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CN111044038B - Strapdown inertial navigation heading transformation method based on coordinate transformation - Google Patents

Strapdown inertial navigation heading transformation method based on coordinate transformation Download PDF

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CN111044038B
CN111044038B CN201911231735.4A CN201911231735A CN111044038B CN 111044038 B CN111044038 B CN 111044038B CN 201911231735 A CN201911231735 A CN 201911231735A CN 111044038 B CN111044038 B CN 111044038B
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inertial navigation
strapdown inertial
coordinate system
angle
gyroscope
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CN111044038A (en
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可伟
李健一
姜晓亮
马西保
王雪
李颖
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Hebei Hanguang Heavy Industry Ltd
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Hebei Hanguang Heavy Industry Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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Abstract

The invention discloses a strapdown inertial navigation heading transformation method based on coordinate transformation, and belongs to the technical field of inertial navigation. Installing the strapdown inertial navigation on a carrier, and constructing a carrier coordinate system and a strapdown inertial navigation coordinate system; acquiring an installation heading, if the installation heading is not consistent with the strapdown inertial navigation heading, selecting a gyro and an accelerometer with consistent zero-bias stability, then outputting gyro output and accelerometer output under 24 sets of strapdown inertial navigation coordinate systems and corresponding roll angle, pitch angle and azimuth angle under the strapdown inertial navigation coordinate system by adopting 24 installation directions in a flow, constructing a coordinate transformation matrix Cbn, and transforming the strapdown inertial navigation heading by adopting the coordinate transformation matrix Cbn to change the heading direction of a product to be consistent with the heading of a carrier. On the premise of not changing product precision, the strapdown inertial navigation heading direction is subjected to online conversion, and the method is short in conversion period, high in efficiency and low in cost.

Description

Strapdown inertial navigation heading transformation method based on coordinate transformation
Technical Field
The invention relates to the technical field of inertial navigation, in particular to a strapdown inertial navigation heading transformation method based on coordinate transformation.
Background
The strapdown inertial navigation is suitable for ships and underwater equipment, and the overall dimension is fixed. When the user uses the device, the situation that the heading direction of the inertial navigation is inconsistent with the heading direction of the carrier can be met, and the online transformation of the heading direction of the inertial navigation cannot be carried out under the situation, so the strapdown inertial navigation needs to be put into operation again, the transformation period of the heading direction of the strapdown inertial navigation is long, and the cost is high.
Therefore, the problem of how to perform online transformation on the heading direction of the strapdown inertial navigation on the basis of not changing the precision of a strapdown inertial navigation product is an urgent need to be solved at present.
Disclosure of Invention
In view of the above, the invention provides a strapdown inertial navigation heading transformation method based on coordinate transformation, which can perform online transformation on the heading direction of the strapdown inertial navigation on the premise of ensuring the precision of the strapdown inertial navigation, and has the advantages of short transformation period, high efficiency and low cost
In order to achieve the purpose, the technical scheme of the invention is as follows: installing strapdown inertial navigation on a carrier, and constructing a carrier coordinate system OXYZ and a strapdown inertial navigation coordinate system OXYZ; and acquiring an installation heading, and if the installation heading is inconsistent with the strapdown inertial navigation heading, performing strapdown inertial navigation heading transformation by adopting the following strapdown inertial navigation heading transformation method to ensure that the installation heading is consistent with the strapdown inertial navigation heading.
The strapdown inertial navigation heading transformation method comprises the following steps:
firstly, strapdown inertial navigation comprises a three-axis gyroscope and a three-axis accelerometer; the zero-offset stability of the three-axis gyroscope and the three-axis accelerometer is respectively consistent.
The three-axis gyroscope comprises an x gyroscope, a y gyroscope and a z gyroscope which respectively correspond to the x axis, the y axis and the z axis of the strapdown inertial navigation coordinate system.
The three-axis accelerometers are respectively an x accelerometer, a y accelerometer and a z accelerometer and respectively correspond to x, y and z axes of the strapdown inertial navigation coordinate system.
And fixedly connecting the strapdown inertial navigation to the three-axis rotary table, and guiding the three-axis rotary table to the north, wherein the fixedly connected strapdown inertial navigation coordinate system oxyz corresponds to the northeast.
The three-axis turntable comprises an inner frame, an outer frame and a middle frame, wherein the x gyroscope corresponds to the middle frame, the y gyroscope corresponds to the inner frame, the Z gyroscope corresponds to the outer frame, the x accelerometer corresponds to the middle frame, the y accelerometer corresponds to the inner frame, and the Z accelerometer corresponds to the outer frame.
