CN112591038A - Method for estimating nonlinear state of dynamic positioning ship under uncertain model parameters - Google Patents

Method for estimating nonlinear state of dynamic positioning ship under uncertain model parameters Download PDF

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CN112591038A
CN112591038A CN202011484573.8A CN202011484573A CN112591038A CN 112591038 A CN112591038 A CN 112591038A CN 202011484573 A CN202011484573 A CN 202011484573A CN 112591038 A CN112591038 A CN 112591038A
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state
dynamic positioning
positioning ship
covariance
ship
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林孝工
田伟达
张伟
刘向波
赵大威
刘叶叶
张超
赖冲浪
李恒
孙晓庆
孙涵
常弘煜
苏江玉
杨化栋
王华霆
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Harbin Engineering University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
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Abstract

The invention belongs to the technical field of dynamic positioning ship state estimation of a nonlinear system, and particularly relates to a dynamic positioning ship nonlinear state estimation method under the condition of uncertain model parameters. According to the north position, the east position and the heading angle of the dynamic positioning ship under the initial condition, the three-degree-of-freedom discrete time state space model of the dynamic positioning ship is converted into a nonlinear system model with uncertain model parameters, and then the state vector estimation value of the dynamic positioning ship is calculated. The invention overcomes the condition that a nonlinear system must be continuously differentiable, does not need to calculate a Jacobi matrix of the system, not only maintains robustness, but also further improves the precision of state prediction and covariance prediction due to the introduction of a volume rule.

Description

Method for estimating nonlinear state of dynamic positioning ship under uncertain model parameters
Technical Field
The invention belongs to the technical field of dynamic positioning ship state estimation of a nonlinear system, and particularly relates to a dynamic positioning ship nonlinear state estimation method under the condition of uncertain model parameters.
Background
Dynamic Positioning (DP) systems are used to counteract the external environmental forces acting on the vessel, such as wind, waves and currents, by controlling the propulsion of the vessel, thereby allowing the vessel to remain in a defined position or to navigate along a desired set trajectory. The DP technology becomes a necessary technology for marine operation of ships, and the body shadow of the DP ship exists in various fields such as marine resource mining, seabed pipe laying, cable laying, marine rescue and the like.
Due to the fact that marine environments are complex and changeable, a system model of an actual DP ship is not very accurate, the system has model parameter uncertainty interference, and in addition, due to the fact that a DP ship system is often nonlinear, the estimation of the actual state of the system has certain difficulty, and further control over the system is not facilitated. In DP ship state estimation, in addition to being affected by additive cross-correlation noise, there are the following problems: an accurate system model and noise interference statistical characteristics cannot be obtained, and meanwhile, a random packet loss phenomenon exists in the sensor unit, namely parameter uncertainty interference exists in the system. Aiming at the DP ship nonlinear system with uncertain system model parameters, the research on the corresponding DP ship nonlinear state estimation algorithm has important practical significance.
Disclosure of Invention
The invention aims to provide a nonlinear state estimation method of a dynamic positioning ship under the condition of uncertain model parameters.
The purpose of the invention is realized by the following technical scheme: the method comprises the following steps:
step 1: initializing a parameter k to be 1, and acquiring the north position, the east position and the heading angle eta of the dynamic positioning ship under the initial condition to be [ x ═ xN,yE,ψ]TConverting a three-degree-of-freedom discrete time state space model of the dynamic positioning ship into a nonlinear system model with uncertain model parameters:
xk＝fk-1(xk-1)+ωk
zk＝hk(xk)+υk
wherein f isk-1() represents a state transition matrix; h isk(. to) represent a quantity transfer matrix; x is the number ofkRepresenting the state vector of the dynamic positioning ship at the moment k, and recording the initial state of a nonlinear system model with uncertain model parameters as
Figure BDA0002838635990000011
Initial estimation error covariance of P0|0；zkRepresenting an observed value; omegakAnd upsilonkIs system noise, satisfies
Figure BDA0002838635990000012
And Q and R represent mean, Q and R represent variance; from an initial state
Figure BDA0002838635990000013
And initial estimation error covariance P0|0The initial volume points obtained are:
Figure BDA0002838635990000014
Figure BDA0002838635990000015
wherein S isk-1|k-1＝chol(Pk-1|k-1) Representing square root factors obtained by Cholesky decomposition, i.e.
