CN107063300B - Inversion-based disturbance estimation method in underwater navigation system dynamic model - Google Patents
Inversion-based disturbance estimation method in underwater navigation system dynamic model Download PDFInfo
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Abstract
the invention discloses a disturbance estimation method in an underwater navigation system dynamic model based on inversion, which comprises the following steps: establishing a nonlinear system state equation and a measurement equation containing unknown disturbance according to a dynamic vector equation of the underwater vehicle; performing state estimation on the underwater vehicle by using cubature Kalman filtering to obtain an innovation sequence of the underwater vehicle; estimating the total force by an innovation sequence by adopting a recursive least square estimation method; correcting the total force by adopting an iterative algorithm; the disturbance force is determined by the total force. The disturbance force model does not need to be established, and the dynamic model is simple; the disturbance force is not limited, and the applicability is strong; the disturbance power is estimated on line without preparing a large amount of sample data, and the method is a disturbance estimation method with strong practicability.
Description
Technical Field
the invention belongs to the technical field of navigation of underwater vehicles, and particularly relates to a disturbance estimation method in a navigation system dynamic model based on inversion.
background
A navigation algorithm with high precision and high robustness is a guarantee for completing complex navigation tasks by an underwater vehicle. The underwater vehicle utilizes the underwater propulsion device to control the speed of the vehicle, changes the course through the rudder device or the vector propulsion device, and has wide application in military or civil use. The dynamic model directly describes the relationship between the motion parameters of the underwater vehicle and the input force/moment, and can effectively avoid the problem of larger navigation error caused by failure or fault of the speed sensor, thereby improving the robustness and fault tolerance of the navigation system. However, the navigation system dynamics model has the characteristics of high nonlinearity, time variation, strong coupling and the like, and it is very difficult to establish an accurate dynamics model according to rigid motion, and the model is randomly disturbed by external environments such as wind, waves and the like during navigation, so that it is of great significance to estimate disturbance force in real time in order to reduce the influence of the disturbance force on the navigation system.
At present, two types of disturbance estimation methods are generally adopted, namely a system parameter identification method based on a disturbance force model is adopted, but the method has certain limitation on external environment disturbance and can increase the complexity of a dynamic model; secondly, a neural network is used for adaptive adjustment of a dynamic model, but the algorithm needs a certain amount of sample data, the sample data is complete and accurate as much as possible, and accurate training data is difficult to obtain or expensive.
Disclosure of Invention
the invention aims to provide a disturbance estimation method in an underwater vehicle dynamic model, which can effectively estimate disturbance force and overcome the defects that the disturbance force model is complex to establish, the disturbance force estimation has certain limitation, a large amount of training data in a neural network model is difficult to realize and the like in the traditional method.
in order to achieve the purpose, the invention adopts the technical scheme that:
A disturbance estimation method in an underwater navigation system dynamic model based on inversion comprises the following steps:
Establishing a nonlinear system state equation and a measurement equation containing unknown disturbance according to a dynamic vector equation of an underwater vehicle;
secondly, performing state estimation on the underwater vehicle by using cubature Kalman filtering to obtain an innovation sequence of the underwater vehicle;
Estimating the total force by an innovation sequence by adopting a recursive least square estimation method;
Step four, correcting the total force by adopting an iterative algorithm;
And step five, solving the disturbance force by the total force.
