CN110082706A - It is a kind of based on delay inequality and phase difference and to be suitable for the asynchronous underwater single beacon method of clock - Google Patents

It is a kind of based on delay inequality and phase difference and to be suitable for the asynchronous underwater single beacon method of clock Download PDF

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CN110082706A
CN110082706A CN201910328805.1A CN201910328805A CN110082706A CN 110082706 A CN110082706 A CN 110082706A CN 201910328805 A CN201910328805 A CN 201910328805A CN 110082706 A CN110082706 A CN 110082706A
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clock
point
coordinate system
auv
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CN110082706B (en
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孙思博
张新宇
付进
王燕
梁国龙
王逸林
王晋晋
张光普
邱龙皓
齐滨
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Harbin Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S1/00—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith
    • G01S1/72—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith using ultrasonic, sonic or infrasonic waves
    • G01S1/76—Systems for determining direction or position line
    • G01S1/80—Systems for determining direction or position line using a comparison of transit time of synchronised signals transmitted from non-directional transducers or transducer systems spaced apart, i.e. path-difference systems
    • G01S1/807—Systems for determining direction or position line using a comparison of transit time of synchronised signals transmitted from non-directional transducers or transducer systems spaced apart, i.e. path-difference systems the synchronised signals being continuous waves or intermittent trains of continuous waves, the intermittency not being for the purpose of determining direction or position line and the transit times being compared by measuring the phase difference

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  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The invention discloses a kind of based on delay inequality and phase difference and is suitable for the asynchronous underwater single beacon method of clock, and method includes: that S100 establishes W-U coordinate system；The Monomial coefficient of S200 calculating signal phase difference；S300 is established and is solved navigation equation；The conversion of S400 coordinate system: being converted by coordinate system, obtains coordinate position of the AUV under target-based coordinate system.For the present invention in the case where clock is asynchronous, navigation accuracy is integrally higher than TDOA method, and can be comparable with the navigation accuracy of TOA (Time of Arrival) air navigation aid in part.

Description

It is a kind of based on delay inequality and phase difference and to be suitable for the asynchronous underwater single beacon of clock and lead Boat method
Technical field
The invention belongs to hydrolocation navigation fields, more particularly to one kind based on delay inequality and phase difference and when being suitable for The asynchronous underwater single beacon method of clock.
Background technique
Single beacon is a kind of novel navigation mode that recent two decades grow up, it only need to lay an acoustic marker just The navigation that a region can be achieved has and structures the formation compared to the navigation mode of traditional Long baselines (LBL) and ultra-short baseline (USBL) The advantages of simply and cost is relatively low.Single beacon not only needs to obtain the distance between acoustic marker and AUV information, it is also necessary to logical The sensor for crossing AUV itself carrying obtains remaining status information, such as depth (pressure sensor), speed (doppler speedmeter Gift of money for a friend going on a journey DVL) and acceleration (Inertial Measurement Unit IMU) etc., then by two kinds of information merged with the position to AUV into Row resolves.For single beacon, common algorithm is TOA (Time of Arrival- signal reaches the time) method and TDOA (Time Difference of Arrival- delay inequality) method.TOA method is suitable for the synchronous situation of clock, asynchronous in clock In the case of there are apparent theoretical defects.Although TDOA method is not limited by clock is asynchronous, its navigation accuracy is generally below TOA Method.Therefore, it finds and a kind of is suitable for that clock is asynchronous and the higher air navigation aid of precision is of great significance for single beacon.
Summary of the invention
The invention discloses a kind of based on delay inequality and phase difference and is suitable for the asynchronous underwater single beacon side of clock Method, to solve the problems, such as that existing air navigation aid precision is lower.