Figure BDA0002838635990000021
[1]iIs a vector point generator for generating initial volume points, n being the number of vector points;
step 2: calculating the state vector estimated value of the dynamic positioning ship at the k moment under the condition of the k-1 moment
Figure BDA0002838635990000022
Sum covariance prediction value Pk|k-1；
Figure BDA0002838635990000023
Figure BDA0002838635990000024
Figure BDA0002838635990000025
Wherein the content of the first and second substances,
Figure BDA0002838635990000026
representing a state transfer volume point;
and step 3: computing measurement estimates
Figure BDA0002838635990000027
And measuring the estimation error ez,k-1|k-1；
Figure BDA0002838635990000028
Figure BDA0002838635990000029
Wherein the content of the first and second substances,
Figure BDA00028386359900000210
is the transfer volume point of the observation equation;
and 4, step 4: calculating innovation
Figure BDA00028386359900000211
And measuring the predicted value
Figure BDA00028386359900000212
Figure BDA00028386359900000213
Figure BDA00028386359900000214
And 5: calculating a square root factor of innovation covariance
Figure BDA00028386359900000215
Figure BDA00028386359900000216
Wherein the content of the first and second substances,
Figure BDA00028386359900000217
step 6: computing an error covariance update value Pk|k；
Figure BDA00028386359900000218
Wherein the content of the first and second substances,
Figure BDA0002838635990000031
and 7: calculating an optimal boundary layer psik；
Figure BDA0002838635990000032
Figure BDA0002838635990000033
Figure BDA0002838635990000034
And 7: calculating a filter gain KkObtaining the state vector estimated value of the dynamic positioning ship at the moment k
Figure BDA0002838635990000035
Figure BDA0002838635990000036
Figure BDA0002838635990000037
Wherein, the parameter is more than 0 and less than 1; the symbol '+' represents the pseudo-inverse; diag (·) is a diagonalized version of ·; symbol
Figure BDA0002838635990000038
Represents the Schur product;
Figure BDA0002838635990000039
representing a diagonalized version of the boundary layer;
Figure BDA00028386359900000310
and 8: judging whether the dynamic positioning ship finishes the task or not; if not, k is made to be k +1, and the process returns to step 2 to estimate the state vector of the dynamic positioning ship at the next time.
The invention has the beneficial effects that:
the invention provides a nonlinear state estimation method of a dynamic positioning ship under the condition of uncertain model parameters, which overcomes the condition that a nonlinear system must be continuous and differentiable, does not need to calculate a Jacobi matrix of the system, not only keeps robustness, but also further improves the precision of state prediction and covariance prediction due to the introduction of a volume rule.
Drawings
Fig. 1 is a diagram depicting the motion coordinates of a DP ship.
FIG. 2 is a graph of the DP vessel north-east-heading position RMSE at known noise.
Fig. 3 is a graph of surge-sway-heading RMSE under known noise.
FIG. 4 is a graph of DP boat north-east-heading position RMSE under unknown noise.
FIG. 5 is a graph of pitch-roll-yaw RMSE for a DP vessel under unknown noise.
FIG. 6 is a flow chart of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention provides a nonlinear state estimation method of a dynamic positioning ship under model parameter uncertainty, and for a model uncertainty continuous differentiable nonlinear system, E-SVSF is an effective filtering algorithm, but still has certain limitations: one is to require the system equation to be reasonably nonlinear and differentiable, and to compute the Jacobi matrix of the system; secondly, due to the limitation of the word length of the computer, the covariance may lose non-negativity due to error accumulation, and the filtering divergence is caused.
