CN116519011B - Long-endurance double-inertial navigation collaborative calibration method based on Psi angle error correction model - Google Patents
Long-endurance double-inertial navigation collaborative calibration method based on Psi angle error correction model Download PDFInfo
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Abstract
The invention belongs to the technical field of navigation, and discloses a Psi angle error correction model-based collaborative calibration method for long-endurance double-inertial navigation, which is suitable for collaborative calibration of a long-endurance double-inertial navigation system without external reference information. According to the invention, through correcting the speed error model, the influence of inaccurate specific force on the calibration precision under the dynamic condition is avoided, on the basis, the relative speed and the relative position of two sets of inertial navigation systems are used as constraint observation, a combined error state Kalman filter based on the Psi angle error correction model is established, and under the condition of no external reference information, the calibration estimation is carried out on the gyro scale factor error, the accelerometer scale factor error and the installation error of the inertial navigation systems to be calibrated. The calibration method provided by the invention is completely autonomous, is not interfered by external environment, is not influenced by absolute errors of a normal working inertial navigation system in calibration precision, can also calibrate in a motion state, and has important engineering significance.
Description
Technical Field
The invention belongs to the technical field of navigation, relates to an external field calibration method of an inertial navigation system, in particular to a long-endurance double-inertial navigation collaborative calibration method based on a Psi angle error correction model, and is suitable for joint calibration between two or more inertial navigation systems with double-shaft or three-shaft indexing mechanisms.
Background
The error calibration technology is one of key technologies of an inertial navigation system, and can be divided into laboratory calibration and outfield calibration according to different calibration environments. The laboratory calibration is to calibrate error parameters of the inertial navigation system by using equipment such as a turntable in a laboratory, and the external field calibration is to install the inertial navigation system on a carrier. The error parameters of the inertial navigation system can change with the use or storage time of the system, so that the inertial navigation system needs to be calibrated regularly. Because the outfield calibration technology does not need to repeatedly disassemble the system, the workload of daily maintenance is reduced, and the method is a research focus of the inertial navigation system calibration technology in recent years.
The traditional external field calibration technology takes external accurate reference information as observation, and realizes system level calibration by using Kalman filtering. However, the use of external calibration techniques is limited in the absence of external reference information, such as underwater environments, GNSS rejection environments, etc. For platforms with external field calibration conditions, a plurality of inertial navigation systems with indexing mechanisms are usually installed, such as a biaxial rotation modulation inertial navigation system, an on-board biaxial rotation modulation main inertial navigation system, a three-self sub inertial navigation system and the like which are configured in a ship-borne redundancy mode. The systematic errors of the inertial navigation system can be estimated by utilizing redundant information of a plurality of sets of inertial navigation systems and reasonably designing the joint indexing sequence of the inertial navigation systems.
Under the application environment without external reference information, the navigation and positioning of the carrier are completed by an inertial navigation system. The positioning error of the inertial navigation system can be accumulated with time, and the Psi angle error model is defined in a calculation coordinate system and is decoupled from the position error, so that the inertial navigation system is more suitable for a long-endurance navigation system. In addition, the specific force term under the navigation coordinate system in the traditional error equation cannot be directly measured, and the specific force term needs to be obtained through differentiation, so that the covariance matrix error of the system is larger in a dynamic environment, and the calibration precision is influenced.
Aiming at the existing problems, the invention provides a long-endurance double-inertial-navigation collaborative calibration method based on a Psi angle error correction model, which is used for avoiding the existence of a specific force term in an error equation after the speed error equation is corrected, solving the problem of inaccurate error equation in a dynamic environment, projecting the speeds and positions of two sets of inertial navigation to the same coordinate system, taking the relative values as constraint observation, establishing a combined state Kalman filter of the long-endurance double-inertial-navigation system based on the Psi angle error correction model, carrying out online calibration on the total error parameter of the inertial-navigation system to be calibrated, and solving the external field calibration problem of the inertial-navigation system when no external reference information exists; the relative error between two inertial navigation systems is taken as observed quantity, the calibration precision is not influenced by the absolute error of the inertial navigation systems, and the autonomous calibration can be carried out under the motion state.
Disclosure of Invention
The invention provides a long-endurance double-inertial navigation collaborative calibration method based on a Psi angle error correction model, which corrects a speed error equation, eliminates a specific force item, solves the problem of inaccurate error equation in a dynamic environment, and realizes the external field calibration of a gyro scale factor, an accelerometer scale factor and an installation error angle of an inertial navigation system with self-calibration capability when no external reference information exists. The calibration scheme is not influenced by the motion state of the carrier, and can complete calibration under the conditions of a static base and a movable base; is not affected by the absolute error of the reference inertial navigation system. The calibration precision of the invention can meet the requirements of navigation-level inertial navigation systems, and has important engineering practical values.
