CN111414696B - Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering - Google Patents

Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering Download PDF

Info

Publication number
CN111414696B
CN111414696B CN202010201392.3A CN202010201392A CN111414696B CN 111414696 B CN111414696 B CN 111414696B CN 202010201392 A CN202010201392 A CN 202010201392A CN 111414696 B CN111414696 B CN 111414696B
Authority
CN
China
Prior art keywords
nonlinear
model
state
linear
ship
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010201392.3A
Other languages
Chinese (zh)
Other versions
CN111414696A (en
Inventor
焦玉召
娄泰山
赵红梅
王晓雷
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhengzhou University of Light Industry
Original Assignee
Zhengzhou University of Light Industry
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhengzhou University of Light Industry filed Critical Zhengzhou University of Light Industry
Priority to CN202010201392.3A priority Critical patent/CN111414696B/en
Publication of CN111414696A publication Critical patent/CN111414696A/en
Application granted granted Critical
Publication of CN111414696B publication Critical patent/CN111414696B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Landscapes

  • Feedback Control In General (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Navigation (AREA)

Abstract

The invention provides a hierarchical state estimation method based on model prediction extended Kalman filtering, which comprises the following steps: firstly, converting a nonlinear coupling system model into a linear hierarchical model and a nonlinear hierarchical model, and respectively predicting a state estimation value at the previous moment based on the linear hierarchical model and the nonlinear hierarchical model by utilizing first-stage extended Kalman filtering to obtain a linear state component estimation value; secondly, feeding back the nonlinear hierarchical model by utilizing the linear state component estimation value to obtain a nonlinear prediction model; and finally, predicting the linear state component estimation value based on a nonlinear prediction model by utilizing two-stage extended Kalman filtering to obtain the nonlinear state component estimation value. The hierarchical state estimation method provided by the invention improves the accuracy of system state estimation, reduces the computational dimension of the estimation process, and is suitable for the state estimation of a high-dimensional and linear state decoupling coupled complex system.