Aiming at the defects of the prior art, the invention provides a volume smooth variable structure filter (C-SVSF) algorithm for calculating a state predicted value, predicting state covariance, measuring the predicted value and measuring the covariance predicted value based on a volume rule, and the new algorithm does not need to calculate a Jacobi matrix of a system, thereby not only improving the estimation precision of the E-SVSF algorithm, but also expanding the application range of the E-SVSF algorithm; meanwhile, covariance positive nature and symmetry are guaranteed by using a square root factor of covariance in a state transfer process, and square root volume smooth variable structure filtering (SRC-SVSF) is obtained, wherein the SRC-SVSF is a filtering algorithm with numerical stability.
A Dynamic Positioning (DP) ship nonlinear state estimation method under model parameter uncertainty is carried out according to the following steps:
the method comprises the steps of firstly, analyzing and calculating key parameters, including the construction of a DP ship mathematical model, and calculating a state prediction value, a state covariance prediction value, a measurement prediction value and a measurement covariance prediction value based on a volume rule.
And secondly, designing a volume smoothing variable structure filter (C-SVSF) algorithm based on the parameters. The new algorithm does not need to calculate a system Jacobi matrix, so that the estimation precision of the E-SVSF algorithm is improved, and the application range of the E-SVSF algorithm is expanded;
and thirdly, calculating a square root factor using covariance in the state transfer process to ensure the covariance positive nature and symmetry, and further obtaining square root volume smooth variable structure filtering (SRC-SVSF), wherein the SRC-SVSF is a filtering algorithm with numerical stability.
Firstly, reviewing a model of a DP ship, secondly, providing a discrete time state model of the DP ship, establishing a measurement equation again, then, filtering steps and a formula of nonlinear system state estimation of a volume Kalman filter, and finally, using a square root factor of covariance in a state transfer process to ensure the normality and symmetry of the covariance so as to obtain square root volume smooth variable structure filtering, wherein the implementation process of the invention is described in detail below.
DP dynamic Ship model
The relationship of three-degree-of-freedom motion of the DP ship in two coordinate systems is shown in fig. 1, and a northeast coordinate system { n } ═ is established (x)n,yn,zn)，onRepresenting the origin of coordinates, xn，ynAnd znPointing to the north, east and earth center, x, respectivelyN，yNAnd ψ denotes a north position, an east position, and a heading angle. And simultaneously establishing a hull fixed coordinate system (b) ═ xb,yb,zb)，obRepresenting the centre of mass or centre, x, of the shipb，ybAnd zbPointing in the heading, the transverse direction and the bottom of the ship respectively, and u, v and r represent the surging speed, the swaying speed and the revolution rate.
The north, east, and heading angles of the DP vessel may be noted as η ═ xN,yE,ψ]TAnd the surging speed, the surging speed and the revolution rate of the DP ship are recorded as upsilon ═ u [ u ]N,vE,r]T. Wherein the heading angle is the superposition of a low-frequency component and a high-frequency component, i.e. psil+ψh，ψlIs a low frequency component, #hIs a high frequency component. Wherein the symbol [ ·]TRepresentation matrix [ ·]The transposing of (1).
Under the condition of low sea, for the motions of three degrees of freedom of the DP ship in the surging direction, the swaying direction and the yawing direction, a corresponding three-degree-of-freedom kinematic model of the DP ship can be established as follows:
Figure BDA0002838635990000051
wherein, the symbol
Figure BDA0002838635990000052
Is the first derivative of the vector eta, the state transition matrix R (psi)l+ψh) Comprises the following steps:
Figure BDA0002838635990000053
meanwhile, since the DP ship is generally operated at a low speed regardless of which mode the DP ship is operated in, the speed variation amount is changed less than the actual speed, and thus, the speed variation can be represented by the following continuous noise acceleration model:
Figure BDA0002838635990000054
wherein, the symbol
Figure BDA0002838635990000055
The second derivative of the vector η is represented and p represents gaussian random noise.