The Underwater acoustic signal processing method includes:
S100 establishes W-U coordinate system: in navigation model, it is straight to cross two navigation spots A and B institutes of acoustic marker O point work Vertical line, intersection point P establish two-dimensional Cartesian coordinate system W-U by origin of P point, and W axis and vector AB are in the same direction, and U axis and vector PO are same To；
The Monomial coefficient of S200 calculating signal phase difference: to the received CW or LFM signal of navigation spots A and B institute (continuous waveform- continuous wave signal, linear frequency modulation- linear FM signal), according to The secondary operation for carrying out envelope alignment, conjugate multiplication, phase unwrapping and linear fit (or quadratic fit), is extracted in fitting result Monomial coefficient；
S300 is established and is solved navigation equation: combining resulting delay inequality information and phase information, foundation exists about AUV The navigation equation of coordinate under W-U coordinate system, and it is solved；
The conversion of S400 coordinate system: being converted by coordinate system, obtains coordinate position of the AUV under target-based coordinate system.
Further, in the step s 100, specifically, acoustic marker is located at underwater O point, and periodically emit acoustical signal SO (t), two-dimensional Cartesian coordinate system X-Y is established by origin of O point, X-axis is directed toward due east direction, and Y-axis is directed toward direct north, in the coordinate In system, AUV moves to B point from A point with speed v, and AUV receives acoustical signal at A and B two and is denoted as S respectivelyA(t) and SB(t), Emission time of the forward position of two signals at acoustic marker it is known that be denoted as t respectivelyOAAnd tOB(acoustic marker clock)；Two signals Forward position can be obtained at the time of reaching AUV by Notch filter (CW signal) or matched filter (LFM signal) measurement, Notch filter is adaptive notch filter.It is denoted as t respectivelyRAAnd tRB(AUV clock)；The forward position of two signals is in aqueous medium Propagation delay be denoted as t respectivelyAAnd tB；The synchronous error of two clocks is tCE, then tOA、 tOB、tRA、tRB、tA、tBAnd tCEMeet Following formula:
tA+tCE=tRA-tOA (1)
tB+tCE=tRB-tOB (2)
It crosses O point and makees the straight vertical line of A and B two o'clock institute, intersection point is denoted as P point, is origin in tri- point institute of O, A and B using P point Two-dimensional Cartesian coordinate system W-U is established in determining plane, wherein W axis and vector AB are in the same direction, and U axis and vector PO are in the same direction, in W-U Under, the coordinate of O point is denoted as wO=[0, uO], the coordinate of A point is denoted as wA=[wA, 0], vector AB's is denoted as wAB=[wAB, 0], wAB Meet following formula:
wAB=| v | (tRB-tRA) (3)
Further, in step s 200, specifically, calculating the Monomial coefficient of signal phase difference,
The emitted signal S of acoustic markerO(t) CW pulse and LFM pulse, concrete form are generally are as follows:
In above formula, f0For the initial frequency of signal, k is the frequency modulation rate of LFM signal,
Under conditions of the length of OA and OB is far longer than the length of AB, signal S is receivedA(t) and SB(t) embody Formula is writeable are as follows:
In above formula, θAAnd θBThe respectively size of ∠ AOP and ∠ BOP, c are the velocity of sound,
Step S200 is specifically further comprising the steps of:
S210 is by signal SA(t) and SB(t) envelope is aligned, i.e., the forward position of two signals is moved to same time point. To signal S on the time shaft of AUVA(t) and SB(t) envelope alignment is carried out to obtain:
PA(t)=SA(t+tA) (7)
PB(t)=SB(t+tB) (8)
S220: to signal PA(t) and PB(t) conjugate multiplication is carried out:
In above formula:
S230 is actually calculating signal SAB(t) when phase information, due to the correlation function default in the instruments such as computer Signal phase be-π~π so that the phenomenon that phase winding occurs in final phase information, for subsequent data processing, need Carry out the operation of phase unwrapping.
For S240 when signal is CW or LFM signal, the phase information after twining to solution carries out linear fit or quadratic fit, and The Monomial coefficient β for extracting gained fitting function, the β known to formula meet following formula:
Further, in step S300, specifically, navigation equation is established and solves,
By formula and the delay inequality for knowing two signals are as follows:
tA-tB=(tRA-tOA)-(tRB-tOB) (11)
By tAAnd tBUse wA、wOAnd wABIt indicates, above formula can be rewritten as:
By the sin θ in formulaAAnd sin θBAlso w is usedA、wOAnd wABIt indicates, can obtain:
Joint type and, coordinate of the A and O two o'clock under W-U coordinate system can be solved.
