CN107063300A - Method of estimation is disturbed in a kind of underwater navigation system kinetic model based on inverting - Google Patents
Method of estimation is disturbed in a kind of underwater navigation system kinetic model based on inverting Download PDFInfo
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Abstract
The invention discloses method of estimation is disturbed in a kind of underwater navigation system kinetic model based on inverting, comprise the following steps：According to the dynamics vector equation of submarine navigation device, non-linear system status equation and measurement equation containing unknown disturbance are set up；State estimation is carried out to submarine navigation device using volume Kalman filtering, its innovation sequence is obtained；Using Recursive Least Squares Estimation method, total power size is estimated by innovation sequence；Required total power is modified using iterative algorithm；By always making every effort to perturbed force.The present invention need not set up perturbed force model, and kinetic model is simple；Perturbed force is not limited, strong applicability；Great amount of samples data need not be prepared, On-line Estimation is carried out to perturbed force, is a kind of practical disturbance method of estimation.
Description
Technical field
The invention belongs to submarine navigation device field of navigation technology, and in particular to a kind of navigation system dynamics based on inverting
Method of estimation is disturbed in model.
Background technology
High accuracy, the navigation algorithm of strong robustness are the guarantees that submarine navigation device completes complicated navigation task.Underwater navigation
Device using underwater propulsion unit to ROV carry out speed of a ship or plane control, changed course by rudder arrangement or vector propulsion device, its
It is military or civilian be all widely used.Kinetic model directly describes kinematic parameter and the input of submarine navigation device
Relation between power/torque, the problem of being prevented effectively from because of velocity sensor failure or failure generation larger navigation error, from
And improve the robustness and fault-tolerance of navigation system.However, navigation system kinetic model there is nonlinearity, it is time-varying, strong
The features such as coupling, accurate kinetic model is set up according to rigid motion extremely difficult, and by wind, ripple, wave etc. during navigation
The random perturbation of external environment, therefore, in order to reduce influence of the perturbed force to navigation system, is estimated to be in real time to perturbed force
Considerable meaning.
At present, two class methods generally disturb method of estimation, one is to use the Parameter identification based on perturbed force model
Method, but environmental perturbation has certain limitation to this method to external world, and the complexity of kinetic model can be increased；Two be to utilize
Neutral net carries out kinetic model automatic adjusument, but the algorithm needs a number of sample data, and sample data
Will it is as complete as possible with it is accurate, but accurate training data is generally difficult to obtain or costs dearly.
The content of the invention
It is an object of the present invention to provide method of estimation is disturbed in a kind of submarine navigation device kinetic model, can effectively it estimate
Perturbed force, to solve to set up in conventional method, perturbed force model is complicated, certain limitation, neutral net are estimated to be to perturbed force
The shortcomings of substantial amounts of training data is difficult in model.
To achieve the above object, the technical solution adopted by the present invention is：
Method of estimation is disturbed in a kind of underwater navigation system kinetic model based on inverting, is comprised the following steps：
Step one, according to the dynamics vector equation of submarine navigation device, the nonlinear system shape containing unknown disturbance is set up
State equation and measurement equation；
Step 2, carries out state estimation to submarine navigation device using volume Kalman filtering, obtains its innovation sequence；
Step 3, using Recursive Least Squares Estimation method, total power size is estimated by innovation sequence；
Step 4, is modified using iterative algorithm to required total power；
Step 5, by always making every effort to perturbed force.