In order to solve the technical problems, the invention provides the following solutions:
the long-endurance double-inertial navigation collaborative calibration method based on the Psi angle error correction model comprises the following steps of:
(1) Constructing error models of two sets of inertial navigation systems;
defining a normal-working biaxial rotation modulation inertial navigation system as inertial navigation 1, and a body coordinate system b thereof 1 Defined as "right-front-up", the inertial navigation system to be calibrated is inertial navigation 2, its body coordinate system b 2 Defined as "right-front-up";
the scale factor error and the installation error of the inertial navigation 1 are small and neglected, and an error model of the inertial navigation 1 is defined as:
wherein,
in the method, in the process of the invention,indicating gyro assembly error of inertial navigation 1, +.>Accelerometer component error indicative of inertial navigation 1, < ->X-axis gyro drift representing inertial navigation 1, < >>Indicating the y-axis gyro drift of inertial navigation 1, < >>Z-axis gyro drift representing inertial navigation 1, < >>Zero offset of the x-axis accelerometer representing inertial navigation 1,>zero offset of the y-axis accelerometer representing inertial navigation 1,>z-axis accelerometer representing inertial navigation 1Zero deviation (I) of (II)>Indicating gyro drift of inertial navigation 1, +.>Accelerometer zero bias indicative of inertial navigation 1, < ->Gyro noise for inertial navigation 1, +.>Is inertial navigation 1 accelerometer noise;
considering the scale factor error, the mounting angle error and the zero offset error, defining an error model of the inertial navigation 2 as:
wherein,
in the method, in the process of the invention,indicating gyro assembly error of inertial navigation 2, +.>Accelerometer component error indicative of inertial navigation 2, < ->Theoretical angular velocity vector representing inertial navigation 2 gyro assembly output,/->Representing the theoretical specific force vector measured by the inertial navigation 2 accelerometer component, +.>X-axis gyro drift representing inertial navigation 2, < >>Representing the y-axis gyro drift of inertial navigation 2, < >>Indicating z-axis gyro drift of inertial navigation 2, < >>Zero offset of the x-axis accelerometer representing inertial navigation 2,>zero offset of the y-axis accelerometer representing inertial navigation 2,>zero offset of the z-axis accelerometer representing inertial navigation 2,>indicating gyro drift of inertial navigation 2 +.>Accelerometer zero bias indicative of inertial navigation 2, < ->Gyro noise for inertial navigation 2 +.>Is inertial navigation 2 accelerometer noise; delta kappa g And delta mu g Representing the scale factor error matrix and the installation error matrix of the gyro, δκ a And delta mu a Representing a scale factor error matrix and a mounting error matrix of the accelerometer;
determining δκ g And delta kappa a ：
In the formula, delta kappa gx 、δκ gy And delta kappa gz Scale factor errors, δκ, respectively representing an x-axis gyroscope, a y-axis gyroscope, and a z-axis gyroscope ax 、δκ ay And delta kappa az Scale factor errors for the x-axis accelerometer, the y-axis accelerometer, and the z-axis accelerometer are represented, respectively;
determination of δμ g And delta mu a ：
In the formula, delta mu gyx 、δμ gzx And delta mu gzy Representing three installation error angles, δμ, of a gyro assembly ayx 、δμ azx 、δμ azy 、δμ axy 、δμ axz And delta mu ayz Representing six mounting error angles of the accelerometer assembly;
(2) The combined state Kalman filter based on the Psi angle error correction model is established by utilizing the related information of the gesture, the speed and the position output by the two sets of inertial navigation systems, and the specific steps are as follows:
(2.1) determining a system joint error equation:
in the psi- 1 ＝[ψ E1 ψ N1 ψ U1 ] T Represents the drift error angle, ψ, of the inertial navigation 1 E1 、ψ N1 、ψ U1 Respectively represent the drift error angles of the east direction, the north direction and the sky direction of the inertial navigation 1,representing the velocity error vector of the inertial navigation 1 after error correction under the platform coordinate system,/for>Respectively representing the speed errors of the inertial navigation 1 in the east direction, the north direction and the sky direction after error correction,/->Representing the position error of inertial navigation 1, +.>Represents east error of inertial navigation 1, +.>Indicating north error of inertial navigation 1, +.>Represents the error in the orientation of inertial navigation 1, +.>Representing the rotational angular velocity of the earth in the inertial navigation 1 calculation coordinate system,/>Representing the angular velocity of transfer in the inertial navigation 1 calculation coordinate system,/>Direction cosine matrix representing inertial navigation 1-body coordinate system to platform coordinate system,/and method for generating the same>Represents the gravity vector, ψ, under the inertial navigation 1 calculation coordinate system 2 ＝[ψ E2 ψ N2 ψ U2 ] T Represents the drift error angle, ψ, of inertial navigation 2 E2 、ψ N2 、ψ U2 Drift error angles of the east direction, the north direction and the sky direction of inertial navigation 2 are respectively represented, and the error angles are +.>Representing the velocity error vector of the inertial navigation 2 after error correction under the platform coordinate system,/for> Respectively representing the speed errors of the inertial navigation 2 in the east direction, the north direction and the sky direction after error correction,/->Indicating the position error of the inertial navigation 2,represents east error of inertial navigation 2, +.>Indicating north error of inertial navigation 2, +.>Represents the tangential error of inertial navigation 2, +.>Representing the rotational angular velocity of the earth in the inertial navigation 2 calculated coordinate system,/>Representing the angular velocity of transfer in inertial navigation 2 calculation coordinate system,/>Direction cosine matrix representing inertial navigation 2-body coordinate system to platform coordinate system,/and method for generating the same>Representing gravity vector v under inertial navigation 2 calculation coordinate system p Representing the speed of the carrier in the platform coordinate system;