Secondly, positioning an inner frame, a middle frame and an outer frame of the three-axis turntable to positions (0, 0); the frame rotates four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; the outer frame stands still for 10 minutes at each position, and the gyroscope output and the accelerometer output under a strapdown inertial navigation coordinate system are respectively recorded, at the moment, the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle;
thirdly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0 and 0); the middle frame rotates to 180 degrees, the outer frame rotates four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; the outer frame stands for 10 minutes at each position, and the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system are respectively recorded, at the moment, the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle;
fourthly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0 and 0); the inner frame is rotated to a 90-degree position, (namely the X gyro points to the sky.) the outer frame is rotated to four positions and is still, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; the outer frame stands for 10 minutes at each position, and the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system are respectively recorded, at the moment, the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle;
fifthly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0 and 0); the middle frame rotates to a position of-90 degrees, the outer frame rotates to four positions to be static, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; the outer frame stands still for 10 minutes at each position, and the gyroscope output and the accelerometer output under a strapdown inertial navigation coordinate system are respectively recorded, at the moment, the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle;
sixthly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0 and 0); the middle frame rotates to a 90-degree position, (namely a Y gyroscope points to the sky.) the outer frame rotates to four positions and is static, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; and (3) allowing the outer frame to stand for 10 minutes at each position, and respectively recording the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system, wherein the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle.
Seventhly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0); the inner frame rotates to a position of-90 degrees, the outer frame rotates to four positions to be static, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; and (3) allowing the outer frame to stand for 10 minutes at each position, and respectively recording the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system, wherein the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle.
Step eight, substituting the gyro output and the accelerometer output under the 24 sets of strapdown inertial navigation coordinate systems recorded in the step two to the step seven and the roll angle, the pitch angle and the azimuth angle under the corresponding strapdown inertial navigation coordinate systems into the formulas (1) and (2) to obtain the gyro output under the carrier coordinate system
Figure BDA0002303743870000031
And accelerometer output ^ under vector coordinate system>
Figure BDA0002303743870000032
Figure BDA0002303743870000041
Figure BDA0002303743870000042
Wherein
Figure BDA0002303743870000043
Is the gyro output under the strapdown inertial navigation coordinate system, N x 、N y 、N z Respectively corresponding to the outputs of the x, y and z gyros under the strapdown inertial navigation coordinate system;
Figure BDA0002303743870000044
Is output of a gyroscope under a strapdown inertial navigation coordinate system，A x 、A y 、A z Outputting the acceleration meters of x, y and z under the strapdown inertial navigation coordinate system; phi is an azimuth angle under a strapdown inertial navigation coordinate system, theta is a pitch angle under the strapdown inertial navigation coordinate system, and gamma is a roll angle under the strapdown inertial navigation coordinate system; n is a radical of hydrogen X 、N Y 、N Z Respectively corresponding to the outputs of the x, y and z gyroscopes in the carrier coordinate system; a. The X 、A Y 、A Z Respectively corresponding to the outputs of the x accelerometer, the y accelerometer and the z accelerometer under the carrier coordinate system.
Outputting the gyroscope in a carrier coordinate system
Figure BDA0002303743870000045
And accelerometer output ^ under vector coordinate system>
Figure BDA0002303743870000046
Substituting into the known attitude error equation formula and speed error equation formula to calculate the pitch angle ^ under the navigation coordinate system>
Figure BDA0002303743870000047
Transverse roll angle
Figure BDA0002303743870000048
Azimuth>
Figure BDA0002303743870000049
Wherein n represents a navigation coordinate system, the navigation coordinate system is Ox n y n z n Origin is the center of gravity of the carrier, x n The axis pointing east, y n The axis pointing north, z n The axis points to the zenith.
Step nine, calculating the pitch angles under all navigation coordinate systems by utilizing the formula
Figure BDA00023037438700000410
Roll angle->
Figure BDA00023037438700000411
Azimuth->
Figure BDA00023037438700000412
And performing data processing on the values, and calculating to obtain a pitch angle standard difference, a roll angle standard difference and an azimuth angle standard difference.
Step ten, if the pitch angle standard difference, the roll angle standard difference and the azimuth angle standard difference obtained in the step nine all meet the set strapdown inertial navigation precision condition, (the fact that the gyroscope and the accelerometer have consistent zero-offset stability) is proved, a coordinate transformation matrix Cbn is constructed, and the coordinate transformation matrix Cbn is adopted to transform the strapdown inertial navigation heading.