the specific method of the first step is as follows:
The underwater vehicle has six-degree-of-freedom motion, and two reference coordinate systems are introduced for describing the motion condition of the vehicle, namely a geodetic coordinate system O-xGyGzG and a carrier coordinate system O-xByBzB with the gravity center of the vehicle as the origin;
The rigid body dynamics vector of the aircraft is expressed as
The vector upsilon is a velocity vector upsilon ═ u, v, w, p, q, r ] T decomposed in a carrier coordinate system, wherein u is a longitudinal oscillation direction velocity, v is a transverse oscillation direction velocity, w is a vertical oscillation direction velocity, p is a longitudinal oscillation angle velocity, q is a transverse oscillation angle velocity, and r is a heading angle velocity; m is a system inertia matrix containing additional mass; c (upsilon) is a Coriolis centripetal force matrix which contains an additional mass; d (upsilon) is a damping coefficient matrix; tau is the main power and moment vector of the propulsion system; τ d is an external environment disturbance force vector;
Under the ground coordinate system, the position vector of the underwater vehicle is eta ═ x, y, z, phi, theta, psi ] T, x, y and z are vehicle positions, phi, theta and psi are attitude angles of the vehicle; the transformation relation between the derivative of the position in the geodetic coordinate system to the time and the speed in the carrier coordinate system is
wherein J (η) is a transformation matrix;
Converting the nonlinear mathematical models expressed by the formulas (1) and (2) into a state space model to obtain a state equation and a measurement equation
wherein H ═ 06X 6I 6X 6%
Wherein X ═ η T υ T ] T is a state variable; w is Gaussian white noise of a system state equation; z is an observation vector; v is the Gaussian white noise of the measurement equation; a is a system state transition matrix; b is an input quantity control matrix; h is a system measurement matrix; 06 × 6 is a zero matrix of 6 × 6; i6 × 6 is a 6 × 6 identity matrix;
Discretizing the formula (3) to obtain a discretization system model at the moment k as
Wherein Φ is a discretized system state transition matrix, Φ is exp (a × Δ T), and Δ T is a sampling interval; Γ is the discretized input quantity control matrix,
the specific method of the second step is as follows:
(2.1) setting initial parameters
Setting a system state value X0, a state covariance P0/0, a system noise covariance Q, a measurement noise covariance R, a sensitivity matrix Ms and a force covariance matrix Pb of the underwater vehicle at an initial moment;
(2.2) time update
Decomposition state estimation error covariance matrix
P＝SS
Wherein Pk/k is a state estimation error covariance matrix at the moment k, and Sk/k is a lower triangular matrix decomposed by the state estimation error covariance matrix at the moment k;
Constructing volume points and propagating through state equations
Wherein, the estimated value is the state value at the k moment; xi, k/k, is the volume point; m is 2n, n is the state vector X dimension; [1] i is the ith column of the point set [1], and [1] ∈ Rn represents the point set;
Calculating state prediction values
(2.3) measurement update
Constructing volume points and propagating through measurement equations
Z＝h(X),i＝1,2,…,m
Wherein Xi, k +1/k, Zi, k +1/k are the corresponding volume points;
calculating the observation prediction value
estimating an innovation auto-covariance matrix
estimating one-step prediction values of a cross-covariance matrix
kalman gain matrix
information sequence
Estimating a state vector at a current time
Error covariance matrix
the concrete method of the third step is as follows:
(3.1) solving the sensitivity matrix at the k +1 moment
B(k+1)＝H[ΦM(k)+I]Γ
M(k+1)＝[I-KH][ΦM(k)+I]
(3.2) gain matrix for estimating force at time k +1
K(k+1)＝γP(k)B(k+1)[B(k+1)γP(k)B(k+1)+P]
Wherein gamma is a gain matrix adjustment factor; pb is the error covariance matrix of the estimated force at time k.
(3.3) estimating the total force at time k +1
(3.4) updating the error covariance matrix of the estimated forces
P(k+1)＝[I-K(k+1)B(k+1)]γP(k)
The concrete method of the step four is as follows:
(4.1)
(4.2)
(4.3) if |. DELTA.F | > σ, looping steps (4.1) and (4.2); otherwise, terminating the circulation; where σ is the allowable range of error.
In the fifth step, the disturbance force is solved through the following formula:
Has the advantages that: the invention provides a disturbance estimation method based on inversion, which utilizes state quantity change caused by disturbance force to invert and calculate the disturbance force. The system state is estimated by establishing a dynamic model and applying cubature Kalman filtering, the total force is estimated by utilizing an innovation sequence through a recursive least square method, the total force is corrected by adopting an iterative algorithm, and finally the disturbance force is obtained. The method does not need to establish a disturbance force model, and the dynamic model is simple; the disturbance power is not limited, the applicability is strong, and the method is a disturbance estimation method with strong practicability.
