CN107990891A - Underwater robot Combinated navigation method based on Long baselines and beacon on-line proving - Google Patents

Underwater robot Combinated navigation method based on Long baselines and beacon on-line proving Download PDF

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CN107990891A
CN107990891A CN201610944484.4A CN201610944484A CN107990891A CN 107990891 A CN107990891 A CN 107990891A CN 201610944484 A CN201610944484 A CN 201610944484A CN 107990891 A CN107990891 A CN 107990891A
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CN107990891B (en
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王轶群
李波
刘健
赵宏宇
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Shenyang Institute of Automation of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The present invention relates to the Combinated navigation method based on the positioning of Long baselines acoustics and beacon on-line proving, realizes the underwater navigation positioning of underwater robot.The present invention includes：Using the single beacon oblique distance measured values of AUV at different moments, each Long baselines beacon position of on-line proving is realized；The Kalman filter based on the positioning of Long baselines acoustics and inertial navigation data fusion is established, calculates the location estimation of integrated navigation.This method can effective integration Long baselines positioning and inertial navigation data, there is higher navigation and positioning accuracy；This method transplanting is convenient, can be adapted for various submariner device underwater navigation positioning.

Description

Underwater robot Combinated navigation method based on Long baselines and beacon on-line proving
Technical field
The present invention relates to underwater robot technical field, more particularly to a kind of unmanned autonomous underwater vehicles (abbreviation AUV) The underwater robot Combinated navigation method based on Long baselines acoustic fix ranging and beacon on-line proving technology, realize that AUV is high-precision under water Spend integrated navigation and location.
Background technology
In being applied in ocean, underwater robot plays an increasingly important role.Underwater robot is divided into two classes：One kind is Distance type has cable underwater robot (abbreviation ROV), and one kind is unmanned autonomous underwater vehicles (abbreviation AUV).ROV needs the water surface female Ship is supported, while is limited be subject to cable length, its operation is apart from limited, general only hundreds of meters；And the self-contained energy of AUV Source, may be located remotely from lash ship, and operating range reaches tens kilometers of even kilometers up to a hundred.So the research of AUV is increasingly subject to various countries Attention, the development of AUV represents the developing direction of following underwater robot.And underwater integrated navigation and location technology is AUV hairs The key of exhibition and the bottleneck restricted.Because the particularity of underwater environment, no image of Buddha land directly uses differential GPS navigator fix, So the positioning of underwater navigation at present mainly has two classes：Inertial navigation data and hydrolocation navigation data.Inertial navigation data is short Positioning accuracy is high during voyage, but as the increase of voyage, the navigation error of accumulation reduce the navigation accuracy of system；Hydrolocation Navigation data is needed with Long baselines positioning accuracy highest, the basic matrix length of Long baselines alignment system (abbreviation LBL) generally in several kms The beacon (4 beacons generally being laid, wherein 1 beacon is backup beacon) of more than 3 is laid in seabed, by measuring AUV The distance between beacon determines the position of AUV.The advantages of Long baselines position is that positioning accuracy is higher, and position error is not Accumulated with the increase of time, efficiently solve the accumulation navigation error problem of inertial navigation system, so extensively will now Long baselines data and inertial navigation data composition integrated navigation system, realize that High Precision Underwater positions.But Long baselines positioning Using there is also some problems, first, it is subject to marine environment to disturb, noise usually occurs in Long baselines positioning, cannot be used directly for Navigator fix；Second, Long baselines beacon stated accuracy is higher under shallow water operating mode, but Long baselines beacon calibration essence under deep water operating mode Spend less desirable.Long baselines need to lay beacon before use and use lash ship progress beacon position calibration, and deepwater environment Middle underwater sound complicated condition, especially more than 2000 meters, lash ship calibration Long baselines beacon calibration result with the increase of the depth of water and by Gradually decline, influence the positioning accuracy of Long baselines alignment system, can not meet the requirement of High Precision Underwater positioning.In deep water operating mode Under, how Long baselines location data and inertial navigation data valid data to be merged, that is, suppress Long baselines positioning noise, and can press down System navigation accumulated error, realizes that High Precision Underwater positions, and is a problem of deep water integrated navigation primary study；How depth is reduced Influence of the Long baselines beacon calibrated error to navigation system under water condition, and the technology urgently to be resolved hurrily of deep water integrated navigation are difficult Topic.