The specific method of step one is as follows：
Submarine navigation device has six-freedom degree motion, to describe the motion conditions of ROV, introduces two kinds of reference frames,
Respectively earth coordinates O-xGyGzGWith the carrier coordinate system O-x using ROV center of gravity as originByBzB；
ROV dynamics of rigid bodies vector representation formula is
In formula, vectorial υ is velocity υ=[u, v, w, p, q, the r] that decomposes under carrier coordinate systemT, wherein, u is surging
Direction speed, v is swaying direction speed, and w is heaving direction speed, and p is angular velocity in pitch, and q is angular velocity in roll, and r is yawing
Angular speed；M is system inertia matrix, wherein including additional mass；C (υ) is Coriolis centripetal force matrix, wherein comprising additional
Quality；D (υ) is damped coefficient matrix；τ is the active force and moment vector of propulsion system；τdForce vector is disturbed for external environment condition；
The position vector of submarine navigation device is η=[x, y, z, φ, θ, ψ] under earth coordinatesT, x, y, z is ROV
Position, φ, θ, ψ are the attitude angle of ROV；Derivative and under carrier coordinate system speed of the position to the time under earth coordinates
The transformational relation of degree is
Wherein, J (η) is transition matrix；
The represented nonlinear mathematical model of formula (1) and formula (2) is changed into state-space model, you can obtain state side
Journey and measurement equation
Wherein,H=[06×6 I6×6]
In formula, X=[ηT υT]TFor state variable；W is the white Gaussian noise of system state equation；Z is observation vector；V is
The white Gaussian noise of measurement equation；A is systematic state transfer matrix；B is input control matrix；H is system measurements matrix；
06×6For 6 × 6 null matrix；I6×6For 6 × 6 unit matrix；
By formula (3) discretization, the discretized system model for obtaining the k moment is
Wherein, Φ is the systematic state transfer matrix of discretization, and Φ=exp (A × △ T), △ T are the sampling interval；Γ is
The input control matrix of discretization,
The specific method of step 2 is as follows：
(2.1) initial parameter is set
Set the system mode value X of initial time submarine navigation device0, state covariance P0/0, system noise covariance Q, amount
Survey noise covariance R, sensitivity matrix Ms, power covariance matrix Pb；
(2.2) time updates
Decomposing state evaluated error covariance matrix
Pk/k=Sk/kSk/k T
Wherein, Pk/kFor k moment state estimation error covariance matrixes, Sk/kIt is k moment state estimations error covariance matrix point
The lower triangular matrix of solution；
Construction volume point is simultaneously propagated through state equation
Wherein,For k moment state estimations；Xi,k/k,It is volume point；M=2n, n are state vector X dimensions；[1]iIt is the i-th row of point set [1], [1] ∈ RnRepresent point set；
Calculate status predication value
(2.3) measurement updaue
Construction volume point is simultaneously propagated through measurement equation
Zi,k+1/k=hk+1(Xi,k+1/k), i=1,2 ..., m
Wherein Xi,k+1/k, Zi,k+1/kIt is corresponding volume point；
Calculating observation amount predicted value
The new breath auto-covariance matrix of estimation
Estimate the one-step prediction value of Cross-covariance
Kalman gain matrix
Innovation sequence
Estimate the state vector at current time
Error co-variance matrix
The specific method of step 3 is as follows：
(3.1) k+1 moment sensitivity matrix is sought
Bs(k+1)=H [Φ Ms(k)+I]Γ
Ms(k+1)=[I-Kk+1H][ΦMs(k)+I]
(3.2) the k+1 moment estimates the gain matrix of power
Kb(k+1)=γ-1Pb(k)BT s(k+1)[Bs(k+1)γ-1Pb(k)BT s(k+1)+Pzz]-1
Wherein, γ is gain matrix regulatory factor；PbThe error covariance matrix of power is estimated for the k moment.
(3.3) total power at k+1 moment is estimated
(3.4) the more error co-variance matrix of new estimation power
Pb(k+1)=[I-Kb(k+1)Bs(k+1)]γ-1Pb(k)
The specific method of step 4 is as follows：
(4.1)
(4.2)
(4.3) if | △ F |>σ, then circulation step (4.1) and (4.2)；Otherwise circulation is terminated；Wherein σ allows for error
Scope.
In step 5, perturbed force is asked by following formula：
Beneficial effect：The present invention proposes a kind of disturbance method of estimation based on inverting, with state caused by perturbed force
Amount change inversion reckoning goes out perturbed force.By setting up kinetic model, system mode is estimated using volume Kalman filtering
Meter, total power is estimated using innovation sequence through least square method of recursion, and total power is modified using iterative algorithm, is finally tried to achieve
Perturbed force.This method need not set up perturbed force model, and kinetic model is simple；Perturbed force is not limited, strong applicability is one
Plant practical disturbance method of estimation.
The inventive method is directly to carry out inverting to perturbed force using motion state compared with traditional disturbance method of estimation
Computing, without to perturbed force modeling analysis, reliability is high；Estimated using volume Kalman filtering and RLS
Power, it is real-time；Total power is estimated using iterative algorithm, estimated accuracy is improved.
Brief description of the drawings
Fig. 1 is the flow schematic block of disturbance method of estimation in the navigation system kinetic model based on inverting of the invention
Figure.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
As shown in figure 1, a kind of underwater navigation system kinetic model disturbance method of estimation based on inverting, including following step
Suddenly：
(1) according to the dynamics vector equation of submarine navigation device, the non-linear system status side containing unknown disturbance is set up
Journey and measurement equation
Under marine environment disturbance, ROV typically has six-freedom degree motion.To describe the motion conditions of ROV, draw
Enter two kinds of reference frames, earth coordinates O-xGyGzGWith the carrier coordinate system O-x using ROV center of gravity as originByBzB.Boat
Row device dynamics of rigid bodies vector representation formula is
In formula, vectorial υ is velocity υ=[u, v, w, p, q, the r] that decomposes under carrier coordinate systemT, wherein, u is surging
Direction speed, v is swaying direction speed, and w is heaving direction speed, and p is angular velocity in pitch, and q is angular velocity in roll, and r is yawing
Angular speed；M is system inertia matrix, wherein including additional mass；C (υ) is Coriolis centripetal force matrix, wherein comprising additional
Quality；D (υ) is damped coefficient matrix；τ is the power and moment vector of propulsion system；τdFor the environment such as wind, wave, stream and outside work
Use force vector.