If the unit matrix is represented by I, the DP ship continuous time three-degree-of-freedom kinematic model without interference is as follows:
Figure BDA0002838635990000056
the DP ship gross motion can be viewed as being composed of wave frequency and low frequency motion components. Thus, when the system noise interference is not considered and in low sea conditions, the low-frequency motion model and the wave-frequency motion model of the three degrees of freedom of the DP ship in the surge direction, the sway direction, and the heading are respectively as follows.
Ideally, when additive correlation noise, multiplicative noise and uncertainty of parameters are not considered, the DP ship continuous-time three-degree-of-freedom low-frequency motion model can be represented by equation (1) and equations (5) to (7):
Figure BDA0002838635990000057
τ＝Buu (6)
Figure BDA0002838635990000058
wherein the content of the first and second substances,
Figure BDA0002838635990000059
in order to input the quantity of the input,
Figure BDA00028386359900000510
representing an n-dimensional state space of the device,
Figure BDA00028386359900000511
representing the constant matrix of the driver, and tau is the force and moment output by the propeller.
Figure BDA00028386359900000512
Is the disturbance force of slowly changing environment such as wind wave flow. M is the DP vessel inertia matrix containing rigid body mass and hydrodynamic additional mass, i.e. M ═ MRB+MA，MRBAs a generalized inertial matrix, MAFor the generalized additional inertia matrix, D is a linear damping matrix, and the expression form thereof can be respectively defined as follows:
Figure BDA00028386359900000513
Figure BDA00028386359900000514
Figure BDA0002838635990000061
Figure BDA0002838635990000062
wherein m is the ship mass; xu、Yv、Yr、NrLinear viscous damping for each coordinate axis direction; i iszAbout z isbAn inertia matrix of the shaft;
Figure BDA0002838635990000063
an additional mass for each coordinate axis direction; x is the number ofGThe coordinates of the gravity center of the rigid body in the x-axis direction.
For convenience of description, a wave approximation model containing second-order wave motion is adopted, that is, a wave frequency approximation model of waves in three degrees of freedom of surging, rolling and yawing can be expressed as follows:
Figure BDA0002838635990000064
wherein σi(i 1-3) is related to the sea wave strength; zetai(i is 1-3) is relative damping coefficient, and the value is 0.05-0.2; omega0iAnd (i is 1-3) is the dominant frequency of the sea wave spectrum, and reflects the sense wave height of the sea wave.
Then, the continuous time state space of the ocean waves in each coordinate axis direction is described as:
Figure BDA0002838635990000065
wherein the content of the first and second substances,
Figure BDA0002838635990000066
are the wave frequency motion components of the north position, east position and heading angle,
Figure BDA0002838635990000067
representing wave frequency motion interference, the state transition matrix components are respectively:
Figure BDA0002838635990000068
Figure BDA0002838635990000069
amplitude matrix Eh2Comprises the following steps:
Figure BDA00028386359900000610
order to
Figure BDA00028386359900000611
The dynamic positioning ship continuous-time three-degree-of-freedom wave frequency motion model can be rewritten into the following form:
Figure BDA0002838635990000071
the north position, east position, heading angle, surging speed, swaying speed and gyration rate information of the DP ship are respectively obtained by sensor units such as DGPS, electric compass or IMU.
The sensor measurement can be seen as a wave frequency motion component ηhWith low-frequency motion components etalSuperimposed, and thus, when additive measurement noise interference is not considered, the sensor observation model can be represented in the following uniform form:
y＝hl(ηl)+hh(ηh) (18)
ηh＝Λhξ12 (19)
wherein y represents a measured value; h ish(. and h)l(. are) a wave frequency measurement matrix and a low frequency measurement matrix, respectively; lambdahIs a wave frequency motion matrix with appropriate dimensions.