Wherein
Figure BDA0002303743870000051
Wherein alpha represents the angle from the strapdown inertial navigation to the carrier pitching rotation, beta represents the angle from the strapdown inertial navigation to the carrier rolling rotation, and eta represents the angle from the strapdown inertial navigation to the carrier azimuth rotation; taking the strapdown inertial navigation coordinate system as a starting point and clockwise as positive.
The pitch alpha is-90 degrees, 0 degrees or 90 degrees; the rolling beta is-180 degrees, -90 degrees, 0 degrees or 90 degrees and 180 degrees; the orientation eta takes the value of-180 degrees, -90 degrees, 0 degrees, 90 degrees or 180 degrees.
Has the advantages that:
according to the strapdown inertial navigation heading transformation method based on coordinate transformation, a gyroscope and an accelerometer with consistent zero-offset stability are selected, then coordinate transformation is carried out in the process, and the heading direction of a product and the heading direction of a carrier are changed to be consistent. On the premise of not changing product precision, the strapdown inertial navigation heading direction is subjected to online conversion, and the method is short in conversion period, high in efficiency and low in cost.
Detailed Description
The present invention will now be described in detail with reference to examples.
The invention provides a strapdown inertial navigation heading transformation method based on coordinate transformation, which is characterized in that,
installing the strapdown inertial navigation on a carrier, and constructing a carrier coordinate system OXYZ and a strapdown inertial navigation coordinate system OXYZ; acquiring an installation heading, and if the installation heading is inconsistent with the strapdown inertial navigation heading, performing strapdown inertial navigation heading transformation by adopting the following strapdown inertial navigation heading transformation method to make the installation heading consistent;
the strapdown inertial navigation heading transformation method comprises the following steps:
firstly, strapdown inertial navigation comprises a three-axis gyroscope and a three-axis accelerometer; the zero-offset stability of the gyroscope and the accelerometer are respectively consistent.
The three-axis gyroscope comprises an x gyroscope, a y gyroscope and a z gyroscope which respectively correspond to the x axis, the y axis and the z axis of the strapdown inertial navigation coordinate system.
The three-axis accelerometers are respectively an x accelerometer, a y accelerometer and a z accelerometer and respectively correspond to x, y and z axes of the strapdown inertial navigation coordinate system.
And fixedly connecting the strapdown inertial navigation to the three-axis rotary table, and carrying out north finding on the three-axis rotary table, wherein the fixedly connected strapdown inertial navigation coordinate system oxyz corresponds to the northeast sky.
The three-axis rotary table comprises an inner frame, an outer frame and a middle frame, wherein the x gyroscope corresponds to the middle frame, the y gyroscope corresponds to the inner frame, the Z gyroscope corresponds to the outer frame, the x accelerometer corresponds to the middle frame, the y accelerometer corresponds to the inner frame, and the Z accelerometer corresponds to the outer frame.
Secondly, positioning an inner frame, a middle frame and an outer frame of the three-axis turntable to positions (0, 0); the frame rotates four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; namely 0 degree, 90 degrees, 180 degrees and 270 degrees, the outer frame stands still for 10 minutes at each position, the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system are respectively recorded, the roll angle under the corresponding strapdown inertial navigation coordinate system at the moment is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle.
Respectively recording three-axis gyroscope output NGx under strapdown inertial navigation coordinate system k(i) ，NGy k(i) ，NGz k(i) And the triaxial accelerometer under the strapdown inertial navigation coordinate system outputs NAx k(i) ，NAy k(i) ，NAz k(i) 。
Wherein NGx k(i) ，NGy k(i) ，NGz k(i) When the rotation angle of the outer frame is k (i), the x gyro output, the y gyro output and the z gyro output in the inertial navigation coordinate system are respectively.
NAx k(i) ，NAy k(i) ，NAz k(i) When the rotation angle of the outer frame is k (i), the output of the x accelerometer, the output of the y accelerometer and the output of the z accelerometer in the inertial navigation coordinate system are respectively.
Thirdly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0); the middle frame rotates to 180 degrees, namely the Z gyro and the Z accelerometer point to the ground. The frame rotates four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; namely 0 °, 90 °, 180 ° and 270 °. And (3) keeping the outer frame at each position for 10 minutes, and respectively recording the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system, wherein the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle.