(2.2) determining a joint state equation:
wherein,
in the formula, 0 i×j A zero matrix representing i rows and j columns,represents the inertial navigation 1 eastern direction, the north direction and the heaven direction speed under the platform coordinate system, L 1 、h 1 Latitude and altitude representing the carrier position of the inertial navigation 1 output, +.>An antisymmetric matrix representing an inertial navigation 1 velocity vector, R N1 、R E1 Represents the radius of the meridian, the circle of the mortise and the circle of the mortise at the output position of the inertial navigation 1, ++>A value representing the acceleration of gravity at the output position of inertial navigation 1,/->Represents the inertial navigation 2 eastern direction, the north direction and the heaven direction speed under the platform coordinate system, L 2 、h 2 Latitude and altitude representing the carrier position of the inertial navigation 2 output, +.>An antisymmetric matrix representing an inertial navigation 2 velocity vector, R N2 、R E2 Represents the radius of the meridian, the circle of the mortise and the circle of the mortise at the output position of the inertial navigation 2,/and%>Value, ω, representing gravitational acceleration at the output position of inertial navigation 2 ie Represents the rotation angular velocity of the earth, C 23 Representation->Second and third columns of matrix, C 3 Representation->The third column of the matrix is designated,output values of the x, y and z axis gyroscopes of inertial navigation 2 are respectively represented by +.>Output values of the x, y and z axis accelerometers of the inertial navigation 2 are respectively represented;
the state vector x (t) is expressed as:
the noise distribution matrix and the noise matrix are expressed as:
(2.3) determining a state constraint observation equation:
the output speeds and positions of the inertial navigation 1 and the inertial navigation 2 are respectively expressed as:
in the method, in the process of the invention,and->Representing the velocity information under the platform coordinate system output by inertial navigation 1 and inertial navigation 2 respectively, +.>And->Respectively representing the position information output by the inertial navigation 1 and the inertial navigation 2, and measuring and calibrating the outer lever arm parameters between the inertial navigation 1 and the inertial navigation 2 after the system is installed, and r c True value representing the position of the common point, +.>An outer lever arm representing the position between two inertial navigation systems, < >>Representing the projection of the outer lever arm between two sets of inertial navigation in the inertial navigation 2-body coordinate system,/->A rotational angular velocity vector representing the inertial navigation 2-body coordinate system relative to the platform coordinate system;
because the two sets of systems reflect the speed information and the position information of the same carrier, the observed quantity forms the constraint of the respective speed errors and the position errors of the inertial navigation 1 and the inertial navigation 2, and the constraint is expressed as follows:
in the formula, v v 、υ r Observing noise for corresponding speed and position; in the application environment of dual inertial navigation, external observation based on altitude informationDetermining a height observation equation:
in the method, in the process of the invention,is the height value of inertial navigation 1, v h Is highly observed noise; the observation equation is expressed as:
z(t)＝H(t)x(t)+υ(t)
wherein,
H 1 ＝[0 0 1]
υ(t)＝[(υ v ) T (υ r ) T υ h ] T
wherein I is 3×3 Representing a 3 row 3 column identity matrix;
(3) Determining the indexing sequence of two inertial navigation systems:
the indexing sequence of the inertial navigation 1 is a biaxial 16 sequence, and the specific indexing flow is as follows:
order 1: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 2: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 3: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 4: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 5: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 6: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 7: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 8: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 9: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
sequence 10: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 11: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
order 12: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 13: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
sequence 14: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
order 15: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 16: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
the indexing sequence of the inertial navigation 2 is 18, and the specific indexing flow is as follows:
order 1: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 2: the y-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 3: the y-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 4: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 5: the z-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 6: the z-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 7: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 8: the x-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 9: the x-axis rotates 180 degrees forward at 9/s, and stops 180s;
sequence 10: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 11: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 12: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 13: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
sequence 14: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 15: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 16: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 17: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 18: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
based on the joint transposition mode, the inertial navigation 1 is in a biaxial rotation modulation navigation state, the inertial navigation 2 is in a calibration state, gyro scale factor errors, accelerometer scale factor errors and installation errors are all excited, and according to the scheme in the step (2), a joint state Kalman filter is established, so that the external field online calibration of the inertial navigation 2 is realized.
