CN109211269A - A kind of dual-axis rotation inertial navigation system attitude error scaling method - Google Patents
A kind of dual-axis rotation inertial navigation system attitude error scaling method Download PDFInfo
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Abstract
The invention proposes a kind of dual-axis rotation inertial navigation system attitude error scaling methods, by constructing multiple coordinate systems, by existing installation deviation angle between the shafting and inner axle and outer annulate shaft of the IMU being installed on inner frame, i.e. rolling misalignment, which calibrates, comes, and reduces influence of the coning error angle to posture；Simultaneously, using the angle of oscillation of non-orthogonal angles and axis itself between kalman filter method calibration rotary shaft, and observation information and navigation data in Kalman filtering process are obtained using 16 position rotary process, further improve the navigation accuracy of the long endurance of posture precision and system.
Description
Technical Field
The invention relates to the field of inertial navigation, in particular to a method for calibrating attitude angle errors of a double-axis rotary inertial navigation system.
Background
The biaxial rotation inertial navigation is a navigation technology which is popular in China in recent years. Due to the maturity and wide application of laser gyroscope technology, the performance of optical fiber gyroscopes is continuously improved, so that optical gyroscopes can use modulation technology. Within the navigational coordinate system, the modulation technique modulates these errors of the gyroscope and accelerometer with their sensitive axes perpendicular to the rotation axis: scale factor asymmetry error, installation error and random constant drift error. After the errors are modulated and averaged, the positioning accuracy of the system can be obviously improved. However, due to the introduction of the rotating mechanism, many errors become sources of cone errors, and further increase of attitude errors is caused. For example, due to the limitation of machining precision and the influence of manual adjustment precision, etc., there may be an installation deviation angle between the axis system of the IMU installed on the inner frame and the inner ring axis and the outer ring axis, that is, the measurement axis of the IMU does not coincide with the rotation axis (the angle is defined as a roll misalignment angle).
In biaxial rotational inertial navigation, two factors are mainly used for causing a cone error angle, one is a rolling misalignment angle between an IMU coordinate system and a platform coordinate system; one is the non-orthogonal angle between the axes of rotation and the angle of oscillation of the axes themselves. Therefore, in order to reduce the influence of the cone error angle on the system attitude, the misalignment angle needs to be calibrated, and modeling and calibration need to be performed on the axis non-orthogonal angle and the axis swing angle, so as to further improve the system attitude accuracy and the navigation accuracy during long-term navigation of the system.
Disclosure of Invention
In order to solve the problems, the invention provides an attitude angle error calibration method of a double-shaft rotary inertial navigation system.
The main content of the invention comprises:
an attitude angle error calibration method for a biaxial rotation inertial navigation system comprises the following steps:
step 1: constructing a coordinate system comprising:
coordinate system of gyroscope assembly, denoted as G system, xgAxis, ygAxis, zgThe axes are the sensitive axes of an x gyroscope, a y gyroscope and a z gyroscope respectively;
accelerometer component coordinate system, denoted as a system, xaAxis, yaAxis, zaThe axes are the sensitive axes of an x accelerometer, a y accelerometer and a z accelerometer respectively;
an IMU coordinate system marked as an S system, wherein the IMU coordinate system is fixedly connected with the platform and rotates along with the platform; the IMU coordinate system is centered on the IMU structure center and the initial etch, ysAxis and ygThe axes are overlapped;
the actual platform coordinate system, denoted as P system, zpPointing "day" as positive and rotating the shaft in the direction of the day, ypIs a horizontal axis and takes the pointing heading as positive;
modulation mean coordinate system, denotedThe modulation average coordinate system is a fixed coordinate system centered at the IMU accelerometer assembly center, and at an initial time,the axis pointing to "day" and zpThe axes are overlapped with each other, and the axes are overlapped,pointing to the bow;
a vector coordinate system, denoted as system b, with its origin at the vector centroid, xbAxis, ybAxis, zbThe shaft points to the right direction, the heading direction and the sky direction of the ship respectively;
system base coordinate system, denoted as O system, whose coordinate center coincides with base structure centroid, where zoAxis perpendicular to mounting base, yoThe axis is parallel to the horizontal axis of the platform;