Fourthly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0 and 0); the inner frame rotates to 90 degrees, namely the X gyro and the X accelerometer are pointed to sky. The outer frame rotates to rest at four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; namely 0 °, 90 °, 180 °, and 270 °. And (3) allowing the outer frame to stand for 10 minutes at each position, and respectively recording the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system, wherein the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle.
Fifthly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0); the middle frame rotates to a-90-degree position, namely the X gyro and the X accelerometer point to the ground. The outer frame rotates to rest at four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; namely 0 °, 90 °, 180 °, and 270 °. The outer frame stands for 10 minutes at each position, and the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system are respectively recorded, at the moment, the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle;
sixthly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0 and 0); the middle frame rotates to 90 degrees, namely the Y gyro and the Y accelerometer refer to the sky. The outer frame rotates to rest at four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; namely 0 °, 90 °, 180 °, and 270 °. The outer frame stands for 10 minutes at each position, and the gyroscope output and the accelerometer output under the strapdown inertial navigation coordinate system are respectively recorded, at the moment, the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle;
seventhly, positioning the inner frame, the middle frame and the outer frame of the three-axis turntable to positions (0, 0 and 0); the inner frame is rotated to a-90 deg. position, i.e. the Y gyro and Y accelerometer are pointing to the ground. The outer frame rotates to rest at four positions, and the rotation angle at the ith position is as follows: k (i) =45 ° × i, i =0,2,4,6; namely 0 °, 90 °, 180 ° and 270 °. The outer frame stands still for 10 minutes at each position, and the gyroscope output and the accelerometer output under a strapdown inertial navigation coordinate system are respectively recorded, at the moment, the roll angle under the corresponding strapdown inertial navigation coordinate system is the inner frame rotation angle, the pitch angle is the middle frame rotation angle, and the azimuth angle is the outer frame rotation angle;
and step eight, step two to step seven, obtaining gyro output and accelerometer output under 4 groups of strapdown inertial navigation coordinate systems and roll angle, pitch angle and azimuth angle under corresponding strapdown inertial navigation coordinate systems, namely obtaining 24 groups.
And substituting the gyro output and the accelerometer output under the 24 sets of strapdown inertial navigation coordinate systems recorded in the second step to the seventh step and the roll angle, the pitch angle and the azimuth angle under the corresponding strapdown inertial navigation coordinate systems into the formulas (1) and (2) to obtain the gyro output under the carrier coordinate system
Figure BDA0002303743870000081
And accelerometer output ^ under vector coordinate system>
Figure BDA0002303743870000082
Figure BDA0002303743870000083
Figure BDA0002303743870000084
Wherein
Figure BDA0002303743870000085
Is the gyro output under the strapdown inertial navigation coordinate system, N x 、N y 、N z Respectively corresponding to the outputs of the x, y and z gyros under the strapdown inertial navigation coordinate system.
Figure BDA0002303743870000086
Is the gyro output under the strapdown inertial navigation coordinate system, A x 、A y 、A z And outputting the x, y and z accelerometers under the strapdown inertial navigation coordinate system.
Phi is an azimuth angle under the strapdown inertial navigation coordinate system, theta is a pitch angle under the strapdown inertial navigation coordinate system, and gamma is a roll angle under the strapdown inertial navigation coordinate system.
N X 、N Y 、N Z And the gyroscope outputs respectively correspond to x, y and z in a carrier coordinate system.
A X 、A Y 、A Z Respectively corresponding to the outputs of the x accelerometer, the y accelerometer and the z accelerometer under the carrier coordinate system.
Outputting the gyroscope under a carrier coordinate system
Figure BDA0002303743870000091
And accelerometer output ^ under vector coordinate system>
Figure BDA0002303743870000092
Substituting into known attitude error equation formula and speed error equation formula to calculate pitch angle ^ under navigation coordinate system>
Figure BDA0002303743870000093
Roll angle
Figure BDA0002303743870000094
Azimuth->
Figure BDA0002303743870000095
Wherein n represents a navigation coordinate system, the navigation coordinate system is Ox n y n z n With the origin at the center of gravity of the carrier, x n The axis points east, y n The axis pointing north, z n The axis points to the zenith.
Step nine, calculating the pitch angles under all navigation coordinate systems by using the formula
Figure BDA0002303743870000096
Roll angle->
Figure BDA0002303743870000097
Azimuth->
Figure BDA0002303743870000098
And performing data processing on the values, and calculating to obtain a pitch angle standard difference, a roll angle standard difference and an azimuth angle standard difference.