Furthermore, the method has no requirement on the motion state of the carrier, and the carrier can be calibrated on line in a mooring state or in a motion state; the carrier has no requirement on the environment where the carrier is located, and is applicable to the underwater environment and the GNSS refusal environment.
Further, the relative postures of the inertial navigation 1 and the inertial navigation 2 in the zero position are calibrated after the installation is finished, and the posture of the inertial navigation 2 at the initial calibration time is obtained through transfer alignment with the inertial navigation 1 based on the relative postures of the two sets of inertial navigation.
Furthermore, the joint indexing sequence in the step (3) is suitable for on-line calibration between two or more sets of inertial navigation systems with double-shaft indexing mechanisms, and is also suitable for on-line calibration between double-shaft and three-shaft inertial navigation systems and between multiple sets of three-shaft inertial navigation systems.
Further, the joint indexing sequence described in step (3) is only a preferred scheme based on two sets of inertial navigation systems with biaxial indexing mechanisms, and it is within the scope of the present invention for the joint indexing scheme to be between other rotational modulation sequences and calibration sequences.
In summary, the invention has the advantages and positive effects that: according to the invention, through the cooperative transposition of the two sets of inertial navigation systems, the external field calibration is completed by fusing the output information of the two sets of inertial navigation systems, the limitation of the traditional external field self-calibration scheme on the motion state of the carrier and external reference information is broken, the problem of inaccurate error equation in a dynamic environment is solved through the Psi angle error correction model, and the method is suitable for calibrating the inertial navigation system in long-endurance and has important engineering practice significance.
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Fig. 1 is a flow chart provided by an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
In some special application environments, such as underwater environments, GNSS refused environments and other carriers lack accurate and reliable external reference information, the navigation positioning of the carrier depends on an inertial navigation system. When the inertial navigation system needs to be calibrated regularly or parts of components need to be calibrated again after the inertial navigation system is in failure, the conventional external field calibration technology cannot meet the requirement, and the accuracy of the inertial navigation system can be affected. In addition, the traditional speed error model has a specific force term, the problem that the system covariance matrix error is increased due to inaccurate specific force calculation in a dynamic environment exists, and the error of the inertial navigation system is accumulated along with time due to the fact that the error of the inertial navigation system is corrected due to the lack of external reference information. In order to solve the technical problems, the invention provides a long-endurance double-inertial navigation collaborative calibration method based on a Psi angle error correction model, which is shown in fig. 1, and the specific implementation method is as follows:
(1) Constructing error models of two sets of inertial navigation systems;
defining a normal-working biaxial rotation modulation inertial navigation system as inertial navigation 1, and a body coordinate system b thereof 1 Defined as "right-front-up", the inertial navigation system to be calibrated is inertial navigation 2, its body coordinate system b 2 Defined as "right-front-up";
the scale factor error and the installation error of the inertial navigation 1 are small and neglected, and an error model of the inertial navigation 1 is defined as:
wherein,
in the method, in the process of the invention,indicating gyro assembly error of inertial navigation 1, +.>Accelerometer component error indicative of inertial navigation 1, < ->X-axis gyro drift representing inertial navigation 1, < >>Indicating the y-axis gyro drift of inertial navigation 1, < >>Z-axis gyro drift representing inertial navigation 1, < >>Zero offset of the x-axis accelerometer representing inertial navigation 1,>zero offset of the y-axis accelerometer representing inertial navigation 1,>zero offset of the z-axis accelerometer representing inertial navigation 1,>indicating gyro drift of inertial navigation 1, +.>Accelerometer zero bias indicative of inertial navigation 1, < ->For gyro noise of the inertial navigation 1,is inertial navigation 1 accelerometer noise;
considering the scale factor error, the mounting angle error and the zero offset error, defining an error model of the inertial navigation 2 as:
wherein,
in the method, in the process of the invention,indicating gyro assembly error of inertial navigation 2, +.>Accelerometer component error indicative of inertial navigation 2, < ->Theoretical angular velocity vector representing inertial navigation 2 gyro assembly output,/->Representing inertial navigation 2 plusTheoretical specific force vector measured by speedometer assembly, < >>X-axis gyro drift representing inertial navigation 2, < >>Representing the y-axis gyro drift of inertial navigation 2, < >>Indicating z-axis gyro drift of inertial navigation 2, < >>Zero offset of the x-axis accelerometer representing inertial navigation 2,>zero offset of the y-axis accelerometer representing inertial navigation 2,>zero offset of the z-axis accelerometer representing inertial navigation 2,>indicating gyro drift of inertial navigation 2 +.>Accelerometer zero bias indicative of inertial navigation 2, < ->Gyro noise for inertial navigation 2 +.>Is inertial navigation 2 accelerometer noise; delta kappa g And delta mu g Representing the scale factor error matrix and the installation error matrix of the gyro, δκ a And delta mu a Representing a scale factor error matrix and a mounting error matrix of the accelerometer;
determining δκ g And delta kappa a ：
In the formula, delta kappa gx 、δκ gy And delta kappa gz Scale factor errors, δκ, respectively representing an x-axis gyroscope, a y-axis gyroscope, and a z-axis gyroscope ax 、δκ ay And delta kappa az Scale factor errors for the x-axis accelerometer, the y-axis accelerometer, and the z-axis accelerometer are represented, respectively;
determination of δμ g And delta mu a ：
In the formula, delta mu gyx 、δμ gzx And delta mu gzy Representing three installation error angles, δμ, of a gyro assembly ayx 、δμ azx 、δμ azy 、δμ axy 、δμ axz And delta mu ayz Representing six mounting error angles of the accelerometer assembly;
(2) The combined state Kalman filter based on the Psi angle error correction model is established by utilizing the related information of the gesture, the speed and the position output by the two sets of inertial navigation systems, and the specific steps are as follows:
(2.1) determining a system joint error equation:
in the psi- 1 ＝[ψ E1 ψ N1 ψ U1 ] T Represents the drift error angle, ψ, of the inertial navigation 1 E1 、ψ N1 、ψ U1 Respectively represent the drift error angles of the east direction, the north direction and the sky direction of the inertial navigation 1,representing the velocity error vector of the inertial navigation 1 after error correction under the platform coordinate system,/for>Respectively representing the speed errors of the inertial navigation 1 in the east direction, the north direction and the sky direction after error correction,/->Representing the position error of inertial navigation 1, +.>Represents east error of inertial navigation 1, +.>Representing the north error of the inertial navigation 1,/>represents the error in the orientation of inertial navigation 1, +.>Representing the rotational angular velocity of the earth in the inertial navigation 1 calculation coordinate system,/>Representing the angular velocity of transfer in the inertial navigation 1 calculation coordinate system,/>Direction cosine matrix representing inertial navigation 1-body coordinate system to platform coordinate system,/and method for generating the same>Represents the gravity vector, ψ, under the inertial navigation 1 calculation coordinate system 2 ＝[ψ E2 ψ N2 ψ U2 ] T Represents the drift error angle, ψ, of inertial navigation 2 E2 、ψ N2 、ψ U2 Drift error angles of the east direction, the north direction and the sky direction of inertial navigation 2 are respectively represented, and the error angles are +.>Representing the velocity error vector of the inertial navigation 2 after error correction under the platform coordinate system,/for> Respectively representing the speed errors of the inertial navigation 2 in the east direction, the north direction and the sky direction after error correction,/->Indicating the position error of the inertial navigation 2,representing the east direction of inertial navigation 2Error (S)>Indicating north error of inertial navigation 2, +.>Represents the tangential error of inertial navigation 2, +.>Representing the rotational angular velocity of the earth in the inertial navigation 2 calculated coordinate system,/>Representing the angular velocity of transfer in inertial navigation 2 calculation coordinate system,/>Direction cosine matrix representing inertial navigation 2-body coordinate system to platform coordinate system,/and method for generating the same>Representing gravity vector v under inertial navigation 2 calculation coordinate system p Representing the speed of the carrier in the platform coordinate system;
(2.2) determining a joint state equation:
wherein,
/>
in the formula, 0 i×j A zero matrix representing i rows and j columns,represents the inertial navigation 1 eastern direction, the north direction and the heaven direction speed under the platform coordinate system, L 1 、h 1 Latitude and altitude representing the carrier position of the inertial navigation 1 output, +.>An antisymmetric matrix representing an inertial navigation 1 velocity vector, R N1 、R E1 Represents the radius of the meridian, the circle of the mortise and the circle of the mortise at the output position of the inertial navigation 1, ++>A value representing the acceleration of gravity at the output position of inertial navigation 1,/->Represents the inertial navigation 2 eastern direction, the north direction and the heaven direction speed under the platform coordinate system, L 2 、h 2 Latitude and altitude representing the carrier position of the inertial navigation 2 output, +.>An antisymmetric matrix representing an inertial navigation 2 velocity vector, R N2 、R E2 Represents the radius of the meridian, the circle of the mortise and the circle of the mortise at the output position of the inertial navigation 2,/and%>Value, ω, representing gravitational acceleration at the output position of inertial navigation 2 ie Represents the rotation angular velocity of the earth, C 23 Representation->Second and third columns of matrix, C 3 Representation->The third column of the matrix is designated,output values of the x, y and z axis gyroscopes of inertial navigation 2 are respectively represented by +.>Output values of the x, y and z axis accelerometers of the inertial navigation 2 are respectively represented;
the state vector x (t) is expressed as:
the noise distribution matrix and the noise matrix are expressed as:
/>
(2.3) determining a state constraint observation equation:
the output speeds and positions of the inertial navigation 1 and the inertial navigation 2 are respectively expressed as:
in the method, in the process of the invention,and->Representing the velocity information under the platform coordinate system output by inertial navigation 1 and inertial navigation 2 respectively, +.>And->Respectively representing the position information output by the inertial navigation 1 and the inertial navigation 2, and measuring and calibrating the outer lever arm parameters between the inertial navigation 1 and the inertial navigation 2 after the system is installed, and r c True value representing the position of the common point, +.>An outer lever arm representing the position between two inertial navigation systems, < >>Representing the projection of the outer lever arm between two sets of inertial navigation in the inertial navigation 2-body coordinate system,/->A rotational angular velocity vector representing the inertial navigation 2-body coordinate system relative to the platform coordinate system;
because the two sets of systems reflect the speed information and the position information of the same carrier, the observed quantity forms the constraint of the respective speed errors and the position errors of the inertial navigation 1 and the inertial navigation 2, and the constraint is expressed as follows:
in the formula, v v 、υ r Observing noise for corresponding speed and position; in the application environment of dual inertial navigation, external observation based on altitude informationDetermining a height observation equation:
in the method, in the process of the invention,is the height value of inertial navigation 1, v h Is highly observed noise; the observation equation is expressed as:
z(t)＝H(t)x(t)+υ(t)
wherein,
H 1 ＝[0 0 1]
υ(t)＝[(υ v ) T (υ r ) T υ h ] T
wherein I is 3×3 Representing a 3 row 3 column identity matrix;
(3) Determining the indexing sequence of two inertial navigation systems:
the indexing sequence of the inertial navigation 1 is a biaxial 16 sequence, and the specific indexing flow is as follows:
order 1: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 2: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 3: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 4: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 5: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 6: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 7: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 8: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 9: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
sequence 10: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 11: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
order 12: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 13: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
sequence 14: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
order 15: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 16: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
the indexing sequence of the inertial navigation 2 is 18, and the specific indexing flow is as follows:
order 1: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 2: the y-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 3: the y-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 4: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 5: the z-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 6: the z-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 7: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 8: the x-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 9: the x-axis rotates 180 degrees forward at 9/s, and stops 180s;
sequence 10: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 11: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 12: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 13: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
sequence 14: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 15: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 16: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 17: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 18: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
based on the joint transposition mode, the inertial navigation 1 is in a biaxial rotation modulation navigation state, the inertial navigation 2 is in a calibration state, gyro scale factor errors, accelerometer scale factor errors and installation errors are all excited, and according to the scheme in the step (2), a joint state Kalman filter is established, so that the external field online calibration of the inertial navigation 2 is realized.
The method has no requirement on the motion state of the carrier, and the carrier can be calibrated on line in a mooring state or in a motion state; the carrier has no requirement on the environment where the carrier is located, and is applicable to the underwater environment and the GNSS refusal environment.
The relative postures of the inertial navigation 1 and the inertial navigation 2 in the zero position are calibrated after the installation is finished, and the posture of the inertial navigation 2 at the initial calibration time is obtained through transfer alignment with the inertial navigation 1 based on the relative postures of the two sets of inertial navigation.
The joint indexing sequence in the step (3) is suitable for on-line calibration between two or more sets of inertial navigation systems with double-shaft indexing mechanisms, and is also suitable for on-line calibration between double-shaft and three-shaft inertial navigation systems and between multiple sets of three-shaft inertial navigation systems.
The joint indexing sequence in the step (3) is only a preferred scheme based on two sets of inertial navigation systems with biaxial indexing mechanisms, and the joint indexing scheme between other rotation modulation sequences and calibration sequences also belongs to the scope of the invention.
The foregoing is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all technical solutions belonging to the present invention are within the scope of the present invention. Improvements and modifications and the like without departing from the principles of the invention are also considered within the scope of the invention.
Claims (3)
1. The long-endurance double-inertial navigation collaborative calibration method based on the Psi angle error correction model is characterized by comprising the following steps of:
(1) Constructing error models of two sets of inertial navigation systems;
defining a normal-working biaxial rotation modulation inertial navigation system as inertial navigation 1, and a body coordinate system b thereof 1 Defined as "right-front-up", the inertial navigation system to be calibrated is inertial navigation 2, its body coordinate system b 2 Defined as "right-front-up";
the scale factor error and the installation error of the inertial navigation 1 are small and neglected, and an error model of the inertial navigation 1 is defined as:
wherein,
in the method, in the process of the invention,indicating gyro assembly error of inertial navigation 1, +.>Accelerometer component error indicative of inertial navigation 1, < ->X-axis gyro drift representing inertial navigation 1, < >>Indicating the y-axis gyro drift of inertial navigation 1, < >>Z-axis gyro drift representing inertial navigation 1, < >>Zero offset of the x-axis accelerometer representing inertial navigation 1,>zero offset of the y-axis accelerometer representing inertial navigation 1,>zero offset of the z-axis accelerometer representing inertial navigation 1,>indicating gyro drift of inertial navigation 1, +.>Accelerometer zero bias indicative of inertial navigation 1, < ->Gyro noise for inertial navigation 1, +.>Is inertial navigation 1 accelerometer noise;
considering the scale factor error, the mounting angle error and the zero offset error, defining an error model of the inertial navigation 2 as:
wherein,
in the method, in the process of the invention,indicating gyro assembly error of inertial navigation 2, +.>Accelerometer component error indicative of inertial navigation 2, < ->Theoretical angular velocity vector representing inertial navigation 2 gyro assembly output,/->Representing the theoretical specific force vector measured by the inertial navigation 2 accelerometer component, +.>X-axis gyro drift representing inertial navigation 2, < >>Representing the y-axis gyro drift of inertial navigation 2, < >>Indicating z-axis gyro drift of inertial navigation 2, < >>Zero offset of the x-axis accelerometer representing inertial navigation 2,>zero offset of the y-axis accelerometer representing inertial navigation 2,>zero offset of the z-axis accelerometer representing inertial navigation 2,>indicating gyro drift of inertial navigation 2 +.>Accelerometer zero bias indicative of inertial navigation 2, < ->Gyro noise for inertial navigation 2 +.>Is inertial navigation 2 accelerometer noise; delta kappa g And delta mu g Representing the scale factor error matrix and the installation error matrix of the gyro, δκ a And delta mu a Representing a scale factor error matrix and a mounting error matrix of the accelerometer;
determining δκ g And delta kappa a ：
In the formula, delta kappa gx 、δκ gy And delta kappa gz Scale factor errors, δκ, respectively representing an x-axis gyroscope, a y-axis gyroscope, and a z-axis gyroscope ax 、δκ ay And delta kappa az Scale factor errors for the x-axis accelerometer, the y-axis accelerometer, and the z-axis accelerometer are represented, respectively;
determination of δμ g And delta mu a ：
In the formula, delta mu gyx 、δμ gzx And delta mu gzy Representing three installation error angles, δμ, of a gyro assembly ayx 、δμ azx 、δμ azy 、δμ axy 、δμ axz And delta mu ayz Representing six mounting error angles of the accelerometer assembly;
(2) The combined state Kalman filter based on the Psi angle error correction model is established by utilizing the related information of the gesture, the speed and the position output by the two sets of inertial navigation systems, and the specific steps are as follows:
(2.1) determining a system joint error equation:
in the psi- 1 ＝[ψ E1 ψ N1 ψ U1 ] T Represents the drift error angle, ψ, of the inertial navigation 1 E1 、ψ N1 、ψ U1 Respectively represent the drift error angles of the east direction, the north direction and the sky direction of the inertial navigation 1,representing the velocity error vector of the inertial navigation 1 after error correction under the platform coordinate system,/for>Respectively represents the speed error of the inertial navigation 1 in the east direction, the north direction and the sky direction after error correction,representing the position error of inertial navigation 1, +.>Represents east error of inertial navigation 1, +.>Indicating north error of inertial navigation 1, +.>Represents the error in the orientation of inertial navigation 1, +.>Representing the rotational angular velocity of the earth in the inertial navigation 1 calculation coordinate system,/>Representing the angular velocity of transfer in the inertial navigation 1 calculation coordinate system,/>Direction cosine matrix representing inertial navigation 1-body coordinate system to platform coordinate system,/and method for generating the same>Represents the gravity vector, ψ, under the inertial navigation 1 calculation coordinate system 2 ＝[ψ E2 ψ N2 ψ U2 ] T Represents the drift error angle, ψ, of inertial navigation 2 E2 、ψ N2 、ψ U2 Drift error angles of the east direction, the north direction and the sky direction of inertial navigation 2 are respectively represented, and the error angles are +.>Representing the velocity error vector of the inertial navigation 2 after error correction under the platform coordinate system,/for> Respectively representing the speed errors of the inertial navigation 2 in the east direction, the north direction and the sky direction after error correction,/->Representing the position error of inertial navigation 2, +.>Represents east error of inertial navigation 2, +.>Indicating north error of inertial navigation 2, +.>Represents the tangential error of inertial navigation 2, +.>Representing the rotational angular velocity of the earth in the inertial navigation 2 calculated coordinate system,/>Representing inertial navigation 2 computationTransfer angular velocity in coordinate system, +.>Direction cosine matrix representing inertial navigation 2-body coordinate system to platform coordinate system,/and method for generating the same>Representing gravity vector v under inertial navigation 2 calculation coordinate system p Representing the speed of the carrier in the platform coordinate system;
(2.2) determining a joint state equation:
wherein,