The position vector of ROV is η=[x, y, z, φ, θ, ψ] under earth coordinatesT, x, y, z is ROV position,
φ, θ, ψ are the attitude angle of ROV.Derivative and turn of under carrier coordinate system speed of the position to the time under earth coordinates
The relation of changing is
Wherein, J (η) is transition matrix.
The represented nonlinear mathematical model of formula (1) and formula (2) is changed into state-space model, you can obtain state side
Journey and measurement equation
Wherein,H=[06×6 I6×6]
In formula, X=[ηT υT]TFor state variable；W is the white Gaussian noise of system state equation；Z is observation vector；V is
The white Gaussian noise of measurement equation；A is systematic state transfer matrix；B is input control matrix；H is system measurements matrix；
06×6For 6 × 6 null matrix；I6×6For 6 × 6 unit matrix.
By formula (3) discretization, the discretized system model for obtaining the k moment is
Wherein, Φ is the systematic state transfer matrix of discretization, and Φ=exp (A × △ T), △ T are the sampling interval；Γ is
The input control matrix of discretization,
(2) state estimation is carried out to submarine navigation device using volume Kalman filtering, obtains its innovation sequence
2.1) initial parameter is set
Set the system mode value X of initial time submarine navigation device0, state covariance P0/0, system noise covariance Q, amount
Survey noise covariance R, sensitivity matrix Ms, power covariance matrix Pb。
2.2) time updates
Decomposing state evaluated error covariance matrix
Pk/k=Sk/kSk/k T
Wherein, Pk/kFor k moment state estimation error covariance matrixes, Sk/kIt is k moment state estimations error covariance matrix point
The lower triangular matrix of solution.
Construction volume point is simultaneously propagated through state equation
Wherein,For k moment state estimations；Xi,k/k,It is volume point；M=2n, n are state vector X dimensions；[1]iIt is the i-th row of point set [1], [1] ∈ RnRepresent point set：
Calculate status predication value
2.3) measurement updaue
Construction volume point is simultaneously propagated through measurement equation
Zi,k+1/k=hk+1(Xi,k+1/k), i=1,2 ..., m
Wherein, Xi,k+1/k, Zi,k+1/kIt is corresponding volume point.
Calculating observation amount predicted value
The new breath auto-covariance matrix of estimation
Estimate the one-step prediction value of Cross-covariance
Kalman gain matrix
Innovation sequence
Estimate the state vector at current time
Error co-variance matrix
(3) total power size is estimated by innovation sequence using LS estimator
3.1) sensitivity matrix is sought
Bs(k+1)=Φ [FMs(k)+I]Γ
Ms(k+1)=[I-K (k+1) H] [Φ Ms(k)+I]
3.2) gain matrix of power is estimated
Kb(k+1)=γ-1Pb(k)BT s(k+1)[Bs(k+1)γ-1Pb(k)BT s(k+1)+Pzz]-1
Wherein, γ is gain matrix regulatory factor；PbThe error covariance matrix of power is estimated for the k moment.
3.3) total power at current time is estimated
3.4) the more error co-variance matrix of new estimation power
Pb(k+1)=[I-Kb(k+1)Bs(k+1)]γ-1Pb(k)
(4) required total power is modified using iterative algorithm
4.1)
4.2)
If 4.3) | △ F |>4.1) and 4.2) σ, then circulate；Otherwise circulation is terminated；Wherein σ is error allowed band.
(5) by following formula by always making every effort to perturbed force
Described above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (6)
1. disturb method of estimation in a kind of underwater navigation system kinetic model based on inverting, it is characterised in that：Including following
Step：
Step one, according to the dynamics vector equation of submarine navigation device, the non-linear system status side containing unknown disturbance is set up
Journey and measurement equation；
Step 2, carries out state estimation to submarine navigation device using volume Kalman filtering, obtains its innovation sequence；
Step 3, using Recursive Least Squares Estimation method, total power size is estimated by innovation sequence；
Step 4, is modified using iterative algorithm to required total power；
Step 5, by always making every effort to perturbed force.