an inner frame angular reading device coordinate system, denoted as S1, fixedly connected with the angular reading device and rotating with the IMU, wherein ys1The direction of the shaft is the positive direction of a rotating vector of a rotor part of the angle reading device;
an inner frame axis coordinate system is marked as a K1 system, and the inner frame axis coordinate system is a fixed coordinate system and is a coordinate system when an angle reading device on the inner frame is at a zero position;
the outer frame plus the angle reading device coordinate system S2, which is fixedly connected with the angle reading device and rotates with the IMU, ys2The direction of the shaft is the positive direction of a rotating vector of a rotor part of the angle reading device;
an outer frame axis coordinate system K2, which is a fixed coordinate system, and the outer frame axis coordinate system is a fixed coordinate system, which refers to a coordinate system when the angle reading device on the outer frame is at zero position;
the system also comprises a terrestrial coordinate system and a navigation coordinate system, wherein the terrestrial coordinate system is marked as an e system, and the navigation coordinate system is marked as an n system;
the above coordinate systems all satisfy the right-hand rule;
step 2: calibrating a rolling misalignment angle between an IMU coordinate system and an actual platform coordinate system, wherein the rolling misalignment angle refers to an installation deviation angle between a shaft system of the IMU arranged on an inner frame and an inner ring shaft and an outer ring shaft;
and step 3: establishing a conversion matrix between an IMU coordinate system and a modulation mean coordinate system by considering an axis swing angle and an axis non-orthogonal angle
Step 4, calibrating an axis swing angle α generated by the rotation of the IMU around the inner ring axis by using a Kalman filtering method1Yaw angle α resulting from IMU rotation about an outer ring axis2And an axial non-orthogonal angle η between the actual platform coordinate system and the modulation mean coordinate system.
Preferably, the roll misalignment angle described in step 2 comprises a pitch angle error Δ θ1Yaw angle error Δ γ1Deflection error angle about the zenith axisAnd an error angle delta gamma about a horizontal axis2Wherein the pitch angle error Δ θ1And said roll angle error Δ γ1The method is characterized in that only a horizontal installation error angle exists between an IMU coordinate system and an inner frame upper angle reading device coordinate system is assumed; said angular error about the zenith axisAnd an error angle delta gamma about a horizontal axis2It is assumed that there is an installation error angle between the outer frame plus the angle reading device coordinate system and the inner frame axis coordinate system in both directions.
Preferably, the step 2 specifically comprises the following steps:
step 21: and (3) carrying out horizontal rough alignment on the system to obtain an initial attitude matrix: the system is adjusted to be in a horizontal state through the leveling mechanism, placed according to the northeast China and enters a navigation state, the inner frames are respectively positioned at a zero position and a 180-degree position, and IMU attitude matrix is respectively obtainedAndwherein when the inner frame is at zero position, it is the inner frameThe rotation angle α around the zenith axis between the frame axis coordinate system and the inner frame angle reading device coordinate system is 0 degree, and the rotation angle α around the zenith axis between the inner frame axis coordinate system and the inner frame angle reading device coordinate system is 180 degrees when the inner frame is at 180 degrees
Step 22: calculating the pitch angle error delta theta by using the IMU attitude matrix in the step 211Yaw angle error Δ γ1(ii) a The calculation process is as follows:
in order to ensure that the water-soluble organic acid,then there is a change in the number of,
step 23: calculating the attitude matrix of the inner frame axis coordinate system relative to the navigation coordinate system
α refers to the rotation angle around the zenith axis between the inner frame axis coordinate system and the inner frame angle reading device coordinate system, and the attitude matrix of the IMU coordinate system relative to the navigation coordinate systemResolved by navigation;
step 24: calculating the deflection error angle around the vertical axisAnd an error angle delta gamma about a horizontal axis2The calculation process is as follows:
in order to ensure that the water-soluble organic acid,then there is
Step 25: calculating the attitude matrix of the outer frame axis coordinate system relative to the navigation coordinate system
Wherein β is the pitch angle between the coordinate system of the outer frame axis and the coordinate system of the angle reading device on the outer frame.