Will pitch angle
Figure BDA0002303743870000099
Roll angle->
Figure BDA00023037438700000910
Azimuth->
Figure BDA00023037438700000911
Are respectively averaged, i.e.>
Figure BDA00023037438700000912
Pitch angle standard deviation formula:
Figure BDA00023037438700000913
roll angle standard deviation formula:
Figure BDA00023037438700000914
azimuth standard deviation formula:
Figure BDA00023037438700000915
m is the number of pitch, roll and azimuth angles.
And step ten, judging whether the pitch angle standard difference, the roll angle standard difference and the azimuth angle standard difference obtained in the step nine all meet the set strapdown inertial navigation precision condition.
The types of the strapdown inertial navigation are different, the setting of the precision conditions is also different, but the setting can be performed according to experience, for example, table 1 gives setting examples of the azimuth precision, the pitch precision and the roll precision of the strapdown inertial navigation with four different technical indexes.
TABLE 1
Figure BDA00023037438700000916
Figure BDA0002303743870000101
Note:
Figure BDA0002303743870000102
is the local latitude.
If the pitch angle standard deviation, the roll angle standard deviation and the azimuth angle standard deviation obtained in the ninth step all meet the set strapdown inertial navigation precision condition, and the gyro and the accelerometer are proved to have consistent zero-bias stability respectively, a coordinate transformation matrix Cbn is constructed, and the strapdown inertial navigation heading is transformed by adopting the coordinate transformation matrix Cbn;
wherein
Figure BDA0002303743870000103
Wherein alpha represents the angle from the strapdown inertial navigation to the carrier pitching rotation, beta represents the angle from the strapdown inertial navigation to the carrier rolling rotation, and eta represents the angle from the strapdown inertial navigation to the carrier azimuth rotation; taking a strapdown inertial navigation coordinate system as a starting point and clockwise as positive;
considering that the installation hole position of the strapdown inertial navigation is fixed, the strapdown inertial navigation can only be fixedly installed by rotating by multiples of 90 degrees. Therefore, the pitch alpha takes the value of-90 degrees, 0 degrees or 90 degrees; the roll beta is-180 degrees, -90 degrees, 0 degrees or 90 degrees and 180 degrees, wherein the-180 degrees and the 180 degrees represent one position and are selected in one position; the orientation eta takes the values of-180 degrees, -90 degrees, 0 degrees, 90 degrees or 180 degrees, wherein the-180 degrees and the 180 degrees represent one position and are selected to be one.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1.一种基于坐标变换的捷联惯导艏向变换方法，其特征在于，1. A method for heading transformation of strapdown inertial navigation systems based on coordinate transformation, characterized in that, 将捷联惯导安装于载体上，构建载体坐标系为OXYZ，捷联惯导坐标系为oxyz；获取安装艏向，若所述安装艏向与所述捷联惯导艏向不一致，采用如下捷联惯导艏向变换方法进行捷联惯导艏向变换，使其与所述安装艏向一致；The strapdown inertial navigation system (INS) is installed on the carrier, and the carrier coordinate system is OXYZ and the INS coordinate system is oxyz. The installation heading is obtained. If the installation heading is inconsistent with the INS heading, the following INS heading transformation method is used to transform the INS heading so that it is consistent with the installation heading. 所述捷联惯导艏向变换方法包括如下步骤：The strapdown inertial navigation heading transformation method includes the following steps: 步骤一、所述捷联惯导包含三轴陀螺和三轴加速度计；三轴陀螺和三轴加速度计零偏稳定性分别一致；Step 1: The strapdown inertial navigation system includes a three-axis gyroscope and a three-axis accelerometer; the zero-bias stability of the three-axis gyroscope and the three-axis accelerometer is consistent. 