Compared with the traditional disturbance estimation method, the method disclosed by the invention has the advantages that the disturbance power is directly subjected to inversion operation by utilizing the motion state, modeling analysis on the disturbance power is not required, and the reliability is high; the force is estimated by using a cubature Kalman filtering and recursive least square algorithm, so that the real-time performance is strong; and the total force is estimated by adopting an iterative algorithm, so that the estimation precision is improved.
Drawings
FIG. 1 is a schematic block diagram of a flow of a disturbance estimation method in an inversion-based navigation system dynamics model according to the present invention.
Detailed Description
the present invention will be further described with reference to the accompanying drawings.
As shown in fig. 1, a disturbance estimation method for an underwater navigation system dynamics model based on inversion includes the following steps:
(1) Establishing a nonlinear system state equation and a measurement equation containing unknown disturbance according to a dynamic vector equation of an underwater vehicle
Under the disturbance of marine environment, the aircraft generally has six degrees of freedom motion. To describe the motion situation of the aircraft, two reference coordinate systems are introduced, namely a geodetic coordinate system O-xGyGzG and a carrier coordinate system O-xByBzB with the gravity center of the aircraft as an origin. The rigid body dynamics vector of the aircraft is expressed as
The vector upsilon is a velocity vector upsilon ═ u, v, w, p, q, r ] T decomposed in a carrier coordinate system, wherein u is a longitudinal oscillation direction velocity, v is a transverse oscillation direction velocity, w is a vertical oscillation direction velocity, p is a longitudinal oscillation angle velocity, q is a transverse oscillation angle velocity, and r is a heading angle velocity; m is a system inertia matrix containing additional mass; c (upsilon) is a Coriolis centripetal force matrix which contains an additional mass; d (upsilon) is a damping coefficient matrix; τ is the force and moment vectors of the propulsion system; τ d is the environment and external force vector of wind, wave, flow, etc.
Under the geodetic coordinate system, the position vector of the aircraft is eta ═ x, y, z, phi, theta, psi ] T, x, y and z are aircraft positions, and phi, theta and psi are attitude angles of the aircraft. The transformation relation between the derivative of the position in the geodetic coordinate system to the time and the speed in the carrier coordinate system is
Wherein J (η) is a transformation matrix.
Converting the nonlinear mathematical models expressed by the formulas (1) and (2) into a state space model to obtain a state equation and a measurement equation
Wherein H ═ 06X 6I 6X 6%
wherein X ═ η T υ T ] T is a state variable; w is Gaussian white noise of a system state equation; z is an observation vector; v is the Gaussian white noise of the measurement equation; a is a system state transition matrix; b is an input quantity control matrix; h is a system measurement matrix; 06 × 6 is a zero matrix of 6 × 6; i6 × 6 is a 6 × 6 identity matrix.
discretizing the formula (3) to obtain a discretization system model at the moment k as
Wherein Φ is a discretized system state transition matrix, Φ is exp (a × Δ T), and Δ T is a sampling interval; Γ is the discretized input quantity control matrix,
(2) State estimation is carried out on the underwater vehicle by adopting cubature Kalman filtering to obtain an innovation sequence thereof
2.1) setting initial parameters
Setting a system state value X0, a state covariance P0/0, a system noise covariance Q, a measurement noise covariance R, a sensitivity matrix Ms and a force covariance matrix Pb of the underwater vehicle at an initial moment.
