CN109596128A - A method of more AUV co-located performances are improved based on more hydrophones - Google Patents
A method of more AUV co-located performances are improved based on more hydrophones Download PDFInfo
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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
- G01C21/20—Instruments for performing navigational calculations
- G01C21/203—Specially adapted for sailing ships
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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
- 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
Abstract
The invention belongs to autonomous underwaters to navigate by water field, and in particular to a method of more AUV co-located performances are improved based on more hydrophones.This method comprises: configuring multiple hydrophones on following AUV, the position of hydrophone and fixed hydrophone are set；Navigator AUV carries out subaqueous sound ranging by hydrophone with AUV is followed, while self-position is broadcast to and follows AUV by the AUV that navigates；Establish the co-located system state space model of single navigator's AUV mode；Using EKF filtering method, to following AUV to position.The position on AUV is being followed by designing multiple hydrophones, is increasing state-space model measurement matrix dimension, the observability of system is greatly improved, effectively reduced to each AUV high maneuverability requirement in single navigator's scheme；Reduce more AUV collaborative navigation system navigator's AUV quantity, avoids the high-precision Inertial Measurement Unit of outfit required for since multiple navigator AUV are arranged, reduce cost；The problem of not being related to more navigator AUV time synchronizations is easy to implement, and positioning accuracy is higher.
Description
Technical field
The invention belongs to autonomous underwaters to navigate by water field, and in particular to one kind is fixed based on the more AUV collaborations of more hydrophones raising
The method of position performance.
Background technique
Collaborative navigation is one of most effective air navigation aid of the more Autonomous Underwater Vehicles of current interlayer region, is had wide
Wealthy application prospect.Autonomous Underwater Vehicle AUV collaborative navigation technology based on underwater sound communication network is with more AUV cooperation system
The new AUV underwater navigation scheme of one kind developed of uniting, navigates compared to traditional inertial navigation, acoustics baseline, collaborative navigation
Not only precision is high, and it is at low cost, robustness is good, can greatly enhance the work compound ability of more AUV systems, have important
Researching value.According to the difference of navigator's AUV number, and single navigator's mode and more navigator's modes can be divided into.Single navigator's mode configuration
Simply, be easy deployment and operation, cost needs it is low, but system overall navigation performance depend on single navigator AUV, to navigator
The reliability requirement of AUV is higher；Secondly, single navigator's AUV mission observability is lower, the AUV that needs to navigate constantly carries out air route machine
The dynamic observability to improve system.For relatively single navigator's AUV scheme, more navigator's scheme increasing due to navigator's AUV number,
System substantially reduces the reliability requirement of single navigator AUV.Simultaneously as the observability of system greatly improves, cooperateing with
It is not usually required to the motor-driven observability to guarantee system in air route by navigator AUV in the process, not only increases the collaboration of system
Positioning performance, while being more advantageous to according to scheduled task formation cooperation execution task.But compared to single navigator's mode for,
Due to increasing for navigator's AUV number, the navigation cost of system be increased.Come from the development trend of underwater collaborative navigation technology
It sees, the collaborative navigation based on single navigator AUV scheme is undoubtedly more attractive, just receives more and more attention and develops.So
And system Observable be realize submarine navigation device collaborative navigation precondition, particularly with for single navigator's scheme to Guan Chong
It wants.If described system be it is observable, carrier self poisoning error can by fusion navigator AUV it is relatively accurate
Location information and the two between apart from measurement information carry out collaboration correction；No matter conversely, then using which type of filtering algorithm
It all cannot achieve the accurate estimation of location status, thus how to enhance the observability of system, to raising more AUV collaborative navigations system
It is most important for the co-located performance of system.
Summary of the invention
The purpose of the present invention is to provide one kind by configuring multiple hydrophones on following AUV and based on nonlinear filtering
More AUV collaborative navigation methods of estimation, can be improved the more AUV collaborative navigation system Observables of master-slave mode under single navigator's mode
Property, and finally improve the co-located performance of system.