Preferably, the transformation matrix between the IMU coordinate system and the modulation mean coordinate system in step 3The calculation process of (2) is as follows:
wherein,λ is z of the IMU around the actual platform coordinate systempThe angle through which the shaft is rotated;refers to the initial phase angle α1As IMU coordinatesZ tied around the actual platform coordinate systempHalf cone angle of the cone generated by shaft rotation;λ' is y of the IMU around the actual platform coordinate systempThe angle of rotation;is the initial phase angle, α2For y of IMU coordinate system around the actual platform coordinate systempHalf cone angle of the cone generated by shaft rotation; and let IMU wrap the z of the actual platform coordinate systempAngles lambda and y through which the shaft rotatespThe rotated angle λ 'is the same and is denoted as λ ═ λ' ═ ω t.
Preferably, the specific steps of step 4 include:
step 41: creating a Kalman filtering state equation;
wherein the state variables are represented as:
the observation equation is: z-HX + V, where the observation matrix is represented as:
l represents latitude; v is an observation noise vector and is white noise;
step 42: and acquiring observation information and navigation data of the Kalman filtering process by adopting a 16-position rotation method.
Preferably, the rotation process of acquiring the observation information and the navigation data of the kalman filtering process by the 16-position rotation method in step 42 is as follows:
(1) starting the system to enter a navigation state under the condition of a static base;
(2) a leveling mechanism and an azimuth adjusting mechanism on the adjusting structure enable a sensitive shaft of the IMU to point to the northeast when the sensitive shaft is in an initial zero position, and a horizontal attitude angle and a heading angle are both zero;
(3) the IMU is rotated according to the rotation sequence set by a 16-position rotation method, and the rotation angular speed is 15 degrees/s under each sequence;
(4) and (5) continuously shifting to know that the estimation variable result is converged, and finishing the calibration.
The invention has the beneficial effects that: the invention provides a method for calibrating attitude angle errors of a biaxial rotation inertial navigation system, which comprises the steps of constructing a plurality of coordinate systems, and calibrating an installation deviation angle, namely a rolling misalignment angle, between a shaft system of an IMU (inertial measurement Unit) arranged on an inner frame and an inner ring shaft and an outer ring shaft, so that the influence of a cone error angle on the attitude of the system is reduced; meanwhile, a Kalman filtering method is adopted to calibrate a non-orthogonal angle between rotating shafts and a swinging angle of the shafts, observation information and navigation data in the Kalman filtering process are obtained by using a 16-position rotation method, and the attitude precision of the system and the navigation precision of the system during long voyage are further improved.
Drawings
FIG. 1 is a schematic representation of various coordinate systems of the inventive construction;
FIG. 2 shows the z-coordinate of the IMU of the present invention around the actual platform coordinate systempA cone diagram generated by shaft rotation;
FIG. 3 shows the IMU of the present invention around the actual platform coordinate system ypA cone diagram generated by shaft rotation;
FIG. 4 is a graph of the projection of the non-orthogonal angles of axes of the present invention in a modulated mean coordinate system;
FIG. 5 is a schematic rotational view of the IMU 16 position rotation method of the present invention;
FIG. 6 is a comparison of compensated front and rear pitch angles of the present invention;
FIG. 7 is a comparison of compensated front and rear roll angles in accordance with the present invention;
FIG. 8 is a comparison graph of compensated forward and aft heading angles for the present invention.
Detailed Description
The technical scheme protected by the invention is specifically explained in the following by combining the attached drawings.
The attitude angle error calibration method provided by the invention is suitable for a general platform type inertial navigation system which mostly adopts a two-frame three-axis structure, namely, the general platform type inertial navigation system comprises a gyroscope, an accelerometer, an outer frame, an inner frame and a platform body, wherein the gyroscope and the accelerometer are arranged on the platform body, and the outer frame, the inner frame and the platform body can respectively rotate around an outer ring axis, an inner ring axis and a platform body axis.
