CN104482941A - Systematic compensation method of fixed-precision navigation of ship optical inertial navigation system when in long voyage - Google Patents

Systematic compensation method of fixed-precision navigation of ship optical inertial navigation system when in long voyage Download PDF

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CN104482941A
CN104482941A CN201410752014.9A CN201410752014A CN104482941A CN 104482941 A CN104482941 A CN 104482941A CN 201410752014 A CN201410752014 A CN 201410752014A CN 104482941 A CN104482941 A CN 104482941A
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msubsup
mrow
msub
munder
mtd
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乔海岩
韩邦杰
可伟
李晓霞
罗晓炜
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Hebei Hanguang Heavy Industry Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005Manufacturing, 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

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Abstract

The invention relates to a systematic compensation method of fixed-precision navigation of a ship optical inertial navigation system when in long voyage. The method comprises the following steps: step I, determining a coordinate system of a ship, and marking the head direction of the system; step II, installing an optical gyroscope and a gauge on a high-strength high-precision hexagonal body; step III, debugging a single-shaft rotating mechanism control system, and designing a transposition scheme by utilizing a mature PID control algorithm; step IV, fixedly installing an IMU to a table-board of a transposition mechanism; step V, acquiring original data of a strap-down inertial navigation system, processing the acquired data, such as temperature compensation, sailing direction effect compensation, systematic calibration and the like; step VI, updating an attitude and calculating speed and position in the design of a pure inertial system in a single-shaft rotating modulation system; and step VII, demodulating the single-shaft rotation in real time. The constant high precision and stability of the inertial navigation system on a working carrier when a water ship is in long voyage can be guaranteed.

Description

System-level compensation method for marine optical inertial navigation long-endurance precision-guaranteed navigation
Technical Field
The invention belongs to the technical field of strapdown inertial navigation, and relates to a marine system-level compensation method for long-endurance precision-preserving navigation based on an optical gyroscope.
Background
The strapdown inertial navigation system is an autonomous navigation system, and the traditional platform type inertial navigation system is gradually replaced by the strapdown inertial navigation system which realizes navigation by means of high speed and precise calculation due to simple structural design along with the rapid development of modern high-speed computers. However, the development of high-precision optical inertial devices is expected to be greatly improved and cannot be achieved in a short time, so that a strapdown inertial navigation system which eliminates the drift of the inertial device by means of a rotation modulation scheme is applied.
The invention is mainly applied to surface ships needing long-time navigation.
The optical inertial navigation system for the ship is mainly characterized by being applied to long-term navigation, serving as a core main inertial navigation device of the ship and bearing the responsibility of providing reference for each weapon system of the ship, so that the requirements on indexes such as position accuracy, attitude accuracy stability and the like of the ship in long-term navigation are high. In order to improve the long-time navigation accuracy of inertial navigation, an extremely high-accuracy gyroscope is adopted to ensure that the navigation error of the system is not out of tolerance, and the extremely high-accuracy gyroscope cannot realize mass production due to the restrictions of process, cost and the like, so that the batch equipment of the system is severely restricted.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a system-level compensation method for the marine optical inertial navigation time-keeping precision navigation, which can ensure the constant high precision and stability of the navigation precision of an inertial navigation system on a working carrier for long-time navigation of a surface ship.
The technical scheme adopted by the invention for solving the technical problem is that the method comprises the following steps: firstly, determining a ship coordinate system, identifying the system heading, and determining the pitch and roll coordinates of the system; mounting an optical gyroscope and a accelerometer on a high-strength and high-precision hexahedron, performing precision machining and strict process guidance, and ensuring the planeness, parallelism and verticality by using three coordinates through manual grinding; debugging a control system of the single-shaft rotating mechanism, designing a transposition scheme by using a mature PID control algorithm, and ensuring extremely high positioning precision and low-speed stability of the scheme by using an optical means for detecting the correctness and precision of the scheme design; step four, the IMU is installed and fixed on a table board of the indexing mechanism, and the table board is provided with a calibrated horizontal base plane and a head-to-head leaning plane, so that the installation of the table board is ensured to have certain repeatability; acquiring and processing original data of the strapdown inertial navigation system, and processing the data, such as temperature compensation, course effect compensation, system-level calibration and other tests; sixthly, attitude updating, speed and position resolving in pure inertial system algorithm design in the single-axis rotation modulation system; and seventhly, carrying out real-time demodulation processing of single-axis rotation.