所述三轴陀螺包括x陀螺、y陀螺和z陀螺，分别对应捷联惯导坐标系的x、y、z轴；The three-axis gyroscope includes an x-gyroscope, a y-gyroscope, and a z-gyroscope, which correspond to the x, y, and z axes of the strapdown inertial navigation coordinate system, respectively. 所述三轴加速度计分别为x加速度计、y加速度计和z加速度计，分别对应捷联惯导坐标系的x、y、z轴；The three-axis accelerometers are x-accelerometer, y-accelerometer and z-accelerometer, which correspond to the x, y and z axes of the strapdown inertial navigation coordinate system, respectively; 将所述捷联惯导固联到三轴转台上，对所述三轴转台进行引北，固联的捷联惯导坐标系oxyz对应东北天；The strapdown inertial navigation system is fixed to the three-axis turntable, and the three-axis turntable is guided to the north. The fixed strapdown inertial navigation coordinate system oxyz corresponds to the northeast sky. 三轴转台包括内框、外框和中框，x陀螺对应中框，y陀螺对应内框，z陀螺对应外框，x加速度计对应中框，y加速度计对应内框，Z加速度计对应外框；The three-axis rotary table includes an inner frame, an outer frame, and a middle frame. The x-gyroscope corresponds to the middle frame, the y-gyroscope corresponds to the inner frame, the z-gyroscope corresponds to the outer frame, the x-accelerometer corresponds to the middle frame, the y-accelerometer corresponds to the inner frame, and the Z-accelerometer corresponds to the outer frame. 步骤二、三轴转台的内框、中框、外框定位到位置(0，0，0)；外框转动四个位置，在第i个位置处转动角度为：k(i)＝45°×i，i＝0，2，4，6；外框在每个位置处静止10分钟，分别记录捷联惯导坐标系下的陀螺输出和加速度计输出，此时对应的捷联惯导坐标系下的横滚角为内框转动角度，俯仰角为中框转动角度，方位角为外框转动角度；Step 2: Position the inner frame, middle frame, and outer frame of the three-axis turntable to position (0, 0, 0); rotate the outer frame to four positions, with the rotation angle at the i-th position being: k(i) = 45° × i, i = 0, 2, 4, 6; keep the outer frame stationary at each position for 10 minutes, and record the gyroscope output and accelerometer output in the strapdown inertial navigation coordinate system. At this time, the roll angle in the strapdown inertial navigation coordinate system is the rotation angle of the inner frame, the pitch angle is the rotation angle of the middle frame, and the azimuth angle is the rotation angle of the outer frame. 步骤三、三轴转台的内框、中框、外框定位到位置(0，0，0)；中框转动到180°位置，外框转动四个位置，在第i个位置处转动角度为：k(i)＝45°×i，i＝0，2，4，6；外框在每个位置静止10分钟，分别记录捷联惯导坐标系下的陀螺输出和加速度计输出，此时对应的捷联惯导坐标系下的横滚角为内框转动角度，俯仰角为中框转动角度，方位角为外框转动角度；Step 3: Position the inner frame, middle frame, and outer frame of the three-axis turntable to position (0, 0, 0); rotate the middle frame to 180° position, and rotate the outer frame to four positions. The rotation angle at the i-th position is: k(i) = 45° × i, i = 0, 2, 4, 6; keep the outer frame stationary at each position for 10 minutes, and record the gyroscope output and accelerometer output in the strapdown inertial navigation coordinate system. At this time, the roll angle in the strapdown inertial navigation coordinate system is the rotation angle of the inner frame, the pitch angle is the rotation angle of the middle frame, and the azimuth angle is the rotation angle of the outer frame. 步骤四、三轴转台的内框、中框、外框定位到位置(0，0，0)；内框转动到90°位置，(即X陀螺指天；)外框转动四个位置静止，在第i个位置处转动角度为：k(i)＝45°×i，i＝0，2，4，6；外框在每个位置静止10分钟，分别记录捷联惯导坐标系下的陀螺输出和加速度计输出，此时对应的捷联惯导坐标系下的横滚角为内框转动角度，俯仰角为中框转动角度，方位角为外框转动角度；Step 4: Position the inner frame, middle frame, and outer frame of the three-axis turntable to position (0, 0, 0); rotate the inner frame to 90° (i.e., the X gyroscope points to the sky); rotate the outer frame to four positions and then stop. The rotation angle at the i-th position is: k(i) = 45° × i, i = 0, 2, 4, 6; the outer frame remains stationary at each position for 10 minutes, and record the gyroscope output and accelerometer output in the strapdown inertial navigation coordinate system. At this time, the roll angle in the strapdown inertial navigation coordinate system is the rotation angle of the inner frame, the pitch angle is the rotation angle of the middle frame, and the azimuth angle is the rotation angle of the outer frame. 步骤五、三轴转台的内框、中框、外框定位到位置(0，0，0)；中框转动到-90°位置，外框转动四个位置静止，在第i个位置处转动角度为：k(i)＝45°×i，i＝0，2，4，6；外框在每个位置静止10分钟，分别记录捷联惯导坐标系下的陀螺输出和加速度计输出，此时对应的捷联惯导坐标系下的横滚角为内框转动角度，俯仰角为中框转动角度，方位角为外框转动角度；Step 5: Position the inner frame, middle frame, and outer frame of the three-axis turntable to position (0, 0, 0); rotate the middle frame to -90° position, and rotate the outer frame to four positions and then stop. The rotation angle at the i-th position is: k(i) = 45° × i, i = 0, 2, 4, 6; the outer frame stays still at each position for 10 minutes, and record the gyroscope output and accelerometer output in the strapdown inertial navigation coordinate system. At this time, the roll angle in the strapdown inertial navigation coordinate system is the rotation angle of the inner frame, the pitch angle is the rotation angle of the middle frame, and the azimuth angle is the rotation angle of the outer frame. 步骤六、三轴转台的内框、中框、外框定位到位置(0，0，0)；中框转动到90°位置，(即Y陀螺指天；)外框转动四个位置静止，在第i个位置处转动角度为：k(i)＝45°×i，i＝0，2，4，6；外框在每个位置静止10分钟，分别记录捷联惯导坐标系下的陀螺输出和加速度计输出，此时对应的捷联惯导坐标系下的横滚角为内框转动角度，俯仰角为中框转动角度，方位角为外框转动角度；Step 6: Position the inner frame, middle frame, and outer frame of the three-axis turntable to position (0, 0, 0); rotate the middle frame to 90° (i.e., the Y-gyroscope points to the sky); rotate the outer frame to four positions and stop. The rotation angle at the i-th position is: k(i) = 45° × i, i = 0, 2, 4, 6; the outer frame stops at each position for 10 minutes, and record the gyroscope output and accelerometer output in the strapdown inertial navigation coordinate system. At this time, the roll angle in the strapdown inertial navigation coordinate system is the rotation angle of the inner frame, the pitch angle is the rotation angle of the middle frame, and the azimuth angle is the rotation angle of the outer frame. 步骤七、三轴转台的内框、中框、外框定位到位置(0，0，0)；内框转动到-90°位置，外框转动四个位置静止，在第i个位置处转动角度为：k(i)＝45°×i，i＝0，2，4，6；外框在每个位置静止10分钟，分别记录捷联惯导坐标系下的陀螺输出和加速度计输出，此时对应的捷联惯导坐标系下的横滚角为内框转动角度，俯仰角为中框转动角度，方位角为外框转动角度；Step 7: Position the inner frame, middle frame, and outer frame of the three-axis turntable to position (0, 0, 0); rotate the inner frame to -90° position, and rotate the outer frame to four positions and stop. The rotation angle at the i-th position is: k(i) = 45° × i, i = 0, 2, 4, 6; the outer frame stays still at each position for 10 minutes, and record the gyroscope output and accelerometer output in the strapdown inertial navigation coordinate system. At this time, the roll angle in the strapdown inertial navigation coordinate system is the rotation angle of the inner frame, the pitch angle is the rotation angle of the middle frame, and the azimuth angle is the rotation angle of the outer frame. 步骤八、将步骤二～步骤七记录的24组捷联惯导坐标系下的陀螺输出和加速度计输出以及对应的捷联惯导坐标系下的横滚角、俯仰角和方位角代入公式(1)和(2)得到载体坐标系下的陀螺输出
Figure QLYQS_1
和载体坐标系下的加速度计输出
Figure QLYQS_2
Step 8: Substitute the 24 sets of gyroscope outputs and accelerometer outputs in the strapdown inertial navigation coordinate system recorded in Steps 2 to 7, along with the corresponding roll, pitch, and azimuth angles in the strapdown inertial navigation coordinate system, into formulas (1) and (2) to obtain the gyroscope outputs in the carrier coordinate system.
Figure QLYQS_1
Accelerometer output in the carrier coordinate system
Figure QLYQS_2
Figure QLYQS_3
Figure QLYQS_3
Figure QLYQS_4
Figure QLYQS_4
 其中
Figure QLYQS_5
为捷联惯导坐标系下的陀螺输出，Nx、Ny、Nz分别对应捷联惯导坐标系下的x、y、z陀螺输出；in
Figure QLYQS_5
N<sub>x</sub> , N<sub>y</sub> , and N<sub>z</sub> are the gyroscope outputs in the strapdown inertial navigation coordinate system, respectively, corresponding to the x, y, and z gyroscope outputs in the strapdown inertial navigation coordinate system.
Figure QLYQS_6
为捷联惯导坐标系下的陀螺输出，Ax、Ay、Az为捷联惯导坐标系下的x、y、z加速度计输出；
Figure QLYQS_6
A<sub>x</sub> , A <sub>y</sub> , and A<sub>z</sub> are the gyroscope outputs in the strapdown inertial navigation coordinate system, and A<sub>x</sub>, A<sub>y</sub>, and A<sub>z</sub> are the x, y, and z accelerometer outputs in the strapdown inertial navigation coordinate system. φ为捷联惯导坐标系下的方位角，θ为捷联惯导坐标系下的俯仰角，γ为捷联惯导坐标系下的横滚角；φ is the azimuth angle in the strapdown inertial navigation system, θ is the pitch angle in the strapdown inertial navigation system, and γ is the roll angle in the strapdown inertial navigation system. NX、NY、NZ分别对应载体坐标系下的x、y、z陀螺输出； NX , NY , and AZ correspond to the x, y, and z gyroscope outputs in the carrier coordinate system, respectively. AX、AY、AZ分别对应载体坐标系下的x、y、z加速度计输出； AX , AY , and AZ correspond to the x, y, and z accelerometer outputs in the carrier coordinate system, respectively. 将载体坐标系下的陀螺输出
Figure QLYQS_7
和载体坐标系下的加速度计输出
Figure QLYQS_8
代入已知的的姿态误差方程公式和速度误差方程公式，计算出导航坐标系下的俯仰角
Figure QLYQS_9
横滚角
Figure QLYQS_10
方位角
Figure QLYQS_11
其中n表示导航坐标系，所述导航坐标系为Oxnynzn，原点为载体重心，xn轴指向东，yn轴指向北，zn轴指向天顶；Output of the gyroscope in the carrier coordinate system
Figure QLYQS_7
Accelerometer output in the carrier coordinate system
Figure QLYQS_8
Substituting the known attitude error equations and velocity error equations, the pitch angle in the navigation coordinate system is calculated.
Figure QLYQS_9
Roll angle
Figure QLYQS_10
Azimuth
Figure QLYQS_11
Where n represents the navigation coordinate system, which is Ox n y n z n , with the origin being the center of gravity of the vehicle, the x n axis pointing east, the y n axis pointing north, and the z n axis pointing to the zenith; 步骤九、利用上式计算出的所有导航坐标系下的俯仰角
Figure QLYQS_12
横滚角
Figure QLYQS_13
方位角
Figure QLYQS_14
值进行数据处理，计算得到俯仰角标准差、横滚角标准差以及方位角标准差；Step 9: Calculate the pitch angles in all navigation coordinate systems using the above formula.
Figure QLYQS_12
Roll angle
Figure QLYQS_13
Azimuth
Figure QLYQS_14
The data is processed to calculate the standard deviation of pitch angle, roll angle, and azimuth angle. 步骤十、若步骤九中得到俯仰角标准差、横滚角标准差以及方位角标准差均满足设定的捷联惯导精度条件，(证明陀螺和加速度计分别具有一致的零偏稳定性；)则构建坐标变换矩阵Cbn，采用坐标变换矩阵Cbn对捷联惯导艏向进行变换；Step 10: If the standard deviations of pitch, roll, and azimuth obtained in Step 9 all meet the set accuracy conditions for strapdown inertial navigation (proving that the gyroscope and accelerometer have consistent zero-bias stability), then construct the coordinate transformation matrix Cbn and use the coordinate transformation matrix Cbn to transform the heading of the strapdown inertial navigation system. 其中
Figure QLYQS_15
in
Figure QLYQS_15
 其中α表示捷联惯导到载体俯仰转动的角度，β表示捷联惯导到载体横滚转动的角度，η表示捷联惯导到载体方位转动的角度；以捷联惯导坐标系为起点，顺时针为正；Where α represents the angle of pitch rotation of the carrier from the strapdown inertial navigation system, β represents the angle of roll rotation of the carrier from the strapdown inertial navigation system, and η represents the angle of azimuth rotation of the carrier from the strapdown inertial navigation system; with the strapdown inertial navigation coordinate system as the starting point, clockwise is positive; 俯仰α取值为-90°、0°或者90°；横滚β取值为-180°、-90°、0°或者90°、180°；方位η取值为-180°、-90°、0°、90°或者180°。Pitch α is set to -90°, 0°, or 90°; roll β is set to -180°, -90°, or 0°, or 90°, or 180°; azimuth η is set to -180°, -90°, 0°, or 90°, or 180°.
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