The object of the present invention is achieved like this:
A method of more AUV co-located performances being improved based on more hydrophones, method includes the following steps:
Step 1: configuring multiple hydrophones on following AUV, the position of hydrophone and fixed hydrophone are set；
Step 2: navigator AUV and follow AUV by hydrophone progress subaqueous sound ranging, obtain following configured on AUV it is multiple
Hydrophone is the distance between to navigator AUV, while self-position is broadcast to and follows AUV by the AUV that navigates；
Step 3: according to the location information of hydrophone, following on AUV hydrophone to the distance between navigator AUV information, neck
Boat AUV location information, the co-located system mode for following the location information of AUV combination pushing to establish single navigator's AUV mode are empty
Between model；
Step 4: utilizing EKF filtering method, obtain the estimated value of system mode, to following AUV to position.
Configuring multiple hydrophones described in step 1 on following AUV includes: to follow the mass center of AUV to build as coordinate origin
Vertical carrier coordinate system Oxbybzb, the x of carrier coordinate systembAxis edge follows AUV horizontal axis to refer to the right side, ybAxis is before following the AUV longitudinal axis to refer to, zb
Axis edge follows AUV vertical pivot and and xb、ybAxis constitutes right hand rectangular coordinate system；It follows AUV to navigate by water along the carrier coordinate system longitudinal axis, follows
The multiple hydrophone positions configured on AUV should be not at the same longitudinal axis；Hydrophone A and hydrophone B are separately fixed at and are followed
The two sides end to end AUV, if hydrophone A and hydrophone B the position coordinates of the carrier coordinate system be respectively (a, b, 0) and (- c ,-d,
0), wherein a be hydrophone xbWheelbase is from c is the x for following AUV mass centerbWheelbase is from b is the y of hydrophonebWheelbase from, d be with
With the y of AUV mass centerbWheelbase is from unit is rice.
The co-located system state space model of the single navigator's AUV mode of foundation described in step 3 is expressed as:
In formula, k+1 indicates tk+1Moment；Xk=(xk,yk,θk)TTo follow AUV in tkThe quantity of state at moment, xkTo navigate
Follow AUV in t in coordinate systemkThe east orientation position coordinates at moment, ykTo follow AUV in tkThe north orientation position coordinates at moment, θkFor with
With AUV in tkThe course angle at moment；Xk+1To follow AUV in tk+1The quantity of state at moment；uk=(Vkθk)TFor tkWhen etching system
Sensor input, VkTo follow AUV in tkThe forward speed at moment；Zk+1For tk+1The measurement vector at moment；It is navigator AUV in tk+1The quantity of state at moment,To follow AUV and navigator AUV in tk+1The east at moment
To position coordinates,It is navigator AUV in tk+1The north orientation position coordinates at moment；wkFor process noise vector, vk+1To measure noise
Vector, and wk、vk+1It is Gauss white noise；Function of stateδ t is the sampling period；
ω is angular speed；Measure function representation are as follows:
Wherein, xk+1To follow AUV in t in navigational coordinate systemk+1The east orientation position coordinates at moment；yk+1To follow AUV to exist
tk+1The north orientation position coordinates at moment；For tk+1Moment hydrophone A to follow east orientation of the AUV mass center in navigational coordinate system away from
From,For tk+1Moment hydrophone A to following north orientation distance of the AUV mass center in navigational coordinate system,For tk+1Moment water is listened
Device B to following east orientation distance of the AUV mass center in navigational coordinate system,For tk+1Moment hydrophone B is being led to following AUV mass center
North orientation distance in boat coordinate system.
Assuming that state vector Xk=[xk,yk]TIn tkWhen etching system posterior probability stateAnd posterior probability density letter
NumberIt is known that PkkFor tkThe state estimation variance matrix at moment, ZkFor tkMoment is obtained by subaqueous sound ranging
To the measurement vector that forms of the distance for following upper two hydrophones of AUV to navigator AUV, the filtering side EKF is utilized described in step 4
Method, comprising the following steps:
Step 4.1: the time updates；
Step 4.2: measuring and update；
Step 4.3: with this process, gradually recursion to state estimation error covariance reaches stationary value.
The update of time described in step 4.1 includes that state one-step prediction equation is expressed as following formula:
Status predication variance matrix indicates are as follows:
Wherein, systematic state transfer matrix For FkTransposition；
System noise motivates battle array For GkTransposition；System noise covariance battle arraywk TFor wkTransposition,For sensor velocity noise variance,For course noise variance.