DP dynamic ship state space model and measurement equation establishment
The DP ship three-degree-of-freedom discrete time state space model can consider the following nonlinear system model with uncertain model parameters;
xk＝fk-1(xk-1)+ωk (20)
zk＝hk(xk)+υk (21)
wherein f isk-1(. and h)k(. cndot.) represents a state transition matrix and a measurement transition matrix,and has uncertainty; x is the number ofkRepresents a state vector; z is a radical ofkRepresenting an observed value; omegakAnd upsilonkIs system noise, satisfies
Figure BDA0002838635990000072
And Q and R represent mean values, and Q and R represent variance. For the above model uncertain dynamic system, the initial state of the system is recorded as
Figure BDA0002838635990000073
Initial estimation error covariance of P0|0。
And calculating a state prediction value based on the volume rule, predicting state covariance, and analyzing and calculating key parameters of the measurement prediction value and the measurement covariance prediction value. The specific implementation steps are as follows:
from an initial value
Figure BDA0002838635990000074
And P0|0Then, the initial volume point is obtained as:
Figure BDA0002838635990000075
wherein S isk-1|k-1＝chol(Pk-1|k-1) Representing square root factors obtained by Cholesky decomposition, i.e.
Figure BDA0002838635990000076
DP ship nonlinear system state estimation volume smooth variable structure filtering
C-SVSF is designed based on Cubasic rules, and the calculation process of the C-SVSF algorithm is as follows:
step 1: computing volume rule based state prediction
Figure BDA0002838635990000081
Sum covariance prediction value Pk|k-1
Figure BDA0002838635990000082
Figure BDA0002838635990000083
Wherein the content of the first and second substances,
Figure BDA0002838635990000084
representing a state transfer volume point.
Step 2: calculating the measurement estimation error e of the last moment in timez,k-1|k-1
First, the transfer volume point of the observation equation is calculated:
Figure BDA0002838635990000085
then a measurement estimate is obtained
Figure BDA0002838635990000086
Comprises the following steps:
Figure BDA0002838635990000087
the measurement estimation error is then:
Figure BDA0002838635990000088
and step 3: computing measurement predictions
Figure BDA0002838635990000089
Innovation error covariance
Figure BDA00028386359900000810
And measuring innovation ez,k|k-1
Figure BDA00028386359900000811
Figure BDA00028386359900000812
Figure BDA00028386359900000813
Step 4, respectively calculating the filtering gain KkUpdating of estimated value
Figure BDA00028386359900000814
Covariance update Pk|kAnd smoothing the boundary layer psik+1。
Calculating a gain K based on the innovation and the measurement errork+1：
Figure BDA00028386359900000815
Wherein, the parameter is more than 0 and less than 1; the symbol '+' represents the pseudo-inverse; diag (·) is a diagonalized version of ·; '| |' is the absolute value of ·; symbol
Figure BDA00028386359900000816
Represents the Schur product (element-by-element multiplication);
Figure BDA00028386359900000817
showing a diagonalized version of the boundary layer.
State estimate update value obtainable from gain
Figure BDA00028386359900000818
Comprises the following steps:
Figure BDA00028386359900000819
computingEstimation error covariance update value Pk+1|k+1：
Figure BDA0002838635990000091
The filter gain K can be calculated based on the equations (31), (32) and (33)kUpdating of estimated value
Figure BDA0002838635990000092
Covariance update Pk|kThen calculating the optimal boundary layer psik+1：
Optimum boundary layer psik+1Can be calculated by combining the covariance Pk+1|k+1Calculating partial derivatives to obtain:
Figure BDA0002838635990000093
it is possible to obtain,
Figure BDA0002838635990000094
wherein the content of the first and second substances,
Figure BDA0002838635990000095
Figure BDA0002838635990000096
the above steps 1 to 4 are the C-SVSF algorithm based on the Cubasic rule.
Similar to CKF, C-SVSF requires computation of an inverse matrix of covariance in the optimal boundary layer computation, and thus the covariance matrix needs to satisfy the requirement of non-negativity. However, the filtering algorithm may diverge due to the fact that the error accumulation made by the computer word size may make the covariance negative or singular. Thus, in order to ensure the stability of C-SVSF, the SRC-SVSF algorithm based on the square root method is given by the method of lower triangular decomposition.