The content of the invention
In order to solve the problems, such as the positioning of filtering Long baselines and suppress navigation system accumulated error, while reduce beacon calibration and miss Influence of the difference to navigator fix, the technical problem to be solved in the present invention is propose that one kind will be based on the positioning of Long baselines acoustics and beacon The novel compositions air navigation aid of on-line proving, the positioning of effective integration Long baselines and inertial navigation location data, filtering Long baselines are determined Interference of the phase perturbation to integrated navigation and location, reduces the accumulated error of navigation system, while on-line proving beacon position, reduces Influence of the calibrated error that lash ship calibration beacon produces under deep water conditions to navigation accuracy.
The used to achieve the above object technical solution of the present invention is：It is underwater based on Long baselines and beacon on-line proving Robot Combinated navigation method, comprises the following steps：
Using the single beacon oblique distance measured values of AUV at different moments, each beacon position of on-line proving obtains each beacon Calibrated error；
Estimate according to calibrated error, by the measurement equation and the predictive equation of inertial navigation that are positioned based on Long baselines acoustics The AUV positions of integrated navigation.
Calibrated error is obtained by following formula
[dxi,dyi]T=A-1B
Wherein,
The AUV positions of t moment, t+1 moment and t+2 moment are respectively (xt,yt,zt),(xt+1,yt+1,zt+1) and (xt+2, yt+2,zt+2), t moment, the oblique distance of t+1 moment and t+2 moment AUV to beacon i are respectively di_t,di_t+1,di_t+2；
T moment, the horizontal distance of t+1 moment and t+2 moment AUV to beacon i are respectively ri_t,ri_t+1,ri_t+2；T moment, The horizontal distance of t+1 moment and t+2 moment AUV to beacon i are estimatedThe lash ship of beacon i is initially marked Positioning is set to (xi,yi,zi)。
It is described according to calibrated error, measurement equation and the predictive equation of inertial navigation by being positioned based on Long baselines acoustics The position of estimation integrated navigation comprises the following steps：
1) the Long baselines position location Z of t moment AUV is calculated according to calibrated errort(xt,yt)；
2) measurement equation is established according to AUV Long baselines position location；
3) predictive equation for establishing integrated navigation obtains the predicted position X of AUVt(xt,yt)；
4) according to the Long baselines position location Z of AUVt(xt,yt) and predicted position Xt(xt,yt) obtain the AUV of integrated navigation Position.
The Long baselines position location Z that t moment AUV is calculated according to calibrated errort(xt,yt), comprise the following steps： [xt,yt]T=A-1(R-D)
Wherein,
The horizontal distance of t moment AUV to beacon 1,2,3 is r1_t,r2_t,r3_t；The lash ship initial alignment position of beacon i is (xi,yi,zi)；The location estimation of beacon 1,2,3 is (x1+dx1,y1+dy1), (x2+dx2,y2+dy2) and (x3+dx3,y3+dy3), dxi,dyiFor calibrated error；
[the x that above formula obtainst,yt]TLong baselines position location Z as t moment AUVt(xt,yt) column vector represent.
The measurement equation is
Wherein, VtIt is the measurement noise of t moment beacon；Represent the measurement expression formula of t moment；When being t The true longitude and true latitude of AUV when carving measurement；Ht=[1,1]TIt is the Jacobin matrix for measuring equation linearization approximate.
The predictive equation is
Wherein, ut, ψ, θ, φ is speed, course angle, Angle of Trim and the roll angle of t moment AUV, Ut=[ut, ψ] and it is system Input matrix；Δ T is the time interval from t-1 moment to t moment；Ht=[1,1]TIt is the Jacobin matrix for measuring equation；System The variance matrix of input noise is Qt；xt-1And yt-1Represent t-1 moment AUV in longitude and Position Latitude respectively；Pt,t-1When representing t Carve the prediction variance of prediction AUV positions；Pt-1Represent that the t-1 moment estimates the estimate variance of AUV positions；It is euler transformation matrix； ReIt is the minor axis radius of the earth；E is earth rotation flattening of ellipsoid.
The Long baselines position location Z according to AUVt(xt,yt) and predicted position Xt(xt,yt) obtain the position of integrated navigation Estimation is put to obtain by following formula
Wherein, t moment AUV estimated locationsWithThe estimated location longitude of t moment AUV is represented respectively And latitude；RtRepresent that t moment measures the variance matrix of noise, h (Xt)=HtXt+Vt。
Behind the position of the estimation integrated navigation, navigation essence is estimated by calculating the location estimation variance of integrated navigation Degree：Wherein, I is unit matrix, PtRepresent t moment AUV integrated navigations Location estimation variance.