An attitude angle error calibration method for a biaxial rotation inertial navigation system comprises the following steps:
step 1: constructing a coordinate system, and FIG. 1 provides a schematic diagram of various coordinate systems constructed by the present invention; the method mainly comprises the following steps:
coordinate system of gyroscope assembly, denoted as G system, oxgAxis, oygAxis, ozgThe axes are the sensitive axes of an x gyroscope, a y gyroscope and a z gyroscope respectively;
accelerometer element coordinate system denoted as system a, oxaAxis, oyaAxis, ozaThe axes are the sensitive axes of an x accelerometer, a y accelerometer and a z accelerometer respectively;
an IMU coordinate system marked as an S system, wherein the IMU coordinate system is fixedly connected with the platform and rotates along with the platform; of the IMU coordinate systemCentered at the IMU structure center, and initial etch, ysAxis and ygThe axes are overlapped; x is the number ofsAxis in plane perpendicular to ys，zsAxis and xsAxis and ysThe axis conforms to the right hand rule;
the actual platform coordinate system is marked as a P system and is defined by two actual axes of the platform; ozpPointing "day" as positive and rotating axis in the direction of day, oypIs a horizontal axis and takes the pointing heading as positive; oxpThe axes meet the right-hand rule, and the center of the actual platform coordinate system is at the intersection point of the two axes;
modulation mean coordinate system, denotedThe modulation mean coordinate system is a fixed coordinate system that is neither the IMU measurement coordinate system nor the actual gyro platform coordinate system, the modulation mean coordinate system is centered at the IMU accelerometer assembly center, and at an initial time,the axis points to "day" and co-zpThe axes are overlapped with each other, and the axes are overlapped,points to the bowPointing to the right;
a vector coordinate system, denoted as system b, with its origin at the vector centroid, xbAxis, ybAxis, zbThe shaft points to the right direction, the heading direction and the sky direction of the ship respectively;
system base coordinate system, denoted as O system, whose coordinate center coincides with base structure centroid, where zoAxis perpendicular to mounting base, yoThe axis is parallel to the horizontal axis of the platform;
a coordinate system of the angle reading device on the inner frame, marked as S1 system, fixedly connected with the angle reading device androtate with the IMU, wherein ys1The direction of the axis is the positive direction of the rotation vector of the rotor part of the angle reading device, and in the invention, for simplifying the calculation, only one horizontal installation error angle is supposed to exist between an IMU coordinate system and an angle reading device coordinate system on the inner frame, and the horizontal installation error angle is defined as a pitching angle error delta theta1Yaw angle error Δ γ1；
An inner frame shaft coordinate system is marked as a K1 system, the inner frame shaft coordinate system is a fixed coordinate system and is a coordinate system when an angle reading device on an inner frame is at a zero position, and a rotating angle between the inner frame shaft coordinate system and the coordinate system of the angle reading device on the inner frame around a zenith shaft is set to be α;
the outer frame plus the angle reading device coordinate system S2, which is fixedly connected with the angle reading device and rotates with the IMU, ys2The direction of the shaft is the positive direction of a rotating vector of a rotor part of the angle reading device; meanwhile, the invention assumes that installation error angles exist between the coordinate system of the angle reading device on the outer frame and the coordinate system of the inner frame shaft in two directions, and the installation error angles are respectively recorded as error angles deflected around the natural axisAnd an error angle delta gamma about a horizontal axis2；
An outer frame axis coordinate system K2, which is a fixed coordinate system, and the outer frame axis coordinate system is a fixed coordinate system, which refers to a coordinate system when the angle reading device on the outer frame is at zero position, so that only one pitch angle β exists from the outer frame axis coordinate system to the outer frame plus the angle reading device coordinate system;
the system further comprises an earth coordinate system and a navigation coordinate system, wherein the earth coordinate system is marked as an e system, in the embodiment, the origin of coordinates of the earth coordinate system is at the earth mass center, and ox thereofeIn the mean astronomical equatorial plane, oyeIn the mean astronomical equatorial plane, and in xeEast 90 ° of the axis, ozeThe axis meets the right hand rule; and the navigation coordinate system is marked as an n system, a local horizontal north-pointing azimuth coordinate system is selected, and the origin of coordinates of the navigation coordinate system is located at the center of mass of the carrier, oxnPoint to the geographical east, oyePoint to the north, oz of geographyeSatisfying the right-hand rule.
Step 2: calibrating a rolling misalignment angle between an IMU coordinate system and an actual platform coordinate system, wherein the rolling misalignment angle refers to an installation deviation angle between a shaft system of the IMU arranged on an inner frame and an inner ring shaft and an outer ring shaft; in this embodiment, the roll misalignment angle includes a pitch angle error Δ θ1Yaw angle error Δ γ1Deflection error angle about the zenith axisAnd an error angle delta gamma about a horizontal axis2(ii) a The calibration process of the above four error angles is as follows:
step 21: and (3) carrying out horizontal rough alignment on the system to obtain an initial attitude matrix: the system is adjusted to be in a horizontal state through the leveling mechanism, placed according to the northeast China and enters a navigation state, the inner frames are respectively positioned at a zero position and a 180-degree position, and IMU attitude matrix is respectively obtainedAndwherein, when the inner frame is at zero position, the rotation angle α around the zenith axis between the inner frame shaft coordinate system and the inner frame angle reading device coordinate system is 0 degree, and when the inner frame is at 180 degree, the rotation angle α around the zenith axis between the inner frame shaft coordinate system and the inner frame angle reading device coordinate system is 180 degree
Step 22: calculating the pitch angle error delta theta by using the IMU attitude matrix in the step 211Yaw angle error Δ γ1(ii) a The calculation process is as follows:
in order to ensure that the water-soluble organic acid,then there is a change in the number of,
step 23: calculating the attitude matrix of the inner frame axis coordinate system relative to the navigation coordinate system
Wherein the IMU coordinate system is relative to the attitude matrix of the navigation coordinate systemResolved by navigation;
step 24: calculating the deflection error angle around the vertical axisAnd an error angle delta gamma about a horizontal axis2The calculation process is as follows:
in order to ensure that the water-soluble organic acid,then there is
Step 25: calculating the attitude matrix of the outer frame axis coordinate system relative to the navigation coordinate system
And step 3: establishing a conversion matrix between an IMU coordinate system and a modulation mean coordinate system by considering an axis swing angle and an axis non-orthogonal angleThe specific calculation process is as follows:
the geometrical projection relation of the pivot angle between the IMU coordinate system and the modulation mean coordinate system is shown in FIGS. 2 and 3, and FIG. 2 shows the oz of the IMUpCone generated by rotation of the shaft, fig. 3 shows the IMU around oypA cone generated by shaft rotation; in particular, the amount of the solvent to be used,λ is z of the IMU around the actual platform coordinate systempThe angle through which the shaft is rotated;refers to the initial phase angle α1Z around the actual platform coordinate system for the IMU coordinate systempHalf cone angle of the cone generated by shaft rotation;λ' is y of the IMU around the actual platform coordinate systempThe angle of rotation;is the initial phase angle, α2For y of IMU coordinate system around the actual platform coordinate systempHalf cone angle of the cone generated by shaft rotation; and let IMU wrap the z of the actual platform coordinate systempAngles lambda and y through which the shaft rotatespThe same angle λ' is used, and is recorded as λ ═ λ′＝ωt。
Step 4, calibrating an axis swing angle α generated by the rotation of the IMU around the inner ring axis by using a Kalman filtering method1Yaw angle α resulting from IMU rotation about an outer ring axis2And an axis non-orthogonal angle η between the actual platform coordinate system and the modulation mean coordinate system figure 4 shows a projection of the axis non-orthogonal angle in the modulation mean coordinate system, wherein the IMU rotates about the inner ring axis to produce an axis yaw angle α1I.e. z around the actual platform coordinate system in the IMU coordinate systempThe half cone angle of the cone created by the rotation of the shaft, and the yaw angle α created by the rotation of the IMU about the outer ring axis2For y of IMU coordinate system around the actual platform coordinate systempThe shaft rotates the half cone angle of the generated cone.
The method specifically comprises the following substeps:
step 41: creating a Kalman filtering state equation;
wherein the state variables are represented as:
the observation equation is: z-HX + V, where the observation matrix is represented as:
l represents latitude; v is an observation noise vector and is white noise;
step 42: and acquiring observation information and navigation data of the Kalman filtering process by adopting a 16-position rotation method.
Preferably, the rotation process of acquiring the observation information and the navigation data of the kalman filtering process by the 16-position rotation method in step 42 is as follows:
(1) starting the system to enter a navigation state under the condition of a static base;
(2) a leveling mechanism and an azimuth adjusting mechanism on the adjusting structure enable a sensitive shaft of the IMU to point to the northeast when the sensitive shaft is in an initial zero position, and a horizontal attitude angle and a heading angle are both zero;
(3) the IMU is rotated according to the rotation sequence set by a 16-position rotation method, and the rotation angular speed is 15 degrees/s under each sequence;
(4) and (5) continuously shifting to know that the estimation variable result is converged, and finishing the calibration.
Fig. 5 shows a schematic rotation diagram of the 16-position rotation method of the present invention, which not only modulates the asymmetry error of the scale factor, but also reduces the position error oscillation caused by the installation error.
Referring to fig. 6, 7 and 8, the curves of the three graphs with stable routing are the variation trends of the pitch angle error, the roll angle error and the course angle error after compensation, and the other curves are the variation trends of the three error angles before compensation; from the above three figures, the attitude result after compensating the attitude angle by using the method of the present invention has the advantages that the errors of the pitch angle and the roll angle are reduced by 4 to 5 times, and the error of the course angle is also reduced by 3 to 4 times.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (6)
1. A method for calibrating attitude angle errors of a biaxial rotation inertial navigation system is characterized by comprising the following steps:
step 1: constructing a coordinate system comprising:
coordinate system of gyroscope assembly, denoted as G system, xgAxis, ygAxis, zgThe axes are the sensitive axes of an x gyroscope, a y gyroscope and a z gyroscope respectively;
accelerometer component coordinate system, denoted as a system, xaAxis, yaAxis, zaThe axes are x, y and z accelerometersA sensitive shaft of (a);
an IMU coordinate system marked as an S system, wherein the IMU coordinate system is fixedly connected with the platform and rotates along with the platform; the IMU coordinate system is centered on the IMU structure center and the initial etch, ysAxis and ygThe axes are overlapped;
the actual platform coordinate system, denoted as P system, zpPointing "day" as positive and rotating the shaft in the direction of the day, ypIs a horizontal axis and takes the pointing heading as positive;
modulation mean coordinate system, denotedThe modulation average coordinate system is a fixed coordinate system centered at the IMU accelerometer assembly center, and at an initial time,the axis pointing to "day" and zpThe axes are overlapped with each other, and the axes are overlapped,pointing to the bow;
a vector coordinate system, denoted as system b, with its origin at the vector centroid, xbAxis, ybAxis, zbThe shaft points to the right direction, the heading direction and the sky direction of the ship respectively;
system base coordinate system, denoted as O system, whose coordinate center coincides with base structure centroid, where zoAxis perpendicular to mounting base, yoThe axis is parallel to the horizontal axis of the platform;
an inner frame angular reading device coordinate system, denoted as S1, fixedly connected with the angular reading device and rotating with the IMU, wherein ys1The direction of the shaft is the positive direction of a rotating vector of a rotor part of the angle reading device;
an inner frame axis coordinate system is marked as a K1 system, and the inner frame axis coordinate system is a fixed coordinate system and is a coordinate system when an angle reading device on the inner frame is at a zero position;
the outer frame plus the angle reading device coordinate system S2, which is fixedly connected with the angle reading device and rotates with the IMU, ys2The direction of the axis being angle-readingSetting the positive direction of the rotation vector of the rotor part;
an outer frame axis coordinate system K2, which is a fixed coordinate system, and the outer frame axis coordinate system is a fixed coordinate system, which refers to a coordinate system when the angle reading device on the outer frame is at zero position;
the system also comprises a terrestrial coordinate system and a navigation coordinate system, wherein the terrestrial coordinate system is marked as an e system, and the navigation coordinate system is marked as an n system;
the above coordinate systems all satisfy the right-hand rule;
step 2: calibrating a rolling misalignment angle between an IMU coordinate system and an actual platform coordinate system, wherein the rolling misalignment angle refers to an installation deviation angle between a shaft system of the IMU arranged on an inner frame and an inner ring shaft and an outer ring shaft;
and step 3: establishing a conversion matrix between an IMU coordinate system and a modulation mean coordinate system by considering an axis swing angle and an axis non-orthogonal angle
Step 4, calibrating an axis swing angle α generated by the rotation of the IMU around the inner ring axis by using a Kalman filtering method1Yaw angle α resulting from IMU rotation about an outer ring axis2And an axial non-orthogonal angle η between the actual platform coordinate system and the modulation mean coordinate system.
2. The method for calibrating attitude angle error of a biaxial rotation inertial navigation system according to claim 1, wherein the roll misalignment angle in step 2 comprises a pitch angle error Δ θ1Yaw angle error Δ γ1Deflection error angle about the zenith axisAnd an error angle delta gamma about a horizontal axis2Wherein the pitch angle error Δ θ1And said roll angle error Δ γ1The method is characterized in that only a horizontal installation error angle exists between an IMU coordinate system and an inner frame upper angle reading device coordinate system is assumed; said angular error about the zenith axisAnd an error angle delta gamma about a horizontal axis2It is assumed that there is an installation error angle between the outer frame plus the angle reading device coordinate system and the inner frame axis coordinate system in both directions.
3. The method for calibrating the attitude angle error of the biaxial rotational inertial navigation system according to claim 2, wherein the step 2 specifically comprises the following steps:
step 21: and (3) carrying out horizontal rough alignment on the system to obtain an initial attitude matrix: the system is adjusted to be in a horizontal state through the leveling mechanism, placed according to the northeast China and enters a navigation state, the inner frames are respectively positioned at a zero position and a 180-degree position, and IMU attitude matrix is respectively obtainedAndwherein, when the inner frame is at zero position, the rotation angle α around the zenith axis between the inner frame shaft coordinate system and the inner frame angle reading device coordinate system is 0 degree, and when the inner frame is at 180 degree, the rotation angle α around the zenith axis between the inner frame shaft coordinate system and the inner frame angle reading device coordinate system is 180 degree
Step 22: calculating the pitch angle error delta theta by using the IMU attitude matrix in the step 211Yaw angle error Δ γ1(ii) a The calculation process is as follows:
in order to ensure that the water-soluble organic acid,then there is a change in the number of,
step 23: calculating the attitude matrix of the inner frame axis coordinate system relative to the navigation coordinate system
α refers to the rotation angle around the zenith axis between the inner frame axis coordinate system and the inner frame angle reading device coordinate system, and the attitude matrix of the IMU coordinate system relative to the navigation coordinate systemResolved by navigation;
step 24: calculating the deflection error angle around the vertical axisAnd an error angle delta gamma about a horizontal axis2The calculation process is as follows:
in order to ensure that the water-soluble organic acid,then there is
Step 25: calculating the attitude matrix of the outer frame axis coordinate system relative to the navigation coordinate system
Wherein β refers to the coordinate system of the axis of the outer frame to the outer frameThe pitch angle between the coordinate systems of the angle reading device.
4. The method for calibrating attitude angle error of a biaxial rotational inertial navigation system according to claim 1, wherein in step 3, the transformation matrix from the IMU coordinate system to the modulation average coordinate systemThe calculation process of (2) is as follows:
wherein,λ is z of the IMU around the actual platform coordinate systempThe angle through which the shaft is rotated;refers to the initial phase angle α1Z around the actual platform coordinate system for the IMU coordinate systempHalf cone angle of the cone generated by shaft rotation;λ' is y of the IMU around the actual platform coordinate systempThe angle of rotation;is the initial phase angle, α2For y of IMU coordinate system around the actual platform coordinate systempHalf cone angle of the cone generated by shaft rotation; and let IMU wrap the z of the actual platform coordinate systempAngles lambda and y through which the shaft rotatespThe rotated angle λ 'is the same and is denoted as λ ═ λ' ═ ω t.
5. The method for calibrating the attitude angle error of the biaxial rotational inertial navigation system according to claim 4, wherein the specific steps in step 4 include:
step 41: creating a Kalman filtering state equation;
wherein the state variables are represented as:
the observation equation is: z-HX + V, where the observation matrix is represented as:
l represents latitude; v is an observation noise vector and is white noise;
step 42: and acquiring observation information and navigation data of the Kalman filtering process by adopting a 16-position rotation method.
6. The method for calibrating the attitude angle error of the biaxial rotational inertial navigation system according to claim 5, wherein the rotation process of the 16-position rotation method for acquiring the observation information and the navigation data of the Kalman filtering process in step 42 is as follows:
(1) starting the system to enter a navigation state under the condition of a static base;
(2) a leveling mechanism and an azimuth adjusting mechanism on the adjusting structure enable a sensitive shaft of the IMU to point to the northeast when the sensitive shaft is in an initial zero position, and a horizontal attitude angle and a heading angle are both zero;
(3) selecting IMUs according to a rotation sequence set by a 16-position rotation method, wherein the rotation angular speed is 15 degrees/s in each sequence;
(4) and (5) continuously shifting to know that the estimation variable result is converged, and finishing the calibration.
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