in the formula, 0 i×j A zero matrix representing i rows and j columns,represents the inertial navigation 1 eastern direction, the north direction and the heaven direction speed under the platform coordinate system, L 1 、h 1 Latitude and altitude representing the carrier position of the inertial navigation 1 output, +.>An antisymmetric matrix representing an inertial navigation 1 velocity vector, R N1 、R E1 Represents the radius of the meridian, the circle of the mortise and the circle of the mortise at the output position of the inertial navigation 1, ++>A value representing the acceleration of gravity at the output position of inertial navigation 1,/->Represents the inertial navigation 2 eastern direction, the north direction and the heaven direction speed under the platform coordinate system, L 2 、h 2 Latitude and altitude representing the carrier position of the inertial navigation 2 output, +.>An antisymmetric matrix representing an inertial navigation 2 velocity vector, R N2 、R E2 Represents the radius of the meridian, the circle of the mortise and the circle of the mortise at the output position of the inertial navigation 2,/and%>Value, ω, representing gravitational acceleration at the output position of inertial navigation 2 ie Represents the rotation angular velocity of the earth, C 23 Representation->Second and third columns of matrix, C 3 Representation->The third column of the matrix is designated,output values of the x, y and z axis gyroscopes of inertial navigation 2 are respectively represented by +.>Output values of the x, y and z axis accelerometers of the inertial navigation 2 are respectively represented;
the state vector x (t) is expressed as:
the noise distribution matrix and the noise matrix are expressed as:
(2.3) determining a state constraint observation equation:
the output speeds and positions of the inertial navigation 1 and the inertial navigation 2 are respectively expressed as:
in the method, in the process of the invention,and->Representing the velocity information under the platform coordinate system output by inertial navigation 1 and inertial navigation 2 respectively, +.>And->Respectively representing the position information output by the inertial navigation 1 and the inertial navigation 2, and measuring and calibrating the outer lever arm parameters between the inertial navigation 1 and the inertial navigation 2 after the system is installed, and r c True value representing the position of the common point, +.>An outer lever arm representing the position between two inertial navigation systems, < >>Representing the projection of the outer lever arm between two sets of inertial navigation in the inertial navigation 2-body coordinate system,/->A rotational angular velocity vector representing the inertial navigation 2-body coordinate system relative to the platform coordinate system;
because the two sets of systems reflect the speed information and the position information of the same carrier, the observed quantity forms the constraint of the respective speed errors and the position errors of the inertial navigation 1 and the inertial navigation 2, and the constraint is expressed as follows:
in the formula, v v 、υ r Observing noise for corresponding speed and position; in the application environment of dual inertial navigation, external observation based on altitude informationDetermining a height observation equation:
in the method, in the process of the invention,is the height value of inertial navigation 1, v h Is highly observed noise; the observation equation is expressed as:
z(t)＝H(t)x(t)+υ(t)
wherein,
H 1 ＝[0 0 1]
υ(t)＝[(υ v ) T (υ r ) T υ h ] T
wherein I is 3×3 Representing a 3 row 3 column identity matrix;
(3) Determining the indexing sequence of two inertial navigation systems:
the indexing sequence of the inertial navigation 1 is a biaxial 16 sequence, and the specific indexing flow is as follows:
order 1: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 2: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 3: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 4: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 5: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 6: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 7: the y-axis rotates 180 degrees in the opposite direction at 9/s, and stops for 100s;
order 8: the z-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 9: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
sequence 10: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 11: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
order 12: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 13: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
sequence 14: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
order 15: the y-axis rotates 180 degrees forward at 9/s, and stops for 100s;
order 16: the z-axis rotates 180 degrees in the opposite direction at 9 degrees/s, and stops for 100s;
the indexing sequence of the inertial navigation 2 is 18, and the specific indexing flow is as follows:
order 1: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 2: the y-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 3: the y-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 4: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 5: the z-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 6: the z-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 7: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 8: the x-axis rotates 180 degrees forward at 9/s, and stops 180s;
order 9: the x-axis rotates 180 degrees forward at 9/s, and stops 180s;
sequence 10: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 11: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 12: the x-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 13: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
sequence 14: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 15: the z-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 16: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 17: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
order 18: the y-axis rotates forward by 90 degrees at 9 degrees/s, and stops for 180 seconds;
based on the joint transposition mode, the inertial navigation 1 is in a biaxial rotation modulation navigation state, the inertial navigation 2 is in a calibration state, the gyro scale factor error, the accelerometer scale factor error and the installation error are all excited, and according to the step (2), a joint state Kalman filter is established, so that the external field online calibration of the inertial navigation 2 is realized.
2. The long-endurance double-inertial navigation collaborative calibration method based on the Psi angle error correction model according to claim 1, wherein the relative posture of the inertial navigation 1 and the inertial navigation 2 when in a zero position is calibrated after installation, and the posture of the inertial navigation 2 at the initial calibration time is obtained by transfer alignment with the inertial navigation 1 based on the relative postures of the two sets of inertial navigation.
3. The long-endurance double-inertial navigation collaborative calibration method based on the Psi angle error correction model according to claim 1, which is characterized in that the joint indexing sequence in the step (3) is suitable for on-line calibration between two or more sets of inertial navigation systems with double-shaft indexing mechanisms, and is also suitable for on-line calibration between double-shaft and three-shaft inertial navigation systems and between multiple sets of three-shaft inertial navigation systems.
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