Further, according to claim 1 a kind of based on delay inequality and phase difference and asynchronous suitable for clock Underwater list beacon method, which is characterized in that in step S400, specifically, coordinate system is converted,
In single beacon, generally with the coordinate x under X-Y coordinateA=[xA,yA] location information of AUV described, xA、wAAnd wOBetween relationship it is as follows:
In above formula, θvFor the angle of v and X-axis.
The beneficial effects of the present invention are: it is proposed by the present invention a kind of based on delay inequality and phase difference and to be suitable for clock different Underwater single beacon method of step, in the case where clock is asynchronous, navigation accuracy is integrally higher than TDOA method, and can be in part The navigation accuracy of TOA (Time of Arrival) air navigation aid is comparable.
Detailed description of the invention
Fig. 1 is single beacon navigation system schematic diagram；
Fig. 2 is of the invention a kind of based on delay inequality and phase difference and to be suitable for the asynchronous underwater single beacon side of clock The algorithm flow chart of method；
The actual motion track (straight path) and use PD method, TOA method and the obtained resolving of TDOA method that Fig. 3 is AUV Result schematic diagram；
Fig. 4 is the horizontal error calculation result signal of three kinds of air navigation aids (PD method, TOA method and TDOA method) of corresponding diagram 3 Figure；
The actual motion track (circular trace) and use PD method, TOA method and the obtained resolving of TDOA method that Fig. 5 is AUV Result schematic diagram；
Fig. 6 is the partial enlarged view of Fig. 5；
Fig. 7 is the horizontal error calculation result signal of three kinds of air navigation aids (PD method, TOA method and TDOA method) of corresponding diagram 5 Figure.
Specific embodiment
Technical solution in the embodiment of the present invention that following will be combined with the drawings in the embodiments of the present invention carries out clear, complete Ground description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this Embodiment in invention, every other reality obtained by those of ordinary skill in the art without making creative efforts Example is applied, shall fall within the protection scope of the present invention.
Referring to shown in Fig. 2, the present invention provides the invention is realized by the following technical scheme: one kind being based on delay inequality and phase Potential difference and the underwater single beacon method asynchronous suitable for clock,
The Underwater acoustic signal processing method includes:
S100 establishes W-U coordinate system: in navigation model, it is straight to cross two navigation spots A and B institutes of acoustic marker O point work Vertical line, intersection point P establish two-dimensional Cartesian coordinate system W-U by origin of P point, and W axis and vector AB are in the same direction, and U axis and vector PO are same To；
The Monomial coefficient of S200 calculating signal phase difference: to received CW (or LFM) signal of navigation spots A and B institute, successively The operation of envelope alignment, conjugate multiplication, phase unwrapping and linear fit or quadratic fit is carried out, is extracted primary in fitting result Term coefficient；
S300 is established and is solved navigation equation: combining resulting delay inequality information and phase information, foundation exists about AUV The navigation equation of coordinate under W-U coordinate system, and it is solved；
The conversion of S400 coordinate system: being converted by coordinate system, obtains coordinate position of the AUV under target-based coordinate system.