Due to the non-negativity of covariance, covariance can be decomposed into the following form
Figure BDA0002838635990000097
Figure BDA0002838635990000098
And in the iterative process of the filter, replacing the covariance by using a state covariance square root factor to obtain the SRC-SVSF algorithm.
DP ship nonlinear system state estimation square root volume smooth variable structure filtering
For the specific description of the SRC-SVSF algorithm, assume the initial state covariance square root factor S0|0And initial estimated value
Figure BDA0002838635990000099
As is known, then the specific SRC-SVSF algorithm is as follows:
step 1: state prediction from equation (23)
Figure BDA00028386359900000910
The lower triangular decomposition of the Tria (-) expression matrix "·" can obtain the square root factor S of the covariance of the prediction errork|k-1Comprises the following steps:
Figure BDA00028386359900000911
wherein the content of the first and second substances,
Figure BDA00028386359900000912
Figure BDA0002838635990000101
then prediction error cross covariance
Figure BDA0002838635990000102
Step 2: calculation of measurement estimates from equations (28) to (30)
Figure BDA0002838635990000103
And measuring the estimation error ez,k-1|k-1(ii) a Calculating the innovation e from equation (30)z,k|k-1(ii) a The measurement prediction value is calculated from the following formula (39)
Figure BDA0002838635990000104
Figure BDA0002838635990000105
And step 3: calculating a square root factor of innovation covariance
Figure BDA0002838635990000106
Figure BDA0002838635990000107
Wherein the content of the first and second substances,
Figure BDA0002838635990000108
Figure BDA0002838635990000109
and 4, step 4: the filter gain K is calculated from equations (31) to (32)kAnd update of the estimated value
Figure BDA00028386359900001010
Calculating a smooth boundary layer according to a formula
Figure BDA00028386359900001011
By the formula
Figure BDA00028386359900001012
The innovation covariance is calculated.
And 5: calculating a square root factor S of the covariancek|kUpdating:
Figure BDA00028386359900001013
wherein the content of the first and second substances,
Figure BDA00028386359900001014
and the estimation error covariance is updated to
Figure BDA00028386359900001015
The invention has the following beneficial effects:
1. the C-SVSF overcomes the condition that a nonlinear system must be continuously differentiable, and a Jacobi matrix of the system does not need to be calculated, so that the robustness of the E-SVSF is kept, and the accuracy of state prediction and covariance prediction is further improved due to the introduction of a volume rule.
2. The SRC-SVSF algorithm of the invention uses the square root factor of covariance in the recursion process, thereby ensuring the numerical stability of the SRC-SVSF algorithm.
3. The C-SVSF and SRC-SVSF algorithms have similar estimation accuracy and are higher than E-SVSF when the covariance of noise measured by the DP ship is unknown, and the accuracy is higher than CKF due to the robustness of noise interference caused by the E-SVSF.
The effects of the present invention can be further illustrated by the following simulation experiment results.
In the simulation experiment, the initial value of the DP ship state is set as x0＝[1,2,0.1,1,1.5,1]', the state noise covariance isQ＝diag([10,10,10,10,10,10]) The measurement noise covariance is R ═ diag ([20,20,20,20,20, 20)]). Measurement matrix hk＝I6×6. Initial estimation value of assumed state
Figure BDA0002838635990000111
Initial value P of covariance of state estimation error0|0＝diag([1,1,1,1,1,1])。
For the DP ship non-linear estimation system, as can be seen from the above analysis, the estimation accuracy of CKF is higher than that of EKF, so CKF is used as a comparison algorithm here. And then performing simulation comparison with E-SVSF, C-SVSF and SRC-SVSF algorithms respectively.
