CN105867122B - Dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation - Google Patents
Dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation Download PDFInfo
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- CN105867122B CN105867122B CN201610201135.3A CN201610201135A CN105867122B CN 105867122 B CN105867122 B CN 105867122B CN 201610201135 A CN201610201135 A CN 201610201135A CN 105867122 B CN105867122 B CN 105867122B
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles
- G05D1/0208—Control of position or course in two dimensions specially adapted to water vehicles dynamic anchoring
Abstract
Dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation, is related to dynamic positioning of vessels field, and in particular to dynamic positioning ship wave frequency model parameter estimation system.Existing limited using precision present in bandpass filtering progress wave filtering in order to solve the problems, such as, the present invention includes：Wave frequency model parameter estimation function activation module, time window extraction module, metrical information sequential extraction procedures module, dominant frequency prediction device, high-pass filter, moving horizon estimation device and model parameter estimation terminate module；Dominant frequency prediction device take out dynamic positioning vessel position and bow to metrical information and carry out Fast Fourier Transform (FFT) and obtain spectral curve and determine initial wave frequency model parameter；High-pass filter, which is filtered metrical information, estimates wave frequency component motion；Then, moving horizon estimation device estimates wave frequency model parameter and wave frequency estimation.The present invention is suitable for dynamic positioning ship wave frequency model parameter estimation.
Description
Technical field
The present invention relates to dynamic positioning of vessels fields, and in particular to dynamic positioning ship wave frequency model parameter estimation system.
Background technology
With the development of technology, the scope of activities of people also gradually expands to far-reaching extra large marine site from littoral and coastal waters.It is every
Ocean engineering is required for ship guarantee and support equipped with dynamic positioning.Dynamic positioning system provides resistance using thruster
The effects that wind, wave, stream environmental forces aboard ship, to make ship be maintained at as much as possible on the position required on sea level.With
The exploitation of offshore oil and gas resource is constantly expanded to deep-sea, and traditional anchoring positioning method is just gradually replaced by dynamic positioning, according to
The main selection that positioning has become deep-sea oil gas production facility is carried out by the self power of marine structure.It positions cost not
It can increase as the depth of water increases, and operation is also more convenient, therefore dynamic positioning technology becomes the crucial skill of ocean petroleum developing
One of art is widely used in offshore drilling ship, platform supports ship, submersible supports ship, pipeline and cable laying ship, scientific investigation
On the ships such as ship, deep-sea lifeboat.
Movement is generated by the effect of wind, wave, stream and thruster when dynamic positioning ship works, apoplexy, second order are low
Movement caused by frequency wave, stream and propeller belongs to low frequency movement, and frequency range is 0~0.25rad/s, and single order wave and high frequency
Movement caused by unrestrained belongs to wave frequency movement, and frequency range is 0.3~1.6rad/s, boundary in ship control bandwidth or
The external world, but within the scope of the responsive bandwidth in ship executing agency.The actual collected signal of power-positioning control system
For integrated information, contain low frequency movement component, wave frequency component motion and measurement noise component.The target of power-positioning control system
It is the low frequency movement for controlling ship, it is therefore desirable to which the feedback states variable to entering control loop is filtered, by its height
Frequency component motion filters out.The performance of filtering depends on the accuracy of model parameter, the especially precision of wave frequency model parameter.Cause
This dynamic positioning ship wave frequency model parameter estimation problem becomes one of the focus of dynamic positioning technology.Lead in dynamic positioning system
Bandpass filtering is often used to carry out wave filtering, obtains the status information of controller needs, but method easy tos produce letter in this
Breath lag and the limited problem of precision, there is presently no a kind of methods that can be effectively improved this problem.
Invention content
The present invention carries out present in wave filtering that precision is limited asks in order to solve existing using bandpass filtering
Topic.
The parameter of model modification flogic system is needed by wave frequency model parameter estimation in ship power-positioning control system
System is estimated, then gained wave frequency model parameter is returned to the model modification system of ship power-positioning control system,
Complete the more new function of wave frequency model.The wave frequency model parameter estimation system of the present invention is fixed for the power based on moving horizon estimation
Position ship wave frequency model parameter estimation system.
Dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation, including：
Wave frequency model parameter estimation function activation module, metrical information sequential extraction procedures module, is dominated time window extraction module
Frequency estimation device, high-pass filter, moving horizon estimation device and model parameter estimation terminate module；
Wave frequency model parameter estimation function activation module, the data for realizing wave frequency model parameter estimation system are initial
Change, such as determines time window length；
Time window extraction module, the data for extracting a period of time from ship power-positioning control system lane database；
Metrical information sequential extraction procedures module, position and bow for extracting dynamic positioning ship in time window are believed to measurement
Breath；
Dominant frequency prediction device, for taken out out of data time window dynamic positioning vessel position and bow to metrical information
η, and Fast Fourier Transform (FFT) is carried out to it, obtain the spectrum curve of metrical information and determines initial wave frequency model parameter θ；
High-pass filter is filtered metrical information η, estimates wave frequency component motion
Moving horizon estimation device estimates wave frequency model parameter and high-pass filter using what dominant frequency prediction device estimated
Estimated wave frequency component motionWave frequency model parameter is estimated；Estimate corresponding wave frequency model parameter estimationWith
Wave frequency estimation
Wave frequency model parameter estimation terminate module, for passing wave frequency model parameter, and by dynamic positioning of vessels
Model modification logic in control system is set as false, completes wave frequency model parameter estimation.
Dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation carries out parameter Estimation, wave frequency mould
The process that gained wave frequency model parameter is returned to ship power-positioning control system by shape parameter estimating system is as follows：
When the model modification flogic system logic in ship power-positioning control system is true, wave frequency model parameter estimation
Function activation module starts, and is initialized to the data of wave frequency model parameter estimation system；Time window extraction module is from ship
Power-positioning control system lane database extracts the data of a period of time；Then metrical information sequential extraction procedures module is in time window
Extract dynamic positioning ship position and bow to metrical information；Dominant frequency prediction device takes out dynamic positioning out of data time window
Vessel position and bow to metrical information η and Fast Fourier Transform (FFT) is carried out to it, obtain the spectrum curve of metrical information and true
Fixed initial wave frequency model parameter；High-pass filter is filtered metrical information η, estimates wave frequency component motionWhen rolling
Domain estimator is transported using the wave frequency estimated estimated by wave frequency model parameter and high-pass filter that dominant frequency prediction device estimates
Dynamic componentWave frequency model parameter is estimated；Wave frequency model parameter estimation terminate module passes out wave frequency model parameter
It goes, and model modification logic is set as false, complete wave frequency model parameter estimation；So far, wave frequency model parameter estimation system is by institute
The model modification system that wave frequency model parameter returns to ship power-positioning control system is obtained, the update work(of wave frequency model is completed
Energy.
The present invention has the following effects that：
The wave frequency model parameter estimation system through the invention can estimate the wave frequency movement shape of ship in real time
State, and be isolated and come, and then obtain the status information of controller needs.Solves the sea that actual marine environment is variation
Unrestrained filtering problem improves the precision of state estimation.And carry out wave frequency model parameter estimation, estimated wave using the present invention
Frequency model parameter has converged near true value, it was demonstrated that wave frequency model parameter estimation system estimation success.Compared to utilizing bandpass filtering
The method for carrying out wave filtering, precision improve 15% or more.
Description of the drawings
Fig. 1 is the structural schematic diagram of the dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation；
Wherein, 1 is ship power-positioning control system, and 2 be wave frequency model parameter estimation system, and 3 be model modification flogic system, and 4 are
Wave frequency model parameter estimation function activation module, 5 be time window extraction module, and 6 be metrical information sequential extraction procedures module, based on 7
Setting frequency prediction device, 8 be high-pass filter, and 9 be moving horizon estimation device, and 10 be model parameter estimation terminate module, and 11 be mould
Type more new system；
Fig. 2 is the comparison diagram of the curve of estimation wave frequency model parameter and emulation wave frequency model parameter true value in embodiment；Its
In, Fig. 2 a are longitudinal dominant frequency comparison diagram, and Fig. 2 b are lateral dominant frequency comparison diagram, and Fig. 2 c are the upward dominant frequency pair of bow
Than figure.