Description

Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering
Technical Field
The invention relates to the technical field of model prediction, in particular to a dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering.
Background
The application of estimation theory in the control field, the navigation and guidance field and the target tracking field is ubiquitous. In estimation theory, however, the system model is usually considered as an ideal linear system model or a non-linear system model. In practical engineering, the system is often a high-dimensional, coupled complex system with both linear and nonlinear states. The state estimation of a high-dimensional and coupling complex system with a linear state capable of being decoupled has the following two problems:
(1) for a complex coupled nonlinear system with linear state drive, the current linear estimation method or nonlinear estimation method cannot meet the requirements of system estimation precision and calculation load at the same time.
(2) Traditional state estimation methods are based on accurate model development, and for complex systems actually containing linear state coupling, the initial system model often contains uncertainty, especially for coupled complex systems with linear state drive.
Aiming at the two problems, the traditional extended Kalman filtering algorithm brings the problems of low precision, large calculated amount and even divergence of the estimation process. At present, an effective state estimation method for a nonlinear coupling system with linear state drive is not available.
Disclosure of Invention
Aiming at the defects in the background technology, the invention provides a dynamic positioning ship hierarchical state estimation method based on model prediction extended Kalman filtering, and solves the technical problems of high calculation complexity and low precision in the existing system state estimation method.
The technical scheme of the invention is realized as follows:
a dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering comprises the following steps:
s1, converting the nonlinear coupling system model containing the linear state based on the model equivalent transformation to obtain a decoupling form of the original model: a linear model and a non-linear hierarchical model;
s2, on the basis of the state estimation value at the previous moment, based on the linear model and the measurement value, obtaining a linear state component estimation value by utilizing first-stage extended Kalman filtering estimation;
s3, feeding back the nonlinear hierarchical model by using the linear state component estimation value in the step S2 to obtain a nonlinear state component prediction model;
and S4, obtaining the nonlinear state component estimation value by utilizing the second-level extended Kalman filtering estimation based on the linear state component estimation value, the nonlinear state component prediction model and the measurement value.
The nonlinear coupling system model including the linear state in step S1 is:
xk＝f(xk-1)+ωk (1)，
yk＝h(xk)+υk (2)，
wherein x iskSystem state at time k, xk-1The system state at time k-1, f (-) is the stateTransition matrix, ωkBeing process noise, ykFor the measurement, h (-) is the measurement transfer matrix, upsilonkTo measure noise.
The linear model and the nonlinear hierarchical model are respectively as follows:
Figure GDA0003591341040000021
Figure GDA0003591341040000022
Figure GDA0003591341040000023
wherein the content of the first and second substances,
Figure GDA0003591341040000024
representing the linear state component at time k,
Figure GDA0003591341040000025
representing the linear state component at time k-1,
Figure GDA0003591341040000026
a linear state transition matrix is represented that,
Figure GDA0003591341040000027
which is indicative of the noise of the linear process,
Figure GDA0003591341040000028
representing the non-linear state component at time k,
Figure GDA0003591341040000029
representing the nonlinear state component at time k-1,
Figure GDA00035913410400000210
and
Figure GDA00035913410400000211
each representing a non-linear state transition matrix associated with a linear state,
Figure GDA00035913410400000212
representing the nonlinear process noise, hk(. -) measurement matrix representing the nonlinear state, BkDenotes a linear measurement matrix, upsilon, related to a non-linear statekRepresenting the measurement noise.
The method for estimating the linear state component estimation value by utilizing the first-stage extended Kalman filtering state comprises the following steps:
s21, respectively calculating the linear state component predicted values according to the linear hierarchical model and the nonlinear hierarchical model
Figure GDA00035913410400000213
And nonlinear state component prediction
Figure GDA00035913410400000214
Figure GDA00035913410400000215
Figure GDA00035913410400000216
Wherein Q islFor linear state noise variance, QnIn order to be the non-linear state noise variance,
Figure GDA00035913410400000217
for the initial estimate of the linear state component,
Figure GDA00035913410400000218
is the initial estimated value of the nonlinear state component;
s22, estimating error covariance according to linear state
Figure GDA00035913410400000219
Computing linear state component covariance predictors
Figure GDA00035913410400000220
Figure GDA00035913410400000221
Wherein T is the transposition of the matrix;