The update of measurement described in step 4.2 includes that filtering gain is expressed as following formula:
Wherein, measurement matrix is expressed as following formula:
Wherein,For Ηk+1Transposition；Measure noise covariance battle array Rk+1=E [vk+1vk+1 T], vk+1 TFor vk+1Transposition；
State estimation is expressed as following formula:
State estimation variance matrix is expressed as following formula:
Pk+1|k+1=[I-Kk+1Hk+1]Pk+1|k
In formula, I is unit battle array,Follow AUV in t by what filtering estimation obtainedk+1The quantity of state at moment；
With this process gradually recursion to state estimation error covariance reach stationary value to get arrive system mode estimation,
To following AUV to position.
The beneficial effects of the present invention are:
1. AUV is followed to be equipped with multiple hydrophones, the position on AUV is being followed by designing multiple hydrophones, is increasing state
Spatial model measurement matrix dimension, the observability of system greatly improve, and effectively reduce to each AUV high in single navigator's scheme
Maneuverability requirement；
2. reducing more AUV collaborative navigation system navigator's AUV quantity, avoid as being arranged required for multiple navigator AUV
The high-precision Inertial Measurement Unit of outfit, reduces cost；
3. the problem of collaborative navigation method based on more hydrophones is not related to more navigator AUV time synchronizations is easy to implement,
And positioning accuracy is higher.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the scheme of installation for following hydrophone on AUV；
Fig. 3 is bi_hydrophone navigator AUV and follows the ranging scheme between AUV；
Fig. 4 is that EKF filters flow chart；
Fig. 5 is navigator AUV and follows the true ship trajectory figure of AUV；
Fig. 6 is that collaborative navigation follows the track AUV comparison diagram；
Fig. 7 position error comparison diagram.
Specific embodiment
The present invention is described further with reference to the accompanying drawing.
More AUV collaborative navigation system costs of single navigator's scheme are low, easy to operate, but it moves navigator AUV with AUV is followed
Conditions dictate is higher.Under single navigator's mode, if the AUV that navigates, the straight line path machine for following AUV to be parallel to each other with identical speed of a ship or plane edge
When dynamic, it is unobservable to will lead to the system overall situation；If the AUV that navigates, following AUV with when synchronized, navigation in the same direction or route speed tangent line
Direction is consistent, and it is locally unobservable to will lead to more AUV collaborative navigation systems.It can be expired by the complicated routeing scheme of design
Observability of the football association with navigation system.However for the AUV system slow for the speed of a ship or plane, mobility is poor, in order to improve system
It is motor-driven often unpractical to carry out complicated air route during practical execution task for observability.In view of the above problems, this
A kind of method for improving more AUV collaborative navigation mission observabilities based on more hydrophones of Patent design, by being filled on following AUV
Standby multiple hydrophones obtain each hydrophone to the distance and hydrophone of navigator AUV by subaqueous sound ranging and follow the seat of AUV mass center
Mark relationship establishes more AUV collaborative navigation system state space models, enhances the observability of system, improves more AUV systems
Co-located performance.
Step 1: hydrophone is configured on following AUV.
To follow the mass center of AUV to establish carrier coordinate system Ox as coordinate originbybzb, the x of carrier coordinate systembAxis edge follows
AUV horizontal axis refers to the right side, ybAxis is before following the AUV longitudinal axis to refer to, zbAxis edge follows AUV vertical pivot and and xb、ybAxis constitutes right hand rectangular co-ordinate
System.It follows AUV to navigate by water along the carrier coordinate system longitudinal axis, follows the multiple hydrophone positions configured on AUV that should be not at same vertical
Axis, and distance is as far as possible between each hydrophone.Follow installed on AUV multiple hydrophones collaborative navigation system can be improved can
Observation, but excessive hydrophone is installed and is not obvious to collaborative navigation system positioning performance is improved, and cost needs are high.With with
For configuring two hydrophones on AUV, hydrophone A and hydrophone B are separately fixed at and following the two sides end to end AUV, if water
Listen device A and hydrophone B the carrier coordinate system position coordinates be respectively (a, b, 0) and (- c ,-d, 0), wherein a, c listen for water
Device and the x for following AUV mass centerbWheelbase is from b, d are hydrophone and the y for following AUV mass centerbWheelbase is from unit is rice.