2.2) time update
Decomposition state estimation error covariance matrix
P＝SS
And Pk/k is a state estimation error covariance matrix at the moment k, and Sk/k is a lower triangular matrix decomposed by the state estimation error covariance matrix at the moment k.
constructing volume points and propagating through state equations
wherein, the estimated value is the state value at the k moment; xi, k/k, is the volume point; m is 2n, n is the state vector X dimension; [1] i is the ith column of the point set [1], and [1] ∈ Rn represents the point set:
Calculating state prediction values
2.3) measurement update
Constructing volume points and propagating through measurement equations
Z＝h(X),i＝1,2,…,m
where Xi, k +1/k, Zi, k +1/k are the corresponding volume points.
Calculating the observation prediction value
Estimating an innovation auto-covariance matrix
estimating one-step prediction values of a cross-covariance matrix
kalman gain matrix
information sequence
estimating a state vector at a current time
error covariance matrix
(3) Estimating total force magnitude from innovation sequence using least squares estimator
3.1) solving the sensitivity matrix
B(k+1)＝Φ[FM(k)+I]Γ
M(k+1)＝[I-K(k+1)H][ΦM(k)+I]
3.2) gain matrix to estimate force
K(k+1)＝γP(k)B(k+1)[B(k+1)γP(k)B(k+1)+P]
Wherein gamma is a gain matrix adjustment factor; pb is the error covariance matrix of the estimated force at time k.
3.3) estimating the total force at the current moment
3.4) updating the error covariance matrix of the estimated forces
P(k+1)＝[I-K(k+1)B(k+1)]γP(k)
(4) correcting the total force by iterative algorithm
4.1)
4.2)
4.3) if Δ F | > σ, cycle 4.1) and 4.2); otherwise, terminating the circulation; where σ is the allowable range of error.
(5) The disturbance force is determined from the total force by
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (5)
1. A disturbance estimation method in an underwater navigation system dynamic model based on inversion is characterized by comprising the following steps: the method comprises the following steps:
Establishing a nonlinear system state equation and a measurement equation containing unknown disturbance according to a dynamic vector equation of an underwater vehicle; the specific method of the first step is as follows:
The underwater vehicle has six-degree-of-freedom motion, and two reference coordinate systems are introduced for describing the motion condition of the vehicle, namely a geodetic coordinate system O-xGyGzG and a carrier coordinate system O-xByBzB with the gravity center of the vehicle as the origin;
The rigid body dynamics vector of the aircraft is expressed as
The vector upsilon is a velocity vector upsilon ═ [ Vx, Vy, Vz, p, q, r ] T decomposed in a carrier coordinate system, wherein Vx is a surging direction velocity, Vy is a swaying direction velocity, Vz is a swaying direction velocity, p is a surging angle velocity, q is a swaying angle velocity, and r is a heading angle velocity; m is a system inertia matrix containing additional mass; c (upsilon) is a Coriolis centripetal force matrix which contains an additional mass; d (upsilon) is a damping coefficient matrix; tau is the main power and moment vector of the propulsion system; τ d is an external environment disturbance force vector;
under the ground coordinate system, the position vector of the underwater vehicle is eta ═ Px, Py, Pz, phi, theta, psi ] T, Px, Py and Pz are vehicle positions, and phi, theta and psi are attitude angles of the vehicle; the transformation relation between the derivative of the position in the geodetic coordinate system to the time and the speed in the carrier coordinate system is
Wherein J (η) is a transformation matrix;
Converting the nonlinear mathematical models expressed by the formulas (1) and (2) into a state space model to obtain a state equation and a measurement equation
Wherein H ═ 06X 6I 6X 6%
wherein X ═ η T υ T ] T is a state variable; w is Gaussian white noise of a system state equation; z is an observation vector; v is the Gaussian white noise of the measurement equation; a is a system state transition matrix; b is an input quantity control matrix; h is a system measurement matrix; 06 × 6 is a zero matrix of 6 × 6; i6 × 6 is a 6 × 6 identity matrix;
Discretizing the formula (3) to obtain a discretization system model at the moment k as
Wherein Φ is a discretized system state transition matrix, Φ is exp (a × Δ T), and Δ T is a sampling interval; Γ is the discretized input quantity control matrix,
Secondly, performing state estimation on the underwater vehicle by using cubature Kalman filtering to obtain an innovation sequence of the underwater vehicle;
estimating the total force by an innovation sequence by adopting a recursive least square estimation method;
Step four, correcting the total force by adopting an iterative algorithm;
And step five, solving the disturbance force by the total force.