s23, predicting value by using Jacobian matrix and linear state component covariance
Figure GDA00035913410400000222
Calculating a first order filter gain Kl：
Figure GDA00035913410400000223
Wherein the content of the first and second substances,
Figure GDA00035913410400000224
and
Figure GDA00035913410400000225
jacobian matrices each representing a nonlinear observation matrix, R being the measurement noise upsilonkThe variance of (a);
s24, obtaining a first-order filtering gain K according to the step S23lPredicting linear state component covariance at time k
Figure GDA0003591341040000031
Figure GDA0003591341040000032
Wherein I is an identity matrix;
s25, gain K according to first-order filteringlLinear state component prediction
Figure GDA0003591341040000033
And the measured value ykCalculating linear state component estimates
Figure GDA0003591341040000034
Figure GDA0003591341040000035
The nonlinear state component prediction model is as follows:
Figure GDA0003591341040000036
wherein the content of the first and second substances,
Figure GDA0003591341040000037
representing the non-linear state component at time k,
Figure GDA0003591341040000038
representing the nonlinear state component at time k-1,
Figure GDA0003591341040000039
and
Figure GDA00035913410400000310
each representing a non-linear state transition matrix associated with a linear state,
Figure GDA00035913410400000311
which is indicative of the non-linear process noise,
Figure GDA00035913410400000312
is a linear state component estimate.
The method for estimating the nonlinear state component estimation value by utilizing the two-stage extended Kalman filtering comprises the following steps:
s41, estimating the value according to the Jacobian matrix and the linear state component
Figure GDA00035913410400000313
Computing nonlinear state component covariance predictors
Figure GDA00035913410400000314
Figure GDA00035913410400000315
Wherein the content of the first and second substances,
Figure GDA00035913410400000316
jacobian matrix, Q, representing a model of a nonlinear statenIn order to be the non-linear state noise variance,
Figure GDA00035913410400000317
representing a non-linear state transition matrix associated with a linear state;
s42, predicting the covariance of the nonlinear state components in step S41
Figure GDA00035913410400000318
Calculating a second order filter gain Kn：
Figure GDA00035913410400000319
Wherein the content of the first and second substances,
Figure GDA00035913410400000320
and
Figure GDA00035913410400000321
jacobian matrices each representing a nonlinear observation matrix, R being the measurement noise upsilonkThe variance of (a);
s43, using second-order filter gain KnPredicting nonlinear state component covariance at time k
Figure GDA00035913410400000322
Figure GDA00035913410400000323
S44 obtaining a second-order filter gain KnNonlinear state component prediction
Figure GDA00035913410400000324
And the measured value ykCalculating a nonlinear state component estimate
Figure GDA00035913410400000325
Figure GDA00035913410400000326
The beneficial effect that this technical scheme can produce:
(1) the model reconstruction is carried out on the initial coupling system based on the model reconstruction principle, so that the practical application problem of the existing estimation theory under the complex coupling system model is solved;
(2) according to the invention, by decoupling the line state, the system dimension in the estimation process can be reduced, and the calculation amount in the estimation process is reduced.
(3) A Kalman filtering framework under linear state and nonlinear measurement can be obtained by calculating a Jacobian matrix for a nonlinear observation model, and an estimation value of a linear state component can be obtained based on a first-stage linear state estimation method.
(4) Through the first-stage estimation under decoupling, the influence of nonlinear state estimation of a coupling system on linear state estimation can be reduced, and the linear state estimation precision is improved.
(5) Model prediction is carried out on the coupling nonlinear state component based on the first-stage linear state estimation, and the accuracy of the coupling nonlinear system model can be improved and the influence of model uncertainty on nonlinear estimation can be inhibited by feeding back the first-stage estimation output to the coupling nonlinear model.
(6) Based on a two-stage nonlinear state estimation method, the dependence of the traditional method on a model can be overcome by estimating the nonlinear state component on the basis of model prediction.
In conclusion, the method can solve the problem of state estimation of the coupling nonlinear system under the condition that the linear state can be decoupled, overcomes the problems of high dependency, insufficient estimation precision and overlarge calculated amount of a traditional algorithm model, and achieves a better estimation effect.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a functional block diagram of the present invention;
FIG. 3 is a diagram of a linear component first order estimate of the present invention;
FIG. 4 is a block diagram of the two-stage estimation of the nonlinear component of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1, the invention provides a dynamic positioning vessel classification state estimation method based on model prediction extended kalman filtering, which comprises the following specific steps:
s1, converting the nonlinear coupling system model containing the linear state into a linear hierarchical model and a nonlinear hierarchical model based on model equivalent transformation; wherein, the nonlinear coupling system model containing the linear state is as follows:
xk＝f(xk-1)+ωk (1)，
yk＝h(xk)+υk (2)，
wherein x iskSystem state at time k, xk-1Is the system state at time k-1, f (-) is the state transition matrix, ωkBeing process noise, ykFor the measurement, h (-) is the measurement transfer matrix, upsilonkTo measure noise.
For a linear state decoupling hybrid model, converting a nonlinear coupling system model containing a linear state into a linear hierarchical model and a nonlinear hierarchical model based on model equivalent transformation:
Figure GDA0003591341040000051
Figure GDA0003591341040000052
Figure GDA0003591341040000053
wherein the content of the first and second substances,
Figure GDA0003591341040000054
representing the linear state component at time k,
Figure GDA0003591341040000055
representing the linear state component at time k-1,
Figure GDA0003591341040000056
a linear state transition matrix is represented and,
Figure GDA0003591341040000057
representing linear process noise, linear process noise
Figure GDA0003591341040000058
Has a mean value of 0, linear process noise
Figure GDA0003591341040000059
Has a variance of Ql，
Figure GDA00035913410400000510
Representing the non-linear state component at time k,
Figure GDA00035913410400000511
representing the nonlinear state component at time k-1,
Figure GDA00035913410400000512
and
Figure GDA00035913410400000513
each representing a non-linear state transition matrix associated with a linear state,
Figure GDA00035913410400000514
representing non-linear process noise, non-linear process noise
Figure GDA00035913410400000515
Has a mean value of 0, nonlinear process noise
Figure GDA00035913410400000516
Has a variance of Qn，hk(. -) measurement matrix representing the nonlinear state, BkDenotes a linear measurement matrix, upsilon, related to a non-linear statekRepresenting measurement noise, vkHas a mean value of 0, measures the noise upsilonkThe variance of (c) is R. Compared with the original system, the sum of the dimensions of the converted linear and nonlinear hierarchical models is equal to the dimension of the original system, and then the state estimation process is executed based on the hierarchical model, so that the dimension of the system estimation process is effectively reduced, and the calculation amount of the estimation process is reduced. Meanwhile, the hierarchical model can separate the linear state from the nonlinear state, and a corresponding estimation method can be designed in a targeted manner.
And S2, on the basis of the state estimation value at the previous moment, based on the linear model and the measurement value, utilizing the linear state component estimation value obtained by the first-stage extended Kalman filtering state estimation.
For the linear state component, a linear component primary estimation structure diagram is designed, and as shown in fig. 3, a linear state component estimation value is obtained by utilizing primary extended kalman filter estimation, and the specific method is as follows:
s21, respectively calculating the linear state component predicted values according to the linear hierarchical model and the nonlinear hierarchical model
Figure GDA00035913410400000517
And nonlinear state component prediction
Figure GDA00035913410400000518
Figure GDA00035913410400000519
Figure GDA00035913410400000520
Wherein the content of the first and second substances,
Figure GDA0003591341040000061
for the initial estimate of the linear state component,
Figure GDA0003591341040000062
for initial estimation of the nonlinear state component, QlFor linear state noise variance, QnIs the nonlinear state noise variance;
s22, estimating error covariance according to linear state
Figure GDA0003591341040000063
Computing linear state component covariance predictors
Figure GDA0003591341040000064
Figure GDA0003591341040000065
Wherein T is the transposition of the matrix;
s23, predicting value by using Jacobi (Jacobi) matrix and linear state component covariance
Figure GDA0003591341040000066
Calculating a first order filter gain Kl：
Figure GDA0003591341040000067
Wherein the content of the first and second substances,
Figure GDA0003591341040000068
and
Figure GDA0003591341040000069
jacobian matrices each representing a nonlinear observation matrix, R being the measurement noise upsilonkThe variance of (a);
s24, obtaining a first-order filtering gain K according to the step S23lPredicting linear state component covariance at time k
Figure GDA00035913410400000610
Figure GDA00035913410400000611
Wherein I is an identity matrix;
s25 obtaining a first-order filter gain KlLinear state component prediction
Figure GDA00035913410400000612
And the measured value ykCalculating linear state component estimates
Figure GDA00035913410400000613
Figure GDA00035913410400000614
Based on steps S21 through S25, the next linear state component estimation value is obtained
Figure GDA00035913410400000615
The linear state component estimation value is used as an external correction signal to predict a nonlinear component model, namely, the linear state component estimation value
Figure GDA00035913410400000616
And substituting the nonlinear prediction model into a nonlinear hierarchical model to obtain a nonlinear prediction model.