The invention has the advantages that and advantage：
1. can either be had using Integrated Navigation Algorithm relative to traditional Long baselines positioning and inertial navigation data, this method Interference of the effect filtering Long baselines positioning noise to integrated navigation, while effectively suppress the accumulation navigation error of integrated navigation, improve AUV Underwater Navigation precision.
2. traditional lash ship calibration deep water Long baselines beacon position exists as the increase of the depth of water, stated accuracy are gradually reduced The problem of.And this method demarcates position as primary quantity using lash ship, beacon stated accuracy is improved by on-line proving technology, reduces letter Influence of the calibrated error to navigation accuracy is marked, improves the Underwater Navigation precision of AUV.
3. have a wide range of application.The present invention can be applied not only to AUV underwater navigations, can be also used for the water of other submariner devices Lower navigation.
4. for effective integration Long baselines location data and inertial navigation data, while beacon calibrated error is reduced to navigation Integrated navigation technology based on Long baselines and beacon on-line proving technology are combined by the influence of positioning, the present invention, not only effectively Long baselines location data is filtered, and inhibits the accumulated error of navigation system；On-line proving Long baselines beacon position, reduces Influence of the calibrated error to navigation accuracy, improves the precision of AUV integrated navigation location estimations.
Brief description of the drawings
Fig. 1 is the composition schematic diagram of the present invention.
Embodiment
The present invention is described in further detail with reference to the accompanying drawings and embodiments.
The hardware requirement of the present invention is an AUV, and depth gauge is carried on AUV and is fathomed, and carries Doppler measurement and dives device Present speed, carry the latent device of attitude angle transducer measurement current course angle, Angle of Trim and roll angle, carry hydroacoustic range finder AUV is measured to the distance of Long baselines beacon, 4 fixed Long baselines beacons are laid in seabed.
As shown in Figure 1, AUV under water operation when, automatically by the speed of Doppler measurement, heading sensor measure speed Degree and AUV calculate the submarine site of AUV automatically in real time into the distance input Integrated Navigation Algorithm of beacon.
4 anchors tie up to the acoustic marker and an AUV in seabed, installed wherein on AUV subaqueous sound ranging device, Doppler log, Attitude angle transducer and depth gauge, wherein attitude angle transducer measurement AUV current course angles, Angle of Trim and roll angle, Doppler Tachometer measures AUV present speeds, and subaqueous sound ranging device measures AUV to the oblique distance of acoustic marker.
The method of the present invention includes two contents：Content one, using the single beacon oblique distance measured values of AUV at different moments, Line demarcates each beacon position；Content two, establishes the card of the data fusion based on the positioning of Long baselines acoustics and inertial navigation data Thalmann filter, calculates the location estimation of integrated navigation.
1st, single beacon oblique distance measured value using AUV at different moments, each beacon position of on-line proving
Using the single beacon oblique distance measured values of AUV at different moments, the effect of each beacon position of on-line proving is to solve mother Ship demarcate Long baselines beacon stated accuracy with the increase of the depth of water and stated accuracy decline the problem of.Its thought is by lash ship mark Fixed initial position is primary quantity, and calibrated error is calculated using on-line proving algorithm, then obtains the beacon than lash ship calibration The calibration result of positional precision higher.The lash ship initial alignment position for defining beacon i (1≤i≤N, N are beacon total numbers) is (xi,yi,zi), which is known quantity；The calibrated error for defining beacon i is (dxi,dyi, 0), which is variable to be solved； Define t moment, t+1 moment and the AUV positions (x at t+2 momentt,yt,zt),(xt+1,yt+1,zt+1) and (xt+2,yt+2,zt+2), should Variable is known quantity；Define t moment, the oblique distance of t+1 moment and t+2 moment AUV to beacon i are respectively di_t,di_t+1,di_t+2, The variable is known quantity；The then calibration of the beacon i of the oblique distance equation composition of t moment, t+1 moment and t+2 moment beacons i to AUV Equation group is as follows：
Its solve equation for：
[dxi,dyi]T=A-1B
Wherein,
Wherein, t moment, the horizontal distance r of t+1 moment and t+2 moment AUV to beacon i are definedi_t,ri_t+1,ri_t+2；It is fixed Adopted t moment, the estimation of the horizontal distance of t+1 moment and t+2 moment AUV to beacon iSo horizontal distance and The definition expression formula of horizontal distance estimation is as follows：
2nd, the Kalman filter based on the positioning of Long baselines acoustics and inertial navigation data fusion is established
The effect for establishing the Kalman filter based on the positioning of Long baselines acoustics and inertial navigation data fusion is comprehensive profit The inertial navigation datas such as the attitude angle measured with Long baselines acoustics location data, the speed of Doppler measurement, attitude transducer, are obtained Obtain high-precision integrated navigation location estimation.