The invention provides an improved single-shaft rotation modulation system transposition scheme based on the basic principle of rotation type modulation inertial navigation, which has the greatest advantages that on the premise of not improving the level of the existing inertial device, a constant value error of a horizontal inertial device is counteracted by using an IMU with medium and high precision through a rotation way, the reliability of the system can be better improved by using the transposition scheme in the invention, the unpredictable long-term stability problem caused by the fact that a single-shaft continuous rotation system selects a conductive slip ring is avoided, and the system cost can be reduced to a certain extent.
Drawings
FIG. 1 is a block diagram of the relationship between north gyro drift and longitude error according to the present invention;
FIG. 2 is a schematic diagram of a single-shaft forward and reverse rotation stop rotation modulation inertial navigation periodic rotation scheme according to the present invention;
FIG. 3 is a block diagram of a single-axis indexing optical inertial system for a ship according to the present invention;
FIG. 4 is a flow chart of a strapdown calculation of an inertial navigation system in a single-axis indexing manner according to the present invention;
FIG. 5 is a schematic diagram of the system of the present invention;
FIG. 6 is a position error caused by a constant error in a non-rotating system according to the present invention;
FIG. 7 is a graph of the position error caused by the constant error in the single axis rotation system of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The invention provides a system-level single-axis rotation modulation type strapdown inertial navigation system new transposition method based on the basic principle of single-axis rotation modulation type strapdown inertial navigation, which is used in a surface ship optical gyro inertial navigation system. The optical gyro single-axis rotation inertial navigation system is a strapdown inertial navigation system. The inertial measurement unit formed by the optical gyroscope and the accelerometer is relatively and fixedly connected with the carrier (can rotate around the zenith axis), and the navigation computer calculates navigation information such as the attitude, the speed and the position of the carrier according to the measured angular velocity information and the acceleration signal.
In the system, an Inertial Measurement Unit (IMU) is installed on a single-shaft rotating mechanism, a rotation modulation technology is adopted, slow variation errors in a gyroscope and an accelerometer are not required to be identified and compensated, a single-shaft indexing mechanism is used for carrying out periodic rotation and rotation stopping technology on the IMU to eliminate the influence of zero drift on the navigation precision of the system when the horizontal gyroscope and the accelerometer are located at opposite positions, and error sources such as installation errors caused by rotation are eliminated through the rotation stopping mode, so that high-precision navigation information is obtained.
Uniaxial modulation mechanism analysis and specific transposition implementation mode:
suppose p is a rotation coordinate system, n is a navigation coordinate system, i is an inertia coordinate system, and b is a hull coordinate system. By the working principle of a single-axis rotation inertial navigation system and the combination of a typical strapdown inertial navigation system error equation, a system error propagation equation can be described as follows:
<math> <mrow> <munderover> <mi>&phi;</mi> <mo>&OverBar;</mo> <mo>&CenterDot;</mo> </munderover> <mo>=</mo> <mo>-</mo> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>in</mi> <mi>n</mi> </msubsup> <mo>+</mo> <munder> <mi>&phi;</mi> <mo>&OverBar;</mo> </munder> <mo>+</mo> <mi>&delta;</mi> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>in</mi> <mi>n</mi> </msubsup> <mo>-</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>b</mi> <mi>n</mi> </msubsup> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <mi>&delta;</mi> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>ip</mi> <mi>p</mi> </msubsup> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <munder> <mi>v</mi> <mo>&OverBar;</mo> </munder> <mo>=</mo> <msup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>n</mi> </msup> <mo>&times;</mo> <mi>&phi;</mi> <mo>+</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>b</mi> <mi>n</mi> </msubsup> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <mi>&delta;</mi> <msubsup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>ie</mi> <mi>n</mi> </msubsup> <mo>+</mo> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>en</mi> <mi>n</mi> </msubsup> <mo>)</mo> </mrow> <mo>&times;</mo> <mi>&delta;</mi> <munder> <mi>v</mi> <mo>&OverBar;</mo> </munder> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mi>&delta;</mi> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>ie</mi> <mi>n</mi> </msubsup> <mo>+</mo> <mi>&delta;</mi> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>en</mi> <mi>n</mi> </msubsup> <mo>)</mo> </mrow> <mo>&times;</mo> <munder> <mi>v</mi> <mo>&OverBar;</mo> </munder> <mo>-</mo> <mi>&delta;</mi> <munder> <mi>g</mi> <mo>&OverBar;</mo> </munder> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <munderover> <mi>p</mi> <mo>&OverBar;</mo> <mo>&CenterDot;</mo> </munderover> <mo>=</mo> <mi>&delta;</mi> <munder> <mi>v</mi> <mo>&OverBar;</mo> </munder> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
it can be seen that the difference between equation (1) and the error propagation equation of the conventional typical strapdown inertial navigation system is that the output error amounts of the gyroscope and the adder are transformed in the propagation process, and the formed transformation array is related to time.