Specific implementation mode
Specific implementation mode one：
The parameter of model modification flogic system 3 needs to estimate by wave frequency model parameter in ship power-positioning control system 1
Meter systems 2 are estimated, then gained wave frequency model parameter is returned to the model modification system of ship power-positioning control system 1
System 11 completes the more new function of wave frequency model.The wave frequency model parameter estimation system 2 of the present invention is based on moving horizon estimation
Dynamic positioning ship wave frequency model parameter estimation system.Dynamic positioning ship wave frequency model parameter estimation schematic diagram is as shown in Figure 1.
Dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation, including：
Wave frequency model parameter estimation function activation module 4, time window extraction module 5, metrical information sequential extraction procedures module 6,
Dominant frequency prediction device 7, high-pass filter 8, moving horizon estimation device 9 and model parameter estimation terminate module 10；
Wave frequency model parameter estimation function activation module 4, the data for realizing wave frequency model parameter estimation system 2 are initial
Change, such as determines time window length；
Time window extraction module 5, the number for extracting a period of time from 1 lane database of ship power-positioning control system
According to；
Metrical information sequential extraction procedures module 6, the position and bow for extracting dynamic positioning ship in time window are to measurement
Information；
Dominant frequency prediction device 7, for taken out out of data time window dynamic positioning vessel position and bow to measurement letter
η is ceased, and Fast Fourier Transform (FFT) is carried out to it, obtain the spectrum curve of metrical information and determines initial wave frequency model parameter θ；
High-pass filter 8 is filtered metrical information η, estimates wave frequency component motion
Moving horizon estimation device 9 estimates wave frequency model parameter and high-pass filtering using what dominant frequency prediction device 7 estimated
Wave frequency component motion estimated by device 8Wave frequency model parameter is estimated；Estimate corresponding wave frequency model parameter estimationWith wave frequency estimation
Wave frequency model parameter estimation terminate module 10 for passing wave frequency model parameter, and ship power is determined
Model modification logic in level controlling system 1 is set as false, completes wave frequency model parameter estimation.
Dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation carries out parameter Estimation, wave frequency mould
The process that gained wave frequency model parameter is returned to ship power-positioning control system 1 by shape parameter estimating system 2 is as follows：
When 3 logic of model modification flogic system in ship power-positioning control system 1 is true, wave frequency model parameter is estimated
It counts function activation module 4 to start, the data of wave frequency model parameter estimation system 2 is initialized；Time window extraction module 5 from
1 lane database of ship power-positioning control system extracts the data of a period of time；Then metrical information sequential extraction procedures module 6 from when
Between in window the position of extraction dynamic positioning ship and bow to metrical information；Dominant frequency prediction device 7 takes out out of data time window
Dynamic positioning vessel position and bow to metrical information η and Fast Fourier Transform (FFT) is carried out to it, obtain the frequency spectrum of metrical information
Curve simultaneously determines initial wave frequency model parameter；High-pass filter 8 is filtered metrical information η, estimates wave frequency component motionMoving horizon estimation device 9 estimates 8 institute of wave frequency model parameter and high-pass filter using what dominant frequency prediction device 7 estimated
The wave frequency component motion of estimationWave frequency model parameter is estimated；Wave frequency model parameter estimation terminate module 10 is by wave frequency
Model parameter passes, and model modification logic is set as false, completes wave frequency model parameter estimation；So far, wave frequency model is joined
Gained wave frequency model parameter is returned to the model modification system 11 of ship power-positioning control system 1 by number estimating system 2, is completed
The more new function of wave frequency model.
Specific implementation mode two：
By time window when wave frequency model parameter estimation function activation module 4 described in present embodiment carries out data initialization
Length is determined as 500 seconds and calls the content of database record.