Step 2: navigator AUV carries out subaqueous sound ranging with AUV is followed, and navigator AUV broadcasts self-position.
Navigator AUV carries out subaqueous sound ranging by hydrophone with AUV is followed, and can respectively obtain two for following and configuring on AUV
Hydrophone the distance between to navigator AUV, meanwhile, navigator AUV, which broadcasts to own location information, follows AUV.
Step 3: single navigator AUV co-located system state space model based on bi_hydrophone is established.
In practical underwater co-located, the depth of AUV and horizontal position are independent from each other, can by pressure sensor
It to obtain accurate depth information, therefore can be two dimension by three-dimensional co-located problem reduction, under discussion arrive model projection
It is analyzed in two-dimensional level face.In navigational coordinate system OxtytIn, definition follows AUV in tkMoment and tk+1The position vector at moment
Respectively (xk,yk) and (xk+1,yk+1), position vector of the navigator AUV at tk moment and tk+1 moment is respectivelyWith Respectively follow AUV and navigator AUV in tkThe east orientation position coordinates at moment；Respectively follow
AUV and navigator AUV are in tkThe north orientation position coordinates at moment；Respectively follow AUV and navigator AUV in tk+1Moment
East orientation position coordinates；Respectively follow AUV and navigator AUV in tk+1The north orientation position coordinates at moment.Based on opposite position
Set the collaborative navigation system state equation of measurement specifically:
In formula, xkAnd xk+1Respectively follow AUV in t in navigational coordinate systemkMoment and tk+1The east orientation position at moment is sat
Mark；ykAnd yk+1Respectively follow AUV in tkMoment and tk+1The north orientation position coordinates at moment；δ t is the sampling period；VkTo follow
AUV is in tkThe forward speed at moment, θkFor follow AUV in tkThe course angle at moment；ω is angular speed.
The hydrophone A to the x for following AUV mass center that will be followed on AUVbWheelbase from and ybWheelbase is projected from by carrier coordinate system
It is obtained to navigational coordinate system:
In formula,For hydrophone A to the east orientation distance that follows AUV centroid distance to project in navigational coordinate system and
North orientation distance, then hydrophone A position vector in navigational coordinate system be
Similarly:
In formula,For hydrophone B to the east orientation distance that follows AUV centroid distance to project in navigational coordinate system and
North orientation distance, obtaining hydrophone B position vector in navigational coordinate system is
Follow AUV in tkThe opposite observation information that moment is obtained by underwater sound communication is navigator AUV in tkBelieve the position at moment
BreathAnd it navigates and AUV and follows the relative distance measurement information between AUV to be respectivelyWithMeasure vectorNavigator AUV can be obtained by information above and follow the coordinate position relationship between AUV are as follows:
In formula,Navigator AUV is in t respectively in navigational coordinate systemkMoment and tk+1The east orientation at moment, north orientation position
Set coordinate；
Based on formula (1) and formula (2), the discrete-time state-space model (state equation of more AUV co-located systems is established
And measurement equation) it is as follows:
In formula, k+1 indicates tk+1Moment；Xk=(xk,yk,θk)TTo follow AUV in tkThe quantity of state at moment；Xk+1To follow
AUV is in tk+1The quantity of state at moment；uk=(Vkθk)TFor tkWhen etching system sensor input；Zk+1For tk+1The measurement at moment to
Amount；It is navigator AUV in tk+1The quantity of state at moment；wkFor process noise vector, vk+1For measure noise to
Amount, and wk、vk+1It is Gauss white noise；Function of stateMeasure function For tk+1Moment hydrophone
A to following east orientation distance and north orientation distance of the AUV mass center in navigational coordinate system,For tk+1Moment hydrophone B to
With east orientation distance and north orientation distance of the AUV mass center in navigational coordinate system.
Step 4: utilizing EKF filtering method, obtain the estimated value of system mode, determines to realize the collaboration for following AUV
Position.
Assuming that state vector Xk=[xk,yk]TIn tkWhen etching system posterior probability stateAnd posterior probability density letter
NumberIt is known that PkkFor tkThe state estimation variance matrix at moment, ZkFor tkMoment is obtained by subaqueous sound ranging
To follow upper two hydrophones of AUV to navigator AUV distance form measurement vector.