In the scheme, assuming that the rotating coordinate system p system is coincident with the hull coordinate system b system at the initial time and the IMU rotates around the zenith axis, the system rotation angle position is θ (t) at any time t, and according to the above assumption, the transformation matrix from the hull coordinate system b system to the rotating coordinate system p system is:
<math> <mrow> <msubsup> <mi>C</mi> <mi>b</mi> <mi>p</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>cos</mi> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>sin</mi> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>sin</mi> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>cos</mi> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
assuming the angular rate input of the b system of the hull coordinate system asThe specific force input of the b system of the hull coordinate system isThen the actual inputs to the gyro and the adder table in the IMU are:
<math> <mrow> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>=</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>b</mi> <mi>p</mi> </msubsup> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>+</mo> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>bp</mi> <mi>p</mi> </msubsup> </mrow> </math>
<math> <mrow> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>=</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>b</mi> <mi>p</mi> </msubsup> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>+</mo> <msubsup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>bp</mi> <mi>p</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein, <math> <mrow> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>bp</mi> <mi>p</mi> </msubsup> <mo>=</mo> <msup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mover> <mi>&theta;</mi> <mo>&CenterDot;</mo> </mover> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> <msubsup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>bp</mi> <mi>p</mi> </msubsup> <mo>=</mo> <munder> <mn>0</mn> <mo>&OverBar;</mo> </munder> <mo>.</mo> </mrow> </math>
in the above equation, the projection of the actual values of the gyro and the adder table on the p-system is:
<math> <mrow> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>~</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>=</mo> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>+</mo> <mi>&delta;</mi> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>ip</mi> <mi>p</mi> </msubsup> </mrow> </math>
<math> <mrow> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>~</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>=</mo> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>+</mo> <mi>&delta;</mi> <msubsup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
projection of gyroscopic and tabulated measurements onto a p-systemAndtransformation from p to b is:
<math> <mrow> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>~</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>=</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>~</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>+</mo> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>pb</mi> <mi>b</mi> </msubsup> </mrow> </math>
<math> <mrow> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>=</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>+</mo> <msubsup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>pb</mi> <mi>b</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein, <math> <mrow> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>b</mi> <mi>p</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>,</mo> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>pb</mi> <mi>b</mi> </msubsup> <mo>=</mo> <msup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>-</mo> <mover> <mi>&theta;</mi> <mo>&CenterDot;</mo> </mover> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>,</mo> <msubsup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>pb</mi> <mi>b</mi> </msubsup> <mo>=</mo> <munder> <mn>0</mn> <mo>&OverBar;</mo> </munder> <mo>.</mo> </mrow> </math>
substituting formulae (2), (3) and (4) into formula (5) to obtain:
<math> <mrow> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>~</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>=</mo> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>+</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <mi>&delta;</mi> <msubsup> <munder> <mi>&omega;</mi> <mo>&OverBar;</mo> </munder> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>=</mo> <msubsup> <munderover> <mi>&omega;</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>+</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msubsup> <mi>&omega;</mi> <mi>ip</mi> <mi>px</mi> </msubsup> <mi>cos</mi> <mi>&theta;</mi> <mo>-</mo> <msubsup> <mi>&delta;&omega;</mi> <mi>ip</mi> <mi>py</mi> </msubsup> <mi>sin</mi> <mi>&theta;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&delta;&omega;</mi> <mi>ip</mi> <mi>px</mi> </msubsup> <mi>sin</mi> <mi>&theta;</mi> <mo>+</mo> <msubsup> <mi>&delta;&omega;</mi> <mi>ip</mi> <mi>py</mi> </msubsup> <mi>cos</mi> <mi>&theta;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&delta;&omega;</mi> <mi>ip</mi> <mi>pz</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