S3, feeding back the nonlinear hierarchical model by using the linear state component estimation value in the step S2 to obtain a nonlinear state component prediction model:
Figure GDA00035913410400000617
wherein the content of the first and second substances,
Figure GDA00035913410400000618
representing the non-linear state component at time k,
Figure GDA00035913410400000619
representing the nonlinear state component at time k-1,
Figure GDA00035913410400000620
and
Figure GDA00035913410400000621
each representing a non-linear state transition matrix associated with a linear state,
Figure GDA00035913410400000622
which is indicative of the non-linear process noise,
Figure GDA00035913410400000623
is a linear state component estimate.
And S4, obtaining the nonlinear state component estimation value by utilizing the second-stage extended Kalman filtering state estimation based on the state component first-stage state estimation value, the nonlinear state prediction model and the measurement value.
Based on a nonlinear prediction model-formula (12) and a measurement equation-formula (5), a structure diagram of a nonlinear component secondary estimation is designed, as shown in fig. 4, a nonlinear state component estimation value is predicted by using a secondary extended kalman filter, and the specific method is as follows:
s41, estimating the value according to the Jacobian matrix and the linear state component
Figure GDA0003591341040000071
Computing nonlinear state component covariance predictors
Figure GDA0003591341040000072
Figure GDA0003591341040000073
Wherein the content of the first and second substances,
Figure GDA0003591341040000074
a jacobian matrix representing a nonlinear state model,
Figure GDA0003591341040000075
represents the nonlinear state component at time k-1;
s42, predicting the covariance of the nonlinear state components in step S41
Figure GDA0003591341040000076
Calculating a second order filter gain Kn：
Figure GDA0003591341040000077
S43, using second-order filter gain KnPredicting nonlinear state component covariance at time k
Figure GDA0003591341040000078
Figure GDA0003591341040000079
S44 obtaining a second-order filter gain KnNonlinear state component prediction
Figure GDA00035913410400000710
And the measured value ykCalculating a nonlinear state component estimate
Figure GDA00035913410400000711
Figure GDA00035913410400000712
Based on the steps S41 to S44, the estimated value of the nonlinear state component can be obtained
Figure GDA00035913410400000713
Taking a dynamic positioning ship as an example:
(1) kinematic model
When the dynamic positioning vessel is operated in low sea conditions, the motions of the vessel in the three directions of rolling, pitching and heaving are negligible, so that only the motions of rolling, pitching and yawing of the dynamic positioning vessel are considered here. The following three-degree-of-freedom low-frequency kinematic model is established.
Figure GDA00035913410400000714
Wherein eta is [ x, y, psi ═ x, y, psi]T，υ＝[u,v,r]T(ii) a And x is the north position of the ship and y is the east position of the shipThe heading position psi is the ship heading angle; u is the ship surging speed, v is the ship swaying speed, and r is the ship heading rate. J (ψ) represents a coordinate conversion matrix expressed as follows:
Figure GDA00035913410400000715
dynamic positioning ships generally run at low speed, namely, the speed variation is small, so that a first-order acceleration model can be established:
Figure GDA00035913410400000716
where ω represents zero-mean gaussian noise.
Order to
Figure GDA00035913410400000717
The above system can be reconstructed into the following form by a model equivalence transformation:
Figure GDA0003591341040000081
wherein the north and east positions are influenced by the heading angle psi, while the heading angle and the yaw rate both satisfy a linear state relationship. The method can be converted into the following linear and nonlinear hierarchical model forms through a splitting system:
the heading single-degree-of-freedom model is as follows:
Figure GDA0003591341040000082
the two-degree-of-freedom model from north to east is as follows:
Figure GDA0003591341040000083
to utilize the method disclosed above, the kinematic models (21) and (22) were transformed by the euler method into the following hierarchical discretization forms (23) and (24), respectively:
Figure GDA0003591341040000084
where Δ t is the sampling time,
Figure GDA0003591341040000085
indicating the heading and yaw rate at time k + 1.
Figure GDA0003591341040000086
Wherein the content of the first and second substances,
Figure GDA0003591341040000087
represents the north position, east position, surging speed and swaying speed at time k + 1.
(2) Measurement model
The measurement model can be expressed as:
Figure GDA0003591341040000088
therefore, the temperature of the molten metal is controlled,
Figure GDA0003591341040000089
Figure GDA00035913410400000810
based on the method, estimated values of the heading and the heading rate of the ship are obtained through first-stage state estimation, the estimated values are substituted into a nonlinear state model to obtain a prediction model, and the northbound position, the eastern position, the total oscillation speed and the transverse oscillation speed of the ship can be obtained through second-stage state estimation further based on the prediction model and the heading estimated values.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (6)