1st step, calculates the AUV Long baselines positioning Z of t momentt(xt,yt), Long baselines positioning calculation equation is as follows：
[xt,yt]T=A-1(R-D)
Wherein,
Wherein, the horizontal distance for defining t moment AUV to beacon 1,2,3 is r1_t,r2_t,r3_t, it is known quantity；Beacon 1,2, 3 location estimation is (x1+dx1,y1+dy1), (x2+dx2,y2+dy2) and (x3+dx3,y3+dy3), variable dxi,dyiIt is upper one The result of calculation of step calibration beacon position.
2nd step, defines the AUV acoustics positioning Z of t momentt(xt,yt), wherein xtAnd ytRepresent t moment AUV in x directions respectively With the acoustics position location in y directions, the measurement equation that Long baselines acoustics positions is established：
Wherein, VtIt is the measurement noise of t moment beacon, it is zero mean Gaussian white noise, and measuring noise square difference matrix is Rt, the variance matrix of beacon noise is device attribute；It is the measurement expression formula of t moment, its accurate expression can not be obtained Formula, is its linearization approximate expression formula here；The true longitude and true latitude of AUV when being t moment measurement, is Unknown quantity；Define Ht=[1,1]TIt is the Jacobin matrix for measuring equation linearization approximate, is constant.
3rd step, the predicted position for defining t moment AUV is Xt(xt,yt), wherein xtAnd ytT moment prediction AUV is represented respectively Longitude and latitude, establish the predictive equation of integrated navigation：
Wherein, ut, ψ, θ, φ is speed, course angle, Angle of Trim and the roll angle of t moment AUV, they can pass through respectively Doppler and attitude transducer measurement obtain, and are known quantities；So define Ut=[ut, ψ] and it is system input matrix；Δ T is from t- 1 moment was known quantity to the time interval of t moment；Define Ht=[1,1]TIt is the Jacobin matrix for measuring equation, is constant；Wt It is the system input noise of t moment, it is zero mean Gaussian white noise, and the variance matrix for defining system input noise is Qt, QtIt is Heading sensor and the device attribute of Doppler, so the variance matrix Q of input noisetIt is known quantity；xt-1And yt-1Respectively Represent that t-1 moment AUV is known quantity in longitude and Position Latitude；Pt,t-1Represent the prediction variance of t moment prediction AUV positions, not The amount of knowing；Pt-1Represent that the t-1 moment estimates the estimate variance of AUV positions, be known quantity；It is euler transformation matrix, Doppler is surveyed The rate conversion based on AUV coordinate systems of amount is known quantity into north-eastern coordinate system speed；ReIt is the short of earth WGS-84 models Axis radius, value are 6 378 137 meters；E is earth WGS-84 model rotation ellipsoid ellipticities, value 1/298.257.
By the predictive equation of integrated navigation, the predicted position for calculating t moment AUV is Xt(xt,yt)；
4th step, calculates the location estimation of integrated navigation：Define t moment AUV estimated locations WithRespectively Represent the estimated location longitude and latitude of t moment AUV；RtRepresent that t moment measures the variance matrix of noise, be device attribute；h (Xt) represent to measure expression formula h (Xt)=HtXt+Vt；
5th step, calculates the location estimation variance of integrated navigation：Define PtRepresent the location estimation of t moment AUV integrated navigations Variance, the estimation of navigation accuracy；Wherein, I is unit matrix.PtIt is bigger Represent that navigation accuracy is lower.

Claims (8)

1. the underwater robot Combinated navigation method based on Long baselines and beacon on-line proving, it is characterised in that including following step Suddenly：
Using the single beacon oblique distance measured values of AUV at different moments, each beacon position of on-line proving obtains the calibration of each beacon Error；
Estimate combination according to calibrated error, by the measurement equation and the predictive equation of inertial navigation that are positioned based on Long baselines acoustics The AUV positions of navigation.