In the preferred embodiment of this part, in the step s 100, specifically, acoustic marker is located at underwater O point, and periodically Emit acoustical signal SO(t), two-dimensional Cartesian coordinate system X-Y is established by origin of O point, X-axis is directed toward due east direction, and Y-axis is directed toward due north Direction, in the coordinate system, AUV moves to B point from A point with speed v, and AUV receives acoustical signal at A and B two and is denoted as respectively SA(t) and SB(t), emission time of the forward position of two signals at acoustic marker it is known that be denoted as t respectivelyOAAnd tOB(when acoustic marker Clock)；It the forward position of two signals can be by Notch filter (CW signal) or matched filter (LFM letter at the time of reaching AUV Number) measurement obtain, be denoted as t respectivelyRAAnd tRB(AUV clock)；The forward position of two signals is denoted as respectively in the propagation delay of aqueous medium tAAnd tB；The synchronous error of two clocks is tCE, then tOA、tOB、tRA、tRB、tA、tBAnd tCEMeet following formula:
tA+tCE=tRA-tOA (1)
tB+tCE=tRB-tOB (2)
It crosses O point and makees the straight vertical line of A and B two o'clock institute, intersection point is denoted as P point, is origin in tri- point institute of O, A and B using P point Two-dimensional Cartesian coordinate system W-U is established in determining plane, wherein W axis and vector AB are in the same direction, and U axis and vector PO are in the same direction, in W-U Under, the coordinate of O point is denoted as wO=[0, uO], the coordinate of A point is denoted as wA=[wA, 0], vector AB's is denoted as wAB=[wAB, 0], wAB Meet following formula:
wAB=| v | (tRB-tRA) (3)
Further, in step s 200, specifically, calculating the Monomial coefficient of signal phase difference,
The emitted signal S of acoustic markerO(t) CW pulse and LFM pulse, concrete form are generally are as follows:
In above formula, f0For the initial frequency of signal, k is the frequency modulation rate of LFM signal,
Under conditions of the length of OA and OB is far longer than the length of AB, signal S is receivedA(t) and SB(t) embody Formula is writeable are as follows:
In above formula, θAAnd θBThe respectively size of ∠ AOP and ∠ BOP, c are the velocity of sound,
Step S200 is specifically further comprising the steps of:
S210 is by signal SA(t) and SB(t) envelope is aligned, i.e., the forward position of two signals is moved to same time point. To signal S on the time shaft of AUVA(t) and SB(t) envelope alignment is carried out to obtain:
PA(t)=SA(t+tA) (7)
PB(t)=SB(t+tB) (8)
S220: to signal PA(t) and PB(t) conjugate multiplication is carried out:
In above formula:
S230 is actually calculating signal SAB(t) when phase information, due to the correlation function default in the instruments such as computer Signal phase be-π~π so that the phenomenon that phase winding occurs in final phase information, for subsequent data processing, need Carry out the operation of phase unwrapping.
For S240 when signal is CW or LFM signal, the phase information after twining to solution carries out linear fit or quadratic fit, and The Monomial coefficient β for extracting gained fitting function, the β known to formula meet following formula:
Further, in step S300, specifically, navigation equation is established and solves,
By formula and the delay inequality for knowing two signals are as follows:
tA-tB=(tRA-tOA)-(tRB-tOB) (11)
By tAAnd tBUse wA、wOAnd wABIt indicates, above formula can be rewritten as:
By the sin θ in formulaAAnd sin θBAlso w is usedA、wOAnd wABIt indicates, can obtain:
Joint type and, coordinate of the A and O two o'clock under W-U coordinate system can be solved.
It is a kind of based on delay inequality and phase difference and to be suitable for the asynchronous underwater single beacon method of clock, in step S400 In, specifically, coordinate system is converted,
In single beacon, generally with the coordinate x under X-Y coordinateA=[xA,yA] location information of AUV described, xA、wAAnd wOBetween relationship it is as follows:
In above formula, θvFor the angle of v and X-axis.
Implement example one:
It is CW signal, signal center frequency f that acoustic marker, which emits signal,0For 5000Hz, signal pulsewidth is 0.5s, signal transmitting Period is 10s, and velocity of sound c is 1500m/s, clock synchronous error tCEFor 5ms.Acoustic marker is located at origin, is 0 in acoustic marker clock At the moment, acoustic marker starts to emit signal, while AUV is from x0Start at the m of=[- 500, -300] with speed v=[5,0] m/s boat Row, AUV hours underway are 200s, receive 251 frame signals altogether.Acoustic marker location error, latency measurement error, acoustic velocity measutement miss Difference, INS error and Monomial coefficient error obey the Gaussian Profile that mean value is zero, corresponding standard deviation be respectively 3m, 0.5ms, 3m/s, 0.2% and 0.04rad/s.
For simplicity, the present invention is referred to PD (Phase Difference) method below.Fig. 3 is the practical fortune of AUV Dynamic rail mark and use PD method, TOA method and the obtained calculation result of TDOA method, wherein the solid line of black is the practical fortune of AUV Dynamic rail mark, diamond shape represent the calculation result of PD method, and equilateral triangle represents the calculation result of TOA method, and up-side down triangle represents TDOA method Calculation result；Fig. 4 compares the navigation error of above-mentioned three kinds of methods, and the meaning of each shape is identical as Fig. 3 in figure, Each shape represents actual horizontal error.From Fig. 3 and Fig. 4 it can be concluded that
1) in entire hours underway section, the navigation accuracy of PD method is higher than TDOA method；
2) in this section of section of 50s-150s, the navigation accuracy of PD method can be comparable with TOA method.