1. A dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering is characterized by comprising the following steps:
s1, establishing a three-degree-of-freedom low-frequency kinematics model based on surging, swaying and yawing motions of the dynamic positioning ship;
the three-degree-of-freedom low-frequency kinematic model is expressed as:
Figure FDA0003605777080000011
wherein eta is [ x, y, psi ═ x, y, psi]T，υ＝[u,v,r]TX is the north position of the ship, y is the east position of the ship, and psi is the heading of the ship; u is the ship surging speed, v is the ship swaying speed, and r is the ship bow rate; j (ψ) represents a ship state coordinate conversion matrix expressed as follows:
Figure FDA0003605777080000012
the speed variation of the dynamic positioning ship is small, and a first-order acceleration model is established:
Figure FDA0003605777080000013
wherein ω represents zero-mean gaussian noise;
order to
Figure FDA0003605777080000014
Reconstructing the three-degree-of-freedom low-frequency kinematic model into the following parts by model equivalent transformation:
Figure FDA0003605777080000015
splitting the reconstructed three-degree-of-freedom low-frequency kinematic model to respectively obtain a heading single-degree-of-freedom linear classification model and a north-east two-degree-of-freedom nonlinear classification model as follows:
Figure FDA0003605777080000016
Figure FDA0003605777080000017
the measurement model is expressed as:
Figure FDA0003605777080000018
wherein, yk+1Measured at time k +1, I is the identity matrix,
Figure FDA0003605777080000019
represents a linear state component composed of heading and yaw rate at the moment of k +1,
Figure FDA00036057770800000110
representing a nonlinear state component upsilon consisting of a north position, an east position, a surging speed and a swaying speed of the ship at the moment of k +1k+1Representing measurement noise;
s2, discretizing the heading single-degree-of-freedom linear hierarchical model and the north-east two-degree-of-freedom nonlinear hierarchical model by utilizing an Eulerian method to obtain a discretization form;
s3, based on the discretization form, obtaining linear state component estimation values of ship heading and heading rate at the moment k through first-stage extended Kalman filtering state estimation
Figure FDA0003605777080000021
S4, estimating the linear state
Figure FDA0003605777080000022
Substituting the two-degree-of-freedom nonlinear hierarchical model into the north-east to obtain a prediction model;
s5, based on the prediction model, the linear state component estimation value and the measured value, obtaining the nonlinear state component estimation values of the north position, the east position, the surging speed and the surging speed of the ship at the moment k through second-order extended Kalman filtering state estimation
Figure FDA0003605777080000023
2. The method for estimating the classification state of the dynamically positioned vessel based on the model-predictive extended kalman filter according to claim 1, wherein in step S2, the obtained discretization forms are respectively expressed as:
Figure FDA0003605777080000024
where Δ t is the sampling time,
Figure FDA0003605777080000025
the heading and the yaw rate at the k +1 moment are represented;
Figure FDA0003605777080000026
wherein the content of the first and second substances,
Figure FDA0003605777080000027
represents the north position, east position, surging speed and swaying speed at time k + 1.
3. The die-based according to claim 2The method for estimating the classification state of the dynamic positioning ship based on the model prediction extended Kalman filtering is characterized by comprising the following steps of
Figure FDA0003605777080000028
Figure FDA0003605777080000029
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00036057770800000210
a linear state transition matrix representing the vessel heading and yaw rate,
Figure FDA00036057770800000211
which is indicative of the noise of the linear process,
Figure FDA00036057770800000212
a non-linear state transition matrix representing an east position, a surge speed, and a surge speed associated with the linear state,
Figure FDA00036057770800000213
representing nonlinear process noise, Bk(. cndot.) represents a linear measurement matrix associated with a non-linear state.
4. The hierarchical state estimation method for a dynamically positioned vessel based on model-predictive extended Kalman filter according to claim 3, characterized in that in step S3, the estimated value of the linear state component is obtained
Figure FDA0003605777080000031
The method comprises the following specific steps:
s31, calculating the linear state component prediction value of heading and heading rate based on the discretization forms (7) and (8)