2. the underwater robot Combinated navigation method according to claim 1 based on Long baselines and beacon on-line proving, its It is characterized in that calibrated error is obtained by following formula
[dxi,dyi]T=A-1B
Wherein,
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>B</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>-</mo> <mo>(</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> <mo>-</mo> <mo>(</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>i</mi> <mo>_</mo> <msup> <mi>t</mi> <mrow> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>
The AUV positions of t moment, t+1 moment and t+2 moment are respectively (xt,yt,zt),(xt+1,yt+1,zt+1) and (xt+2,yt+2, zt+2), t moment, the oblique distance of t+1 moment and t+2 moment AUV to beacon i are respectively di_t,di_t+1,di_t+2；
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msqrt> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>t</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <msqrt> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <msqrt> <mrow> <msubsup> <mi>d</mi> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>,</mo> <msub> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>i</mi> <mo>_</mo> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>
T moment, the horizontal distance of t+1 moment and t+2 moment AUV to beacon i are respectively ri_t,ri_t+1,ri_t+2；When t moment, t+1 Carve and the estimation of the horizontal distance of t+2 moment AUV to beacon i is respectivelyThe lash ship initial alignment position of beacon i For (xi,yi,zi)。
3. the underwater robot Combinated navigation method according to claim 1 based on Long baselines and beacon on-line proving, its It is characterized in that described according to calibrated error, measurement equation and the predictive equation of inertial navigation by being positioned based on Long baselines acoustics The position of estimation integrated navigation comprises the following steps：
1) the Long baselines position location Z of t moment AUV is calculated according to calibrated errort(xt,yt)；
2) measurement equation is established according to AUV Long baselines position location；
3) predictive equation for establishing integrated navigation obtains the predicted position X of AUVt(xt,yt)；
4) according to the Long baselines position location Z of AUVt(xt,yt) and predicted position Xt(xt,yt) obtain the AUV positions of integrated navigation.
4. the underwater robot Combinated navigation method according to claim 3 based on Long baselines and beacon on-line proving, its It is characterized in that the Long baselines position location Z that t moment AUV is calculated according to calibrated errort(xt,yt), comprise the following steps： [xt,yt]T=A-1(R-D)
Wherein,
The horizontal distance of t moment AUV to beacon 1,2,3 is r1_t,r2_t,r3_t；The lash ship initial alignment position of beacon i is (xi, yi,zi)；The location estimation of beacon 1,2,3 is (x1+dx1,y1+dy1), (x2+dx2,y2+dy2) and (x3+dx3,y3+dy3), dxi, dyiFor calibrated error；
[the x that above formula obtainst,yt]TLong baselines position location Z as t moment AUVt(xt,yt) column vector represent.
5. the underwater robot Combinated navigation method according to claim 3 based on Long baselines and beacon on-line proving, its It is characterized in that the measurement equation is
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mi>t</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>V</mi> <mi>t</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>H</mi> <mi>t</mi> </msub> <msub> <mover> <mi>X</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>V</mi> <mi>t</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>H</mi> <mi>t</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>X</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mo>,</mo> <msub> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, VtIt is the measurement noise of t moment beacon；Represent the measurement expression formula of t moment；It is that t moment is surveyed The true longitude and true latitude of AUV during amount；Ht=[1,1]TIt is the Jacobin matrix for measuring equation linearization approximate.
6. the underwater robot Combinated navigation method according to claim 3 based on Long baselines and beacon on-line proving, its It is characterized in that the predictive equation is
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>U</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>V</mi> <mi>t</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <msub> <mi>&amp;Delta;Tu</mi> <mi>t</mi> </msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mn>1</mn> <mrow> <msub> <mi>R</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mi> </mi> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mn>1</mn> <mrow> <msub> <mi>R</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>e</mi> <mo>+</mo> <mn>3</mn> <mi>e</mi> <mi> </mi> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>H</mi> <mi>t</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>&amp;Delta;</mi> <mi>T</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;psi;</mi> <mo>,</mo> <mo>-</mo> <mi>&amp;Delta;</mi> <mi>T</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;psi;</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <msub> <mi>Q</mi> <mi>t</mi> </msub> <mo>&amp;lsqb;</mo> <mi>&amp;Delta;</mi> <mi>T</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;psi;</mi> <mo>,</mo> <mo>-</mo> <mi>&amp;Delta;</mi> <mi>T</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;psi;</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>sin</mi> <mi>&amp;psi;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mi>cos</mi> <mi>&amp;psi;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;phi;</mi> <mo>+</mo> <mi>sin</mi> <mi>&amp;phi;</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;theta;</mi> <mi>sin</mi> <mi>&amp;psi;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mi>&amp;psi;</mi> <mi>cos</mi> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mi>&amp;psi;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;phi;</mi> <mo>+</mo> <mi>cos</mi> <mi>&amp;psi;</mi> <mi>sin</mi> <mi>&amp;theta;</mi> <mi>sin</mi> <mi>&amp;phi;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, ut, ψ, θ, φ is speed, course angle, Angle of Trim and the roll angle of t moment AUV, Ut=[ut, ψ] and it is system input Matrix；Δ T is the time interval from t-1 moment to t moment；Ht=[1,1]TIt is the Jacobin matrix for measuring equation；System inputs The variance matrix of noise is Qt；xt-1And yt-1Represent t-1 moment AUV in longitude and Position Latitude respectively；Pt,t-1Represent that t moment is pre- Survey the prediction variance of AUV positions；Pt-1Represent that the t-1 moment estimates the estimate variance of AUV positions；It is euler transformation matrix；ReIt is The minor axis radius of the earth；E is earth rotation flattening of ellipsoid.