Other modules and parameter are same as the specific embodiment one.
Specific implementation mode three：
Dominant frequency prediction device 7 described in present embodiment estimates dominant frequency based on fuzzy algorithmic approach determination.
Other modules and parameter are the same as one or two specific embodiments.
Specific implementation mode four：
Present embodiment
The design process of high-pass filter 8 described in present embodiment is as follows：
The characteristics of according to ship thrust response characteristic and wave frequency component motion, the technical indicator of high-pass filter is set as
Wherein, ω is circular frequency (also referred to as angular frequency), and j indicates imaginary number；
It when designing high-pass filter, is generally designed based on prototype lowpass filter, is then become by mapping
Get the high-pass filter of needs in return；Prototype lowpass filter is normalized prototype lowpass filter, and cutoff frequency is
ωc=1 (2)
The transmission function of prototype lowpass filter is
Wherein, s is transmission function variable, and n is transmission function exponent number；Parameter b1-bn+1And a1-an+1, using 10 ranks
Butterworth approach methods determine；
The cutoff frequency of target high-pass filter is
Frequency mapping relations are
Wherein, s' is the ssystem transfer function variable of high-pass filter；
Obtain the ssystem transfer function of high-pass filter：
By discretization, following form is turned to by the ssystem transfer function of above-mentioned high-pass filter is discrete
So far, high-pass filter is obtained by the normalization prototype of low-pass filter is frequency converted again.
Other modules and parameter are identical as one of specific implementation mode one to three.
Specific implementation mode five：
The design process of moving horizon estimation device 9 described in present embodiment is as follows：
Wave frequency movement estimation model be
Wherein, subscriptIndicate estimated value,For wave frequency state estimation vector, Aw(θ) and CwFor wave frequency model parameter square
Battle array, ε are estimation residual vector, and L is estimated gain matrix；For the wave frequency component motion of estimation；
White noise is not sound-driving in above-mentioned wave frequency model, the reason is that, when estimating wave frequency model parameter, wave frequency model
It is driven by estimation residual error；Wave frequency model parameter is denoted as
θ=[ωx ωy ωψ]T (9)
Wherein, ωxωyωψDominant frequency longitudinally, laterally upward with bow is indicated respectively；
In view of wave frequency model parameter is slowly varying variable, therefore reasonably assume that
The augmented state of wave frequency model in the parameter estimation process is denoted as
X=[θT ξT]T (11)
Measurand is denoted as
Estimate that residual error is
Wherein, k is current sample time；C is output matrix；
Then augmentation estimation model is
Estimate the function of state in model for augmentation；
Assuming that the sampling time is Ts, to augmentation estimation model carry out single order before it is discrete to Euler, then have
Wherein
K (k)=TsL(k) (17)
Known state prior estimateNormal Distribution Indicate mean value, P0Indicate variance；Estimation
Time domain length is N, and the cost function for choosing moving horizon estimation is
Wherein,The arrival cost of information before being reached for estimation time domain, using prior estimate come when compensating estimation
The estimated bias of state trajectory in domain；Q and R is respectively to be estimated systematic procedure noise and the covariance matrix of output noise；
For nonlinear system, above-mentioned cost function is by following constraint：
Formula (18)~(21) describe a Complete Information problem；In view of constraints has
Wherein, X is the set of feasible solution of state；
The moving horizon estimation problem of formula (18)~(22) description, the joint that can be equivalently converted to state trajectory are general
Rate very dense value problem
Based on moving horizon estimation technology, current time optimal State Estimation is obtained
Assuming that the probability distribution near optimal estimation is multivariate normal distributions, then under current probability distribution, nonlinear system
There are multiple locally optimal solutions；In order to solve the problems, such as this, introduce 7 offer of dominant frequency prediction device estimates dominant frequency as whole
The wave frequency model parameter initial value of a moving horizon estimation；Optimal wave frequency model parameter is
Wherein h=[I3×3 03×6]；So far the optimal State Estimation of augmented system is obtainedAccording to the state of augmented system
Definition, obtains corresponding optimal estimation：Wave frequency model parameter optimal estimationOptimal estimation is moved with wave frequency
By wave frequency model parameter optimal estimationOptimal estimation is moved with wave frequencyAs wave frequency model parameter estimationWith
Wave frequency estimationFinal estimated result.
Other modules and parameter are identical as one of specific implementation mode one to four.
Embodiment
In order to verify the wave frequency Model Distinguish effect of the present invention, wave frequency Model Distinguish l-G simulation test is carried out.
The purpose of experiment is in order to verify the wave frequency Model Distinguish effect of the present invention, therefore it is required that there are two moulds for l-G simulation test tool
Type：Emulate wave frequency model and identification wave frequency model.Wave frequency model parameter includes leading on relative damping ratio and three degree of freedom
Frequency.Relative damping ratio ζ=0.1 of simulation model is chosen, dominant frequency is respectively ωx=0.5, ωy=0.5 and ωψ=0.5.
Relative damping ζ=0.1 of identification model is chosen, the dominant frequency in state estimation can be provided arbitrarily, the initialization of parameter Estimation
Dominant frequency is determined by leading wave frequency prediction device.Time window length is 500 seconds, and the sampling time is 0.5 second.Moving horizon estimation
Weight matrix Qident=diag ([5e-3 5e-3 5e-2 5e-1 5e-1 1e-1 8e-1 8e-1 1e-1]).
Measuring signal obtains wave frequency motion filtering value after high-pass filterThen Kalman is extended to it
Filtering estimation obtains wave frequency model parameter estimation value, curve and the emulation wave frequency model parameter of estimated wave frequency model parameter
True value compare as shown in Fig. 2, wave frequency model estimates of parameters rapidly stablize near true value, therefore it may be concluded that
This l-G simulation test demonstrates the validity of the wave frequency model parameter estimation method based on moving horizon estimation.
Claims (4)
1. the dynamic positioning ship wave frequency model parameter estimation system based on moving horizon estimation, it is characterised in that it includes：
Wave frequency model parameter estimation function activation module (4), time window extraction module (5), metrical information sequential extraction procedures module
(6), dominant frequency prediction device (7), high-pass filter (8), moving horizon estimation device (9) and model parameter estimation terminate module
(10)；
Wave frequency model parameter estimation function activation module (4), the data for realizing wave frequency model parameter estimation system (2) are initial
Change；
Time window extraction module (5), the number for extracting a period of time from ship power-positioning control system (1) lane database
According to；
Metrical information sequential extraction procedures module (6), position and bow for extracting dynamic positioning ship in time window are believed to measurement
Breath；
Dominant frequency prediction device (7), for taken out out of data time window dynamic positioning vessel position and bow to metrical information
η, and Fast Fourier Transform (FFT) is carried out to it, obtain the spectrum curve of metrical information and determines initial wave frequency model parameter θ；
High-pass filter (8), is filtered metrical information η, estimates wave frequency component motion
Moving horizon estimation device (9) estimates wave frequency model parameter and high-pass filtering using what dominant frequency prediction device (7) estimated
Wave frequency component motion estimated by device (8)Wave frequency model parameter is estimated；Corresponding wave frequency model parameter is estimated to estimate
MeterWith wave frequency estimation
The design process of the moving horizon estimation device (9) is as follows：
Wave frequency movement estimation model be
Wherein, subscript ^ indicates estimated value,For wave frequency state estimation vector, Aw(θ) and CwFor wave frequency model parameter matrix, ε
To estimate residual vector, L is estimated gain matrix；For the wave frequency component motion of estimation；
Wave frequency model parameter is denoted as
θ=[ωx ωy ωψ]T (9)
Wherein, ωx ωy ωψDominant frequency longitudinally, laterally upward with bow is indicated respectively；
Assuming that
The augmented state of wave frequency model in the parameter estimation process is denoted as
X=[θT ξT]T (11)
Measurand is denoted as
Estimate that residual error is
Wherein, k is current sample time；C is output matrix；
Then augmentation estimation model is
Assuming that the sampling time is Ts, to augmentation estimation model carry out single order before it is discrete to Euler, then have
Wherein
K (k)=TsL(k) (17)
Known state prior estimateNormal DistributionEstimation time domain length is N, chooses rolling time horizon and estimates
The cost function of meter is
Wherein,The arrival cost of information before being reached for estimation time domain is compensated using prior estimate in estimation time domain
The estimated bias of state trajectory；Q and R is respectively to be estimated systematic procedure noise and the covariance matrix of output noise；
For nonlinear system, above-mentioned cost function is by following constraint：
Formula (18)~(21) describe a Complete Information problem；In view of constraints has
Wherein, X is the set of feasible solution of state；
The moving horizon estimation problem of formula (18)~(22) description, is equivalently converted to the joint probability density pole of state trajectory
Big value problem
Based on moving horizon estimation technology, current time optimal State Estimation is obtained
Assuming that the probability distribution near optimal estimation is multivariate normal distributions, then under current probability distribution, nonlinear system exists
Multiple locally optimal solutions；Introduce dominant frequency prediction device (7) offer estimates dominant frequency as entire moving horizon estimation
Wave frequency model parameter initial value；Optimal wave frequency model parameter is
Wherein h=[I3×3 03×6]；So far the optimal State Estimation of augmented system is obtainedIt is defined according to the state of augmented system,
Obtain corresponding optimal estimation：Wave frequency model parameter optimal estimationOptimal estimation is moved with wave frequency
By wave frequency model parameter optimal estimationOptimal estimation is moved with wave frequencyAs wave frequency model parameter estimationIt is transported with wave frequency
Dynamic estimationFinal estimated result；
Wave frequency model parameter estimation terminate module (10), for passing wave frequency model parameter, and by dynamic positioning of vessels
Model modification logic in control system (1) is set as false, completes wave frequency model parameter estimation.
2. the dynamic positioning ship wave frequency model parameter estimation system according to claim 1 based on moving horizon estimation,
It is characterized in that the wave frequency model parameter estimation function activation module (4) carry out it is when data initialization that time window length is true
It is set to 500 seconds and calls the content of database record.
3. the dynamic positioning ship wave frequency model parameter estimation system according to claim 2 based on moving horizon estimation,
It is characterized in that the dominant frequency prediction device (7) estimates dominant frequency based on fuzzy algorithmic approach determination.
4. the dynamic positioning ship wave frequency model parameter estimation according to claim 1,2 or 3 based on moving horizon estimation
System, it is characterised in that the design process of the high-pass filter (8) is as follows：
The characteristics of according to ship thrust response characteristic and wave frequency component motion, the technical indicator of high-pass filter is set as
Wherein, ω is circular frequency, and j indicates imaginary number；
When designing high-pass filter, it is designed based on prototype lowpass filter, is then needed by mapping transformation
The high-pass filter wanted；Prototype lowpass filter is normalized prototype lowpass filter, and cutoff frequency is
ωc=1 (2)
The transmission function of prototype lowpass filter is
Wherein, s is transmission function variable, and n is transmission function exponent number；Parameter b1-bn+1And a1-an+1, using 10 ranks
Butterworth approach methods determine；
The cutoff frequency of target high-pass filter is
Frequency mapping relations are
Wherein, s' is the ssystem transfer function variable of high-pass filter；
Obtain the ssystem transfer function of high-pass filter：
By discretization, following form is turned to by the ssystem transfer function of above-mentioned high-pass filter is discrete
So far, high-pass filter is obtained by the normalization prototype of low-pass filter is frequency converted again.
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| CN102854798A (en) * | 2012-09-11 | 2013-01-02 | 哈尔滨工程大学 | Online adjusting method of dynamic positioning parameter adaptive observer for ship |
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| CN102854798A (en) * | 2012-09-11 | 2013-01-02 | 哈尔滨工程大学 | Online adjusting method of dynamic positioning parameter adaptive observer for ship |
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