(1) time updates
State one-step prediction equation:
Status predication variance matrix:
Wherein systematic state transfer matrix For FkTransposition；
System noise motivates battle array For GkTransposition；System noise covariance battle arraywk TFor wkTransposition,WithRespectively sensor velocity noise variance and course noise
Variance.
(2) it measures and updates
Filtering gain:
Wherein measurement matrix For Ηk+1Transposition；Measure noise covariance battle array Rk+1=E [vk+1vk+1 T], vk+1 TFor vk+1Transposition.
State estimation:
State estimation variance matrix:
Pk+1|k+1=[I-Kk+1Hk+1]Pk+1|k (10)
In formula, I is unit battle array,Follow AUV in t by what filtering estimation obtainedk+1The quantity of state at moment.
With this process gradually recursion to state estimation error covariance reach stationary value to get arrive system mode estimation,
To realize the positioning to AUV is followed.
To further illustrate beneficial effects of the present invention, simulation is equipped with inertial navigation set and Doppler in navigator AUV
Tachometer follows AUV to be equipped under MEMS inertia system and Doppler log experimental situation, to based on the more of bi_hydrophone
AUV co-located scheme has carried out simulating, verifying:
Simulation time is 3600s；Sampling period is 1s；Navigator AUV is that 0.1 °/s does curvilinear motion with angular speed size, with
It is at the uniform velocity sailed through to AUV along the direction that course angle is 60 °；Navigator AUV and the speed for following AUV are 4kn；AUV speed is followed to pass
Sensor measures noise and is taken asZero mean Gaussian white noise；The course AUV angular measurement noise is followed to be taken asZero mean Gaussian white noise, and follow heading effect error of the AUV course angle there are 5 °/h；Also draw in emulation
Enter to navigate and AUV and follow the measurement noise of subaqueous sound ranging between AUV, variance is (0.5m)2；Hydrophone A, hydrophone B are installed respectively
In the upper right corner and the lower left corner for following AUV, two hydrophones and to follow the lateral distance of AUV mass center be 2 meters, fore-and-aft distance is equal
It is 5 meters, carries out emulation experiment.
Claims (6)
1. a kind of method for improving more AUV co-located performances based on more hydrophones, which is characterized in that this method includes following step
It is rapid:
Step 1: configuring multiple hydrophones on following AUV, the position of hydrophone and fixed hydrophone are set；
Step 2: navigator AUV carries out subaqueous sound ranging by hydrophone with AUV is followed, and obtains that the multiple water configured on AUV is followed to listen
Device is the distance between to navigator AUV, while self-position is broadcast to and follows AUV by the AUV that navigates；
Step 3: according to the location information of hydrophone, following on AUV hydrophone to the distance between navigator AUV information, navigator AUV
Location information follows the location information of AUV combination pushing to establish the co-located system state space mould of single navigator's AUV mode
Type；
Step 4: utilizing EKF filtering method, obtain the estimated value of system mode, to following AUV to position.
2. a kind of method for improving more AUV co-located performances based on more hydrophones according to claim 1, feature exist
In configuring multiple hydrophones described in step 1 on following AUV includes: to follow the mass center of AUV to establish carrier as coordinate origin
Coordinate system Oxbybzb, the x of carrier coordinate systembAxis edge follows AUV horizontal axis to refer to the right side, ybAxis is before following the AUV longitudinal axis to refer to, zbAxis along with
With AUV vertical pivot and and xb、ybAxis constitutes right hand rectangular coordinate system；It follows AUV to navigate by water along the carrier coordinate system longitudinal axis, follows and match on AUV
The multiple hydrophone positions set should be not at the same longitudinal axis；Hydrophone A and hydrophone B are separately fixed at and follow AUV end to end
Two sides, if hydrophone A and hydrophone B is respectively (a, b, 0) and (- c ,-d, 0), wherein a in the position coordinates of the carrier coordinate system
For the x of hydrophonebWheelbase is from c is the x for following AUV mass centerbWheelbase is from b is the y of hydrophonebWheelbase is from d is to follow AUV mass center
YbWheelbase is from unit is rice.