2. disturbing method of estimation in the underwater navigation system kinetic model according to claim 1 based on inverting, it is special
Levy and be：The specific method of step one is as follows：
Submarine navigation device has six-freedom degree motion, to describe the motion conditions of ROV, introduces two kinds of reference frames, respectively
For earth coordinates O-xGyGzGWith the carrier coordinate system O-x using ROV center of gravity as originByBzB；
ROV dynamics of rigid bodies vector representation formula is
In formula, vectorial υ is velocity υ=[u, v, w, p, q, the r] that decomposes under carrier coordinate systemT, wherein, u is surge direction speed
Degree, v is swaying direction speed, and w is heaving direction speed, and p is angular velocity in pitch, and q is angular velocity in roll, and r is yawing angular speed；
M is system inertia matrix, wherein including additional mass；C (υ) is Coriolis centripetal force matrix, wherein including additional mass；D
(υ) is damped coefficient matrix；τ is the active force and moment vector of propulsion system；τdForce vector is disturbed for external environment condition；
The position vector of submarine navigation device is η=[x, y, z, φ, θ, ψ] under earth coordinatesT, x, y, z is ROV position,
φ, θ, ψ are the attitude angle of ROV；Derivative and turn of under carrier coordinate system speed of the position to the time under earth coordinates
The relation of changing is
Wherein, J (η) is transition matrix；
The represented nonlinear mathematical model of formula (1) and formula (2) is changed into state-space model, you can obtain state equation and
Measurement equation
Wherein,H=[06×6 I6×6]
In formula, X=[ηT υT]TFor state variable；W is the white Gaussian noise of system state equation；Z is observation vector；V is measurement
The white Gaussian noise of equation；A is systematic state transfer matrix；B is input control matrix；H is system measurements matrix；06×6For 6
× 6 null matrix；I6×6For 6 × 6 unit matrix；
By formula (3) discretization, the discretized system model for obtaining the k moment is
Wherein, Φ is the systematic state transfer matrix of discretization, and Φ=exp (A × △ T), △ T are the sampling interval；Γ is discrete
The input control matrix of change,
3. disturbing method of estimation in the underwater navigation system kinetic model according to claim 1 based on inverting, it is special
Levy and be：The specific method of step 2 is as follows：
(2.1) initial parameter is set
Set the system mode value X of initial time submarine navigation device0, state covariance P0/0, system noise covariance Q, measurement makes an uproar
Sound covariance R, sensitivity matrix Ms, power covariance matrix Pb；
(2.2) time updates
Decomposing state evaluated error covariance matrix
Pk/k=Sk/kSk/k T
Wherein, Pk/kFor k moment state estimation error covariance matrixes, Sk/kIt is that k moment state estimations error covariance matrix is decomposed
Lower triangular matrix；
Construction volume point is simultaneously propagated through state equation
Wherein,For k moment state estimations；Xi,k/k,It is volume point；M=2n, n are state vector X dimensions；[1]iIt is the i-th row of point set [1], [1] ∈ RnRepresent point set：
Calculate status predication value
(2.3) measurement updaue
Construction volume point is simultaneously propagated through measurement equation
Zi,k+1/k=hk+1(Xi,k+1/k), i=1,2 ..., m
Wherein Xi,k+1/k, Zi,k+1/kIt is corresponding volume point；
Calculating observation amount predicted value
The new breath auto-covariance matrix of estimation
Estimate the one-step prediction value of Cross-covariance
Kalman gain matrix
Innovation sequence
Estimate the state vector at current time
Error co-variance matrix
4. disturbing method of estimation in the navigation system kinetic model according to claim 1 based on inverting, its feature exists
In：The specific method of step 3 is as follows：
(3.1) k+1 moment sensitivity matrix is sought
Bs(k+1)=H [Φ Ms(k)+I]Γ
Ms(k+1)=[I-Kk+1H][ΦMs(k)+I]
(3.2) the k+1 moment estimates the gain matrix of power
Kb(k+1)=γ-1Pb(k)BT s(k+1)[Bs(k+1)γ-1Pb(k)BT s(k+1)+Pzz]-1
Wherein, γ is gain matrix regulatory factor；PbThe error covariance matrix of power is estimated for the k moment；
(3.3) total power at k+1 moment is estimated
(3.4) the more error co-variance matrix of new estimation power
Pb(k+1)=[I-Kb(k+1)Bs(k+1)]γ-1Pb(k)。
5. disturbing method of estimation in the navigation system kinetic model according to claim 1 based on inverting, its feature exists
In：The specific method of step 4 is as follows：
(4.1)
(4.2)
(4.3) if | △ F |>σ, then circulation step (4.1) and (4.2)；Otherwise circulation is terminated；Wherein σ is error allowed band.
6. disturbing method of estimation in the navigation system kinetic model according to claim 1 based on inverting, its feature exists
In：In step 5, perturbed force is asked by following formula：
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| CN114675644A (en) * | 2022-03-21 | 2022-06-28 | 中国科学院沈阳自动化研究所 | Underwater robot vertical plane motion control method based on parameter identification |
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