Here again, RMSE was used as an algorithm performance indicator function, and 200 monte carlo state estimation simulation experiments were performed. In order to verify the estimation effect of the algorithm on the uncertainty of the model parameters, the algorithm is verified by simulation experiments under the two conditions that the observed noise covariance is known and the observed noise covariance is unknown respectively, and the simulation results are respectively shown as the following (a) and (b):
(a) the measured noise covariance is accurately known
The sampling period of the simulation experiment is 1s, and the sampling time is 1800 s. It is assumed here that the exact value of the covariance of the measurement noise is known, i.e. let R ═ diag ([20,20,20,20,20,20 ]). Then, after 200 monte carlo state estimation simulation experiments, the RMSE values of the northbound position, the east position, the heading angle, the surging speed, the swaying speed and the slew rate of the DP ship under 4 algorithms are shown in fig. 2 and fig. 3, respectively. The RMSE curve of the CKF algorithm is represented by broken lines, the RMSE value of the E-SVSF algorithm is represented by dotted lines, the RMSE value of the C-SVSF algorithm is represented by solid lines, and the RMSE value of the SRC-SVSF algorithm is represented by broken lines.
TABLE 1 average RMSE of known under-noise algorithms
Figure BDA0002838635990000112
When the noise covariance is known, CKF is the optimal state estimation method, so CKF has the minimum RMSE. The E-SVSF error is maximized because the state and covariance predictions introduce the Jacobi matrix. Meanwhile, the introduction of the volume rule enables the accuracy of the C-SVSF algorithm to be higher than that of the E-SVSF algorithm. And SRC-SVSF has the same estimation precision as C-SVSF because it uses the square root factor of covariance for iteration in the estimation process.
Table 1 is the state averaged RMSE under different algorithms. It is known that C-SVSF and its square root form SRC-SVSF have the same estimation error and are both higher than E-SVSF, demonstrating the effectiveness of the algorithm.
(b) Measurement noise covariance unknowns
Let R be diag ([500,500,1000,1000,1000,1000]), assuming that the exact value of the measurement noise covariance is unknown. Then after 200 monte carlo simulation experiments, the values of the state RMSE of the DP ship are shown in fig. 4 and 5, respectively.
The CKF estimation error is greatest because CKF will lose optimality when accurate measurement noise covariance is not available. And based on the E-SVSF filtering method, the uncertainty of the model parameters can be overcome, so that the estimation precision is higher than that of the CKF algorithm. Meanwhile, due to the introduction of the volume rule, the state estimation effects of the C-SVSF and the SRC-SVSF are better than those of the E-SVSF.
Meanwhile, when the covariance of the measurement noise is unknown, the state estimation average RMSE value of the state variable of the DP ship under 4 algorithms is shown in the table 2.
TABLE 2 average RMSE of the algorithm at unknown noise
Figure BDA0002838635990000121
In conclusion: for a DP ship nonlinear state estimation simulation experiment with uncertain model parameters, when the measured noise covariance is known, the C-SVSF, SRC-SVSF and CKF have similar estimation accuracy which is higher than that of E-SVSF; when the measured noise covariance is unknown, the C-SVSF and the SRC-SVSF have similar estimation accuracy and are higher than the E-SVSF, and simultaneously, the accuracy is higher than the CKF due to the robustness of the E-SVSF to noise interference. Further illustrating the effectiveness of the C-SVSF and SRC-SVSF algorithms of the present invention and the robustness of the algorithms in the presence of noise interference.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A nonlinear state estimation method of a dynamic positioning ship under model parameter uncertainty is characterized by comprising the following steps:
step 1: initializing a parameter k to be 1, and acquiring the north position, the east position and the heading angle eta of the dynamic positioning ship under the initial condition to be [ x ═ xN,yE,ψ]TConverting a three-degree-of-freedom discrete time state space model of the dynamic positioning ship into a nonlinear system model with uncertain model parameters:
xk＝fk-1(xk-1)+ωk
zk＝hk(xk)+υk
wherein f isk-1() represents a state transition matrix; h isk(. to) represent a quantity transfer matrix; x is the number ofkRepresenting the state vector of the dynamic positioning ship at the moment k, and recording the initial state of a nonlinear system model with uncertain model parameters as
Figure FDA0002838635980000011
Initial estimation error covariance of P0|0；zkRepresenting an observed value; omegakAnd upsilonkIs system noise, satisfies
Figure FDA0002838635980000012
And Q and R represent mean, Q and R represent variance; from an initial state
Figure FDA0002838635980000013
And initial estimation error covariance P0|0The initial volume points obtained are:
Figure FDA0002838635980000014
Figure FDA0002838635980000015
wherein S isk-1|k-1＝chol(Pk-1|k-1) Representing square root factors obtained by Cholesky decomposition, i.e.
Figure FDA0002838635980000016
[1]iIs a vector point generator for generating initial volume points, n being the number of vector points;
step 2: calculating the state vector estimated value of the dynamic positioning ship at the k moment under the condition of the k-1 moment
Figure FDA0002838635980000017
Sum covariance prediction value Pk|k-1；
Figure FDA0002838635980000018
Figure FDA0002838635980000019
Figure FDA00028386359800000110
Wherein the content of the first and second substances,
Figure FDA00028386359800000111
representing a state transfer volume point;
and step 3: computing measurement estimates
Figure FDA00028386359800000112
And measuring the estimation error ez,k-1|k-1；
Figure FDA00028386359800000113
Figure FDA00028386359800000114
Wherein the content of the first and second substances,
Figure FDA0002838635980000021
is the transfer volume point of the observation equation;
and 4, step 4: calculating innovation ez,k|k-1And measuring the predicted value
Figure FDA0002838635980000022
Figure FDA0002838635980000023
Figure FDA0002838635980000024
And 5: calculating a square root factor of innovation covariance
Figure FDA0002838635980000025
Figure FDA0002838635980000026
Wherein the content of the first and second substances,
Figure FDA0002838635980000027
step 6: computing an error covariance update value Pk|k；
Figure FDA0002838635980000028
Wherein the content of the first and second substances,
Figure FDA0002838635980000029
and 7: calculating an optimal boundary layer psik；
Figure FDA00028386359800000210
Figure FDA00028386359800000211
Figure FDA00028386359800000212
And 7: calculating a filter gain KkObtaining the state vector estimated value of the dynamic positioning ship at the moment k
Figure FDA00028386359800000213
Figure FDA00028386359800000214
Figure FDA00028386359800000215
WhereinThe parameter is more than 0 and less than 1; the symbol '+' represents the pseudo-inverse; diag (·) is a diagonalized version of ·; symbol
Figure FDA00028386359800000216
Represents the Schur product;
Figure FDA00028386359800000217
representing a diagonalized version of the boundary layer;
Figure FDA00028386359800000218
and 8: judging whether the dynamic positioning ship finishes the task or not; if not, k is made to be k +1, and the process returns to step 2 to estimate the state vector of the dynamic positioning ship at the next time.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114879481A (en) * 2022-06-02 2022-08-09 哈尔滨理工大学 Water-power-interference-resistant ship dynamic positioning robust H-infinity control method

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108388738A (en) * 2018-03-01 2018-08-10 青岛科技大学 A kind of Ship Dynamic Positioning Systems Based noise and state real-time estimation adaptive filter method
CN110879535A (en) * 2019-12-26 2020-03-13 大连海事大学 Sliding mode fault-tolerant control method of T-S fuzzy UMV

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108388738A (en) * 2018-03-01 2018-08-10 青岛科技大学 A kind of Ship Dynamic Positioning Systems Based noise and state real-time estimation adaptive filter method
CN110879535A (en) * 2019-12-26 2020-03-13 大连海事大学 Sliding mode fault-tolerant control method of T-S fuzzy UMV

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
林孝工等: "基于容积变换的平滑变结构滤波及应用", 《系统工程与电子技术》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114879481A (en) * 2022-06-02 2022-08-09 哈尔滨理工大学 Water-power-interference-resistant ship dynamic positioning robust H-infinity control method
CN114879481B (en) * 2022-06-02 2022-12-02 哈尔滨理工大学 Ship dynamic positioning robust H-infinity control method resisting water dynamic interference

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