3. a kind of method for improving more AUV co-located performances based on more hydrophones according to claim 2, feature exist
In the co-located system state space model of the single navigator's AUV mode of foundation described in step 3 is expressed as:
In formula, k+1 indicates tk+1Moment；Xk=(xk,yk,θk)TTo follow AUV in tkThe quantity of state at moment, xkFor in navigation coordinate
Follow AUV in t in systemkThe east orientation position coordinates at moment, ykTo follow AUV in tkThe north orientation position coordinates at moment, θkTo follow
AUV in tkThe course angle at moment；Xk+1To follow AUV in tk+1The quantity of state at moment；uk=(Vkθk)TFor tkWhen etching system biography
Sensor input quantity, VkTo follow AUV in tkThe forward speed at moment；Zk+1For tk+1The measurement vector at moment；It is navigator AUV in tk+1The quantity of state at moment,To follow AUV and navigator AUV in tk+1The east at moment
To position coordinates,It is navigator AUV in tk+1The north orientation position coordinates at moment；wkFor process noise vector, vk+1To measure noise
Vector, and wk、vk+1It is Gauss white noise；Function of stateδ t is the sampling period；
ω is angular speed；Measure function representation are as follows:
Wherein, xk+1To follow AUV in t in navigational coordinate systemk+1The east orientation position coordinates at moment；yk+1To follow AUV in tk+1
The north orientation position coordinates at moment；For tk+1Moment hydrophone A to following east orientation distance of the AUV mass center in navigational coordinate system,For tk+1Moment hydrophone A to following north orientation distance of the AUV mass center in navigational coordinate system,For tk+1Moment hydrophone B
To following east orientation distance of the AUV mass center in navigational coordinate system,For tk+1Moment hydrophone B is navigating to following AUV mass center
North orientation distance in coordinate system.
4. a kind of method for improving more AUV co-located performances based on more hydrophones according to claim 3, feature exist
In: assuming that state vector Xk=[xk,yk]TIn tkWhen etching system posterior probability stateAnd posterior probability density functionIt is known that Pk|kFor tkThe state estimation variance matrix at moment, ZkFor tkMoment is obtained by subaqueous sound ranging
The measurement vector that forms of the distance for following upper two hydrophones of AUV to navigator AUV, the filtering side EKF is utilized described in step 4
Method, comprising the following steps:
Step 4.1: the time updates；
Step 4.2: measuring and update；
Step 4.3: with this process, gradually recursion to state estimation error covariance reaches stationary value.
5. a kind of method for improving more AUV co-located performances based on more hydrophones according to claim 4, feature exist
In the update of time described in step 4.1 includes that state one-step prediction equation is expressed as following formula:
Status predication variance matrix indicates are as follows:
Wherein, systematic state transfer matrix For FkTransposition；System
Noise excitation battle array For GkTransposition；System noise covariance battle arraywk TFor wkTransposition,For sensor velocity noise variance,For course noise variance.
6. a kind of method for improving more AUV co-located performances based on more hydrophones according to claim 4, feature exist
In the update of measurement described in step 4.2 includes that filtering gain is expressed as following formula:
Wherein, measurement matrix is expressed as following formula:
Wherein,For Ηk+1Transposition；Measure noise covariance battle array Rk+1=E [vk+1vk+1 T], vk+1 TFor vk+1Transposition；
State estimation is expressed as following formula:
State estimation variance matrix is expressed as following formula:
Pk+1|k+1=[I-Kk+1Hk+1]Pk+1|k
In formula, I is unit battle array,Follow AUV in t by what filtering estimation obtainedk+1The quantity of state at moment；
With this process gradually recursion to state estimation error covariance reach stationary value to get arrive system mode estimation, to
It is positioned with AUV.
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| CN110908393A (en) * | 2019-10-31 | 2020-03-24 | 中国矿业大学 | Underwater unmanned vehicle formation cooperation method based on detection and communication integration |
| CN110954107A (en) * | 2019-12-04 | 2020-04-03 | 宁波羽声海洋科技有限公司 | Unmanned aircraft cluster collaborative navigation method and device |
| CN111256727A (en) * | 2020-02-19 | 2020-06-09 | 广州蓝胖子机器人有限公司 | Method for improving accuracy of odometer based on Augmented EKF |
| CN111595348A (en) * | 2020-06-23 | 2020-08-28 | 南京信息工程大学 | Master-slave mode cooperative positioning method of autonomous underwater vehicle combined navigation system |
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