7. the underwater robot Combinated navigation method according to claim 3 based on Long baselines and beacon on-line proving, its It is characterized in that the Long baselines position location Z according to AUVt(xt,yt) and predicted position Xt(xt,yt) obtain the position of integrated navigation Estimation is put to obtain by following formula
<mrow> <msub> <mover> <mi>X</mi> <mo>^</mo> </mover> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>H</mi> <mi>t</mi> <mi>T</mi> </msubsup> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>H</mi> <mi>t</mi> </msub> <msub> <mi>P</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mi>H</mi> <mi>t</mi> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>R</mi> <mi>t</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;lsqb;</mo> <msub> <mi>Z</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mn>1</mn> <mrow> <msub> <mi>R</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mi> </mi> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mn>1</mn> <mrow> <msub> <mi>R</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>e</mi> <mo>+</mo> <mn>3</mn> <mi>e</mi> <mi> </mi> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>
Wherein, t moment AUV estimated locations WithThe estimated location longitude and latitude of t moment AUV is represented respectively Degree；RtRepresent that t moment measures the variance matrix of noise, h (Xt)=HtXt+Vt。
8. the underwater robot Combinated navigation method according to claim 1 based on Long baselines and beacon on-line proving, its After being characterized in that the position of the estimation integrated navigation, navigation essence is estimated by calculating the location estimation variance of integrated navigation Degree：Wherein, I is unit matrix, PtRepresent t moment AUV integrated navigations Location estimation variance.
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CN109490927A (en) * 2018-12-26 2019-03-19 天津水运工程勘察设计院 A kind of leveling frame positioning system and its localization method under water
CN109782289A (en) * 2018-12-26 2019-05-21 中国电子科技集团公司第二十研究所 A kind of submarine navigation device localization method based on the constraint of baseline geometry
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CN109856659A (en) * 2019-01-21 2019-06-07 同济大学 Preventing seabed base positions time service and data record system and method
CN109856659B (en) * 2019-01-21 2021-02-12 同济大学 Seabed-based positioning time service and data recovery system and method
JP2020169953A (en) * 2019-04-05 2020-10-15 株式会社Ihi Method for calibrating inertia navigation device
CN110057383B (en) * 2019-05-05 2023-01-03 哈尔滨工程大学 Lever arm error calibration method of AUV (autonomous Underwater vehicle) push navigation system
CN110057383A (en) * 2019-05-05 2019-07-26 哈尔滨工程大学 A kind of AUV pushing navigation system lever arm error Calibration Method
CN110309581A (en) * 2019-06-27 2019-10-08 哈尔滨工程大学 A kind of underwater subsurface buoy position Synthesis calibration measurement point rapid Optimum layout method
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CN110542884A (en) * 2019-08-28 2019-12-06 中国科学院声学研究所 Long baseline navigation positioning method based on inertial navigation correction
CN111708008A (en) * 2020-05-08 2020-09-25 南京工程学院 Underwater robot single-beacon navigation method based on IMU and TOF
CN112698273A (en) * 2020-12-15 2021-04-23 哈尔滨工程大学 Multi-AUV single-standard distance measurement cooperative operation method
CN117146830A (en) * 2023-10-31 2023-12-01 山东科技大学 Self-adaptive multi-beacon dead reckoning and long-baseline tightly-combined navigation method
CN117146830B (en) * 2023-10-31 2024-01-26 山东科技大学 Self-adaptive multi-beacon dead reckoning and long-baseline tightly-combined navigation method

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