Figure FDA0003605777080000032
And the north position, east position, surging speed and swaying of the shipNonlinear state component prediction of velocity
Figure FDA0003605777080000033
Figure FDA0003605777080000034
Figure FDA0003605777080000035
Wherein QlIs the linear state noise variance, QnIn order to be a non-linear state noise variance,
Figure FDA0003605777080000036
is the initial estimated value of the linear state of the heading and the yawing rate of the ship,
Figure FDA0003605777080000037
the initial estimated values of the ship north position, east position, surging speed and swaying speed in the nonlinear state,
Figure FDA0003605777080000038
representing a nonlinear state transition matrix associated with a linear state;
s32, estimating error covariance according to the initial linear state of ship heading and heading rate at the k-1 moment
Figure FDA0003605777080000039
Calculating linear state component covariance predicted value of ship heading and heading rate at moment k
Figure FDA00036057770800000310
Figure FDA00036057770800000311
Wherein T is the transposition of the matrix;
s33, using Jacobian matrix and the linear state component covariance prediction value
Figure FDA00036057770800000312
First-order filtering gain K for calculating heading and heading rate at moment Kl：
Figure FDA00036057770800000313
Wherein the content of the first and second substances,
Figure FDA00036057770800000314
and
Figure FDA00036057770800000315
jacobian matrices each representing a nonlinear observation matrix, R being the measurement noise upsilonkVariance of hk() a measurement matrix representing a nonlinear state;
s34, obtaining the first-order filter gain K according to the step S33lPredicting linear state component covariance of heading and yaw rate at time k
Figure FDA00036057770800000316
Figure FDA00036057770800000317
S35, according to the first-order filtering gain KlThe linear state component prediction value
Figure FDA00036057770800000318
And the measured value y at the time kkCalculating the linear state component estimated value at k-time of heading and yaw rate
Figure FDA00036057770800000319
Figure FDA00036057770800000320
Wherein the content of the first and second substances,
Figure FDA00036057770800000321
5. the method for estimating the hierarchical state of the dynamically positioned ship based on the model prediction extended kalman filter according to claim 4, wherein in step S4, the specific steps of obtaining the prediction model are as follows:
using the linear state component estimated value obtained in S3
Figure FDA00036057770800000322
Feeding back the discretization form formula (8) to obtain a k-moment north-east two-degree-of-freedom nonlinear state component prediction model:
Figure FDA0003605777080000041
6. the method according to claim 5, wherein the estimated value of the nonlinear state component is obtained in step S5
Figure FDA0003605777080000042
The method comprises the following specific steps:
s51, estimating the value according to the Jacobian matrix and the linear state component
Figure FDA0003605777080000043
Calculating north position and east of ship at time kNonlinear state component covariance prediction for location, surge velocity, and sway velocity
Figure FDA0003605777080000044
Figure FDA0003605777080000045
Wherein the content of the first and second substances,
Figure FDA0003605777080000046
a jacobian representing the nonlinear state transition matrix at time k,
Figure FDA0003605777080000047
represents the nonlinear state component at time k-1;
s52, predicting the covariance of the nonlinear state components according to the k time in the step S51
Figure FDA0003605777080000048
Calculating the second-order filter gain K at the moment of Kn：
Figure FDA0003605777080000049
S53, utilizing the K moment second-order filter gain KnPredicting the covariance of nonlinear state components of the north position, the east position, the surging speed and the surging speed of the ship at the moment k
Figure FDA00036057770800000410
Figure FDA00036057770800000411
S54, according to the K time second-order filter gain KnThe nonlinear state component pre-Measured value
Figure FDA00036057770800000412
And the measured value y at the time kkAnd calculating the estimated values of the nonlinear state components of the north position, the east position, the surging speed and the swaying speed of the ship at the moment k
Figure FDA00036057770800000413
Figure FDA00036057770800000414
CN202010201392.3A 2020-03-20 2020-03-20 Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering Active CN111414696B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010201392.3A CN111414696B (en) 2020-03-20 2020-03-20 Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010201392.3A CN111414696B (en) 2020-03-20 2020-03-20 Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering

Publications (2)

Publication Number Publication Date
CN111414696A CN111414696A (en) 2020-07-14
CN111414696B true CN111414696B (en) 2022-06-14

Family

ID=71491326

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010201392.3A Active CN111414696B (en) 2020-03-20 2020-03-20 Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering

Country Status (1)

Country Link
CN (1) CN111414696B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111998854B (en) * 2020-08-31 2022-04-15 郑州轻工业大学 Cholesky decomposition calculation-based accurate expansion Stirling interpolation filtering method
CN112591153B (en) * 2020-12-08 2022-06-10 北京航空航天大学 Based on anti-interference multiple target H2/H∞Filtering space manipulator tail end positioning method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106646356A (en) * 2016-11-23 2017-05-10 西安电子科技大学 Nonlinear system state estimation method based on Kalman filtering positioning
CN108489498A (en) * 2018-06-15 2018-09-04 哈尔滨工程大学 A kind of AUV collaborative navigation methods without mark particle filter based on maximum cross-correlation entropy
CN110119588A (en) * 2019-05-21 2019-08-13 杭州电子科技大学 On-line optimization design method based on Extended Kalman filter state estimation

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106646356A (en) * 2016-11-23 2017-05-10 西安电子科技大学 Nonlinear system state estimation method based on Kalman filtering positioning
CN108489498A (en) * 2018-06-15 2018-09-04 哈尔滨工程大学 A kind of AUV collaborative navigation methods without mark particle filter based on maximum cross-correlation entropy
CN110119588A (en) * 2019-05-21 2019-08-13 杭州电子科技大学 On-line optimization design method based on Extended Kalman filter state estimation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
XIAOGONG LIN 等.《An Improved Gaussian Filter for Dynamic Positioning Ships With Colored Noises and Random Measurements Loss》.《IEEE ACCESS》.2018,第6卷正文第6620-6629页. *

Also Published As

Publication number Publication date
CN111414696A (en) 2020-07-14

Similar Documents

Publication Publication Date Title
CN108197350B (en) Unmanned ship speed and uncertainty estimation system and design method
Balchen et al. A dynamic positioning system based on Kalman filtering and optimal control
CN111414696B (en) Dynamic positioning ship grading state estimation method based on model prediction extended Kalman filtering
CN103970021B (en) A kind of lax power-positioning control system based on Model Predictive Control
CN111897225B (en) Fuzzy self-adaptive output feedback control method and system for intelligent ship autopilot system
CN103605886A (en) Multi-model self-adaptive fusion filtering method of ship dynamic positioning system
CN112432644B (en) Unmanned ship integrated navigation method based on robust adaptive unscented Kalman filtering
CN110703605B (en) Self-adaptive fuzzy optimal control method and system for intelligent ship autopilot system
CN112068440B (en) AUV recovery butt joint power positioning control method based on model prediction control
CN104316025A (en) System for estimating height of sea wave based on attitude information of ship
CN111930124A (en) Fuzzy self-adaptive output feedback finite time control method and system for intelligent ship autopilot system
CN111221335A (en) Fuzzy self-adaptive output feedback finite time control method and system for intelligent ship autopilot system
CN111025909B (en) Kalman three-degree-of-freedom decoupling filtering method of ship motion control system
Qian et al. An INS/DVL integrated navigation filtering method against complex underwater environment
CN109739089B (en) Non-periodic sampling remote control system for unmanned ship and design method
CN114777812A (en) Method for estimating alignment and attitude of underwater integrated navigation system during traveling
Zou et al. An adaptive robust cubature Kalman filter based on Sage-Husa estimator for improving ship heave measurement accuracy
CN114035550A (en) Autonomous underwater robot executing mechanism fault diagnosis method based on ESO
Hou et al. Improved exponential weighted moving average based measurement noise estimation for strapdown inertial navigation system/Doppler velocity log integrated system
CN113608534A (en) Unmanned ship tracking control method and system
CN112591038A (en) Method for estimating nonlinear state of dynamic positioning ship under uncertain model parameters
CN113703454B (en) Four-degree-of-freedom-based unmanned ship power parameter real-time identification method
CN115824224B (en) Autonomous dead reckoning method for underwater robot based on AHRS and DVL
Bremnes et al. Sensor-based hybrid translational observer for underwater navigation
Andersson et al. The moving horizon estimator used in iceberg drift estimation and Forecast

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant