ~0C Cd

Cd 0 0 Cltn 0 >~ 00 00

00t0 00 00 Cd00 0fl 0 0

00 00 m~ mtCl \

=1 00 0

Cd

0 00 00 000m

00\~ 00 m

00

0 00 00

(D - l O

04- 000 0 0 0 0

00 0 '0 0 m. ~j) l 00 C '00

Cd

0'.

[0087] It should be understood that although the present description is described in terms of the implementation, not every implementation includes only one separate technical solution, and such a description mode of the description is merely for the sake of clarity. A person skilled in the art should take the description as a whole, and the technical solutions in all the embodiments may be appropriately combined to form other implementations that can be understood by a person skilled in the art.

Claims

What is claimed is:

1. A ranging and speed measurement method by jointing hyperbolic frequency modulation and linear frequency modulation, including the following steps: Si) assuming that a target moves toward a sonar system, its movement speed v being positive; S2) first transmitting an HFM signal, and then transmitting an LFM signal, start-stop frequencies for transmitting the HFM signal and the LFM signal respectively being not restricted by a magnitude relationship, and band pulse widths of the two signals being independently configured;

S3) finding time t, and t 2 when matched filtering maximum values of the HFM signal and the

LFM signal appear, respectively; and S4) calculating a distance R and a target speed v between the target and the sonar system by using a delay relationship between the HFM signal and the LFM signal.

2. The ranging and speed measurement method by jointing hyperbolic frequency modulation and linear frequency modulation according to claim 1, wherein start-stop frequencies for transmitting the HFM signal and the LFM signal respectively being not restricted by a

magnitude relationship in step S2) indicates that fho and arenot restricted by a magnitude

relationship, that is, fho > fhI and fhi > fho, where fh andfrepresentastartfrequency

and a stop frequency of the HFM signal, respectively; fl and fl are also not restricted by a

magnitude relationship, that is, flo >= f, and f, >= f , where fo and f, represent a start

frequency and a stop frequency of the LFM signal, respectively.

3. The ranging and speed measurement method by jointing hyperbolic frequency modulation and linear frequency modulation according to claim 1, wherein band pulse widths of

the two signals being independently configured in step S2) indicates that Th and n are not

restricted by a magnitude relationship, that is, T >= 7 and 7>= T , where Th and T, represent the band pulse widths of the HFM signal and the LFM signal, respectively.

4. The ranging and speed measurement method by jointing hyperbolic frequency modulation and linear frequency modulation according to claim 1, wherein delay relationship fhl xh between the HFM signal and the LFM signal in step S4) indicates - fh= - fhO ri f10 + f I T 2 f - fio where h and represent a delay when a peak of the HFM signal appears and a delay when a peak of the LFM signal appears, respectively.

5. The ranging and speed measurement method by jointing hyperbolic frequency modulation and linear frequency modulation according to claim 1, wherein distance between the

c fI h t1 -2 target and the sonar system in step S4) is R= - fi 1 2 fhl-fho f1liohh Il2 fhlTh0 w iInf watherhO. where c=1500m/s represents the speed of sound in water.