2. The method for disturbance estimation in an inversion-based underwater navigation system kinetic model according to claim 1, characterized in that: the specific method of the second step is as follows:
(2.1) setting initial parameters
setting a system state value X0, a state covariance P0/0, a system noise covariance Q, a measurement noise covariance R, a sensitivity matrix Ms and a force covariance matrix Pb of the underwater vehicle at an initial moment;
(2.2) time update
decomposition state estimation error covariance matrix
P＝SS
wherein Pk/k is a state estimation error covariance matrix at the moment k, and Sk/k is a lower triangular matrix decomposed by the state estimation error covariance matrix at the moment k;
Constructing volume points and propagating through state equations
Wherein, the estimated value is the state value at the k moment; xi, k/k is the state volume point at the moment k, and is the corresponding state transition volume point; fk is a state transfer function at the moment k; m is 2n, n is the state vector X dimension; [1] i is the ith column of the point set [1], and [1] ∈ Rn represents the point set:
calculating state prediction values
Wherein Qk is the covariance of the system noise at the moment k;
(2.3) measurement update
Constructing volume points and propagating through measurement equations
Z＝h(X),i＝1,2,…,m
Wherein Xi, k +1/k are state volume points at the moment of k +1, and Zi, k +1/k are corresponding measurement post-transfer volume points; hk +1 is the measurement transfer function at the moment k + 1;
calculating the observation prediction value
Estimating an innovation auto-covariance matrix
Wherein Rk is the covariance of the measured noise at the moment k;
estimating one-step prediction values of a cross-covariance matrix
Kalman gain matrix
Information sequence
Wherein Z is an observation vector;
estimating a state vector at a current time
Error covariance matrix
3. The method for disturbance estimation in an inversion-based underwater navigation system kinetic model according to claim 1, characterized in that: the concrete method of the third step is as follows:
(3.1) the gain coefficient matrix Bs (k +1) and the sensitivity matrix Ms (k +1) at the time k +1 are:
B(k+1)＝H[ΦM(k)+I]Γ
M(k+1)＝[I-KH][ΦM(k)+I]
wherein H is a system measurement matrix; phi is a discretized system state transition matrix; gamma is a discretized input quantity control matrix; kk +1 is a Kalman gain matrix at the moment of k + 1; i is an identity matrix;
(3.2) gain matrix for estimating force at time k +1
K(k+1)＝γP(k)B(k+1)[B(k+1)γP(k)B(k+1)+P]
Wherein gamma is a gain matrix adjustment factor; pb (k) is an error covariance matrix of the estimated force at the time k; pzz is an innovation autocovariance matrix;
(3.3) estimating the total force at time k +1
Epsilon k is an innovation sequence at the moment k;
(3.4) updating the error covariance matrix of the estimated forces
P(k+1)＝[I-K(k+1)B(k+1)]γP(k)。
4. The method for disturbance estimation in an inversion-based underwater navigation system kinetic model according to claim 1, characterized in that: the concrete method of the step four is as follows:
(4.1)
(4.2)
Wherein epsilon k is an innovation sequence at the moment k; the estimated total force at time k + 1; bs (k +1) is a gain coefficient matrix at the moment k + 1; a gain matrix for estimating the force at the moment when Kb (k +1) is k + 1;
(4.3) if |. DELTA.F | > σ, looping steps (4.1) and (4.2); otherwise, terminating the circulation; where σ is the allowable range of error.
5. the method for disturbance estimation in an inversion-based underwater navigation system kinetic model according to claim 1, characterized in that: in the fifth step, the disturbance force is solved through the following formula:
Where is the estimated total force at time k + 1.
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