Implement example two:
It is LFM signal that acoustic marker, which emits signal, and signal pulsewidth is 0.5s, and signal tuning range is 4500Hz-5000Hz, letter Number transmit cycle is 10s, and velocity of sound c is 1500m/s, clock synchronous error tCEFor 5ms.Acoustic marker is located at origin, in acoustic marker At the time of clock is 0, acoustic marker starts to emit signal, while AUV makees radius by the center of circle of origin as the circular motion of 300m, speed Size is 5m/s, and entire track constitutes a complete circle.Acoustic marker location error, latency measurement error, acoustic velocity measutement error, INS error and Monomial coefficient error obey the Gaussian Profile that mean value is zero, corresponding standard deviation be respectively 1.8m, 0.3ms, 1.5m/s, 0.1% and 0.02rad/s.
Fig. 5 is actual motion track and the use PD method, TOA method and the obtained calculation result of TDOA method of AUV, wherein The solid line of black is the actual motion track of AUV, and diamond shape represents the calculation result of PD method, and equilateral triangle represents the resolving of TOA method As a result, up-side down triangle represents the calculation result of TDOA method；Fig. 6 is the partial enlarged view of Fig. 5；Fig. 7 leads above-mentioned three kinds of methods Boat error compares, and the meaning of each shape is identical as Fig. 6 in figure, and each shape represents actual horizontal error.From figure 5, Fig. 6 and Fig. 7 can be seen that in entire hours underway section, and the navigation accuracy of PD method is higher than TDOA method；And its navigation accuracy can It is comparable with TOA method.

Claims (5)

  1. Based on delay inequality and phase difference and it is suitable for the asynchronous underwater single beacon method of clock 1. a kind of, which is characterized in that The Underwater acoustic signal processing method includes:
    S100 establishes W-U coordinate system: in navigation model, crosses acoustic marker O point and makees two straight vertical lines of navigation spots A and B institute, Intersection point is P, establishes two-dimensional Cartesian coordinate system W-U by origin of P point, W axis and vector AB are in the same direction, and U axis and vector PO are in the same direction；
    The Monomial coefficient of S200 calculating signal phase difference: it to the received CW or LFM signal of navigation spots A and B institute, is successively wrapped A term system in fitting result is extracted in the operation of network alignment, conjugate multiplication, phase unwrapping and linear fit or quadratic fit Number；
    S300 is established and is solved navigation equation: being combined resulting delay inequality information and phase information, is established about AUV in W-U The navigation equation of coordinate under coordinate system, and it is solved；
    The conversion of S400 coordinate system: being converted by coordinate system, obtains coordinate position of the AUV under target-based coordinate system.
  2. A kind of based on delay inequality and phase difference and it be suitable for the asynchronous underwater single beacon of clock 2. according to claim 1 and lead Boat method, which is characterized in that in the step s 100, specifically, acoustic marker is located at underwater O point, and periodically emit acoustical signal SO(t), two-dimensional Cartesian coordinate system X-Y is established by origin of O point, X-axis is directed toward due east direction, and Y-axis is directed toward direct north, in the seat In mark system, AUV moves to B point from A point with speed v, and AUV receives acoustical signal at A and B two and is denoted as S respectivelyA(t) and SB(t), Emission time of the forward position of two signals at acoustic marker it is known that be denoted as t respectivelyOAAnd tOB, tOAAnd tOBFor acoustic marker clock；Two The forward position of a signal can be measured at the time of reaching AUV by Notch filter (CW signal) or matched filter (LFM signal) It arrives, is denoted as t respectivelyRAAnd tRB(AUV clock)；The forward position of two signals is denoted as t in the propagation delay of aqueous medium respectivelyAAnd tB；Two The synchronous error of a clock is tCE, then tOA、tOB、tRA、tRB、tA、tBAnd tCEMeet following formula:
    tA+tCE=tRA-tOA (1)
    tB+tCE=tRB-tOB (2)
    It crosses O point and makees the straight vertical line of A and B two o'clock institute, intersection point is denoted as P point, is origin determined by 3 points of O, A and B using P point Two-dimensional Cartesian coordinate system W-U is established in plane, wherein W axis and vector AB are in the same direction, and U axis and vector PO are in the same direction, at W-U, O point Coordinate be denoted as wO=[0, uO], the coordinate of A point is denoted as wA=[wA, 0], vector AB's is denoted as wAB=[wAB, 0], wABUnder satisfaction Formula:
    wAB=| v | (tRB-tRA) (3)
  3. A kind of based on delay inequality and phase difference and it be suitable for the asynchronous underwater single beacon of clock 3. according to claim 1 and lead Boat method, which is characterized in that in step s 200, specifically, the Monomial coefficient of signal phase difference is calculated,
    The emitted signal S of acoustic markerO(t) CW pulse and LFM pulse, concrete form are generally are as follows:
    In above formula, f0For the initial frequency of signal, k is the frequency modulation rate of LFM signal,
    Under conditions of the length of OA and OB is far longer than the length of AB, signal S is receivedA(t) and SB(t) expression can It is written as:
    In above formula, θAAnd θBThe respectively size of ∠ AOP and ∠ BOP, c are the velocity of sound,
    Step S200 is specifically further comprising the steps of:
    S210 is by signal SA(t) and SB(t) envelope is aligned, i.e., the forward position of two signals is moved to same time point.? To signal S on the time shaft of AUVA(t) and SB(t) envelope alignment is carried out to obtain:
    PA(t)=SA(t+tA) (7)
    PB(t)=SB(t+tB) (8)
    S220: to signal PA(t) and PB(t) conjugate multiplication is carried out:
    In above formula:
    S230 is actually calculating signal SAB(t) when phase information, due to the letter of the correlation function default in the instruments such as computer Number phase is-π~π so that there is the phenomenon that phase winding in final phase information, for subsequent data processing, need into The operation of row phase unwrapping.
    For S240 when signal is CW or LFM signal, the phase information after twining to solution carries out linear fit or quadratic fit, and extracts The Monomial coefficient β of gained fitting function, the β known to formula meet following formula:
  4. A kind of based on delay inequality and phase difference and it be suitable for the asynchronous underwater single beacon of clock 4. according to claim 1 and lead Boat method, which is characterized in that in step S300, specifically, navigation equation is established and solves,
    By formula and the delay inequality for knowing two signals are as follows:
    tA-tB=(tRA-tOA)-(tRB-tOB) (11)
    By tAAnd tBUse wA、wOAnd wABIt indicates, above formula can be rewritten as:
    By the sin θ in formulaAAnd sin θBAlso w is usedA、wOAnd wABIt indicates, can obtain:
    Joint type and, coordinate of the A and O two o'clock under W-U coordinate system can be solved.
  5. A kind of based on delay inequality and phase difference and it be suitable for the asynchronous underwater single beacon of clock 5. according to claim 1 and lead Boat method, which is characterized in that in step S400, specifically, coordinate system is converted,
    In single beacon, generally with the coordinate x under X-Y coordinateA=[xA,yA] location information of AUV, x describedA、wA And wOBetween relationship it is as follows:
    In above formula, θvFor the angle of v and X-axis.
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CN110865338A (en) * 2019-11-22 2020-03-06 哈尔滨工程大学 Unknown periodic acoustic beacon high-precision positioning method based on underwater mobile platform
CN110865338B (en) * 2019-11-22 2022-10-14 哈尔滨工程大学 Unknown periodic acoustic beacon high-precision positioning method based on underwater mobile platform
CN111721284A (en) * 2020-03-04 2020-09-29 哈尔滨工程大学 SINS/USBL combined navigation positioning method in passive mode
CN111721284B (en) * 2020-03-04 2021-08-31 哈尔滨工程大学 SINS/USBL combined navigation positioning method in passive mode
CN113702907A (en) * 2021-08-09 2021-11-26 哈尔滨工程大学 Underwater single beacon navigation method based on propagation delay of direct sound and primary sea surface reflected sound

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