<math> <mrow> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>~</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>=</mo> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>+</mo> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <mi>&delta;</mi> <msubsup> <munder> <mi>f</mi> <mo>&OverBar;</mo> </munder> <mi>ip</mi> <mi>p</mi> </msubsup> <mo>=</mo> <msubsup> <munderover> <mi>f</mi> <mo>&OverBar;</mo> <mo>^</mo> </munderover> <mi>ib</mi> <mi>b</mi> </msubsup> <mo>+</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msubsup> <mi>f</mi> <mi>ip</mi> <mi>px</mi> </msubsup> <mi>cos</mi> <mi>&theta;</mi> <mo>-</mo> <msubsup> <mi>&delta;f</mi> <mi>ip</mi> <mi>py</mi> </msubsup> <mi>sin</mi> <mi>&theta;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&delta;f</mi> <mi>ip</mi> <mi>px</mi> </msubsup> <mi>sin</mi> <mi>&theta;</mi> <mo>+</mo> <msubsup> <mi>&delta;f</mi> <mi>ip</mi> <mi>py</mi> </msubsup> <mi>cos</mi> <mi>&theta;</mi> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&delta;f</mi> <mi>ip</mi> <mi>pz</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>
from the equation (6), it can be concluded that the output error of the horizontal inertial device in the IMU is modulated during the positive and negative rotation and stop processes of the indexing mechanism, the output error curve changes according to the periodic rule, and the output error of the top in the sky is not modulated.
In an error propagation equation of the strapdown inertial navigation system, the gyro drift of the equivalent north direction and the equivalent sky direction causes the divergence of the resolving longitude error along with the time, so the influence of the gyro drift on the system longitude error is listed separately for investigation. Ignoring the cross-coupling term, the single-channel error model under static conditions is:
<math> <mrow> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mi>N</mi> </msub> <msub> <mi>R</mi> <mi>N</mi> </msub> </mfrac> <msub> <mi>&phi;</mi> <mi>U</mi> </msub> <mo>+</mo> <mfrac> <mrow> <mi>&delta;</mi> <msub> <mi>v</mi> <mi>E</mi> </msub> </mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>v</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>g</mi> <msub> <mi>&phi;</mi> <mi>N</mi> </msub> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>E</mi> </msub> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <mover> <mi>&lambda;</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <msub> <mi>&delta;v</mi> <mi>E</mi> </msub> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mi>cos</mi> <mi>L</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein,Nand +EFor equivalent northbound gyro drift and equivalent eastern accelerometer bias, assume the constant drift of the gyro isx,y,zZero-position bias for adding table as vx,▽y,▽zThen the gyro and the tabulated zero offset converted to the navigation coordinate system at time t can be expressed by the following formula:
<math> <mrow> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>U</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
<math> <mrow> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mo>&dtri;</mo> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mo>&dtri;</mo> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mo>&dtri;</mo> <mi>U</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
if only the constant drift of the equivalent northbound gyro is considered, the output error, the initial value error and the gravity acceleration error of other inertial elements are not considered, and the course angle error is omitted. The error equation for the one-way channel is:
<math> <mrow> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>&delta;</mi> <msub> <mi>v</mi> <mi>E</mi> </msub> </mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>v</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>g</mi> <msub> <mi>&phi;</mi> <mi>N</mi> </msub> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <mover> <mi>&lambda;</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <msub> <mi>&delta;v</mi> <mi>E</mi> </msub> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mi>cos</mi> <mi>L</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>
after rotation about the heading axis, the error equation becomes:
<math> <mrow> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>&delta;</mi> <msub> <mi>v</mi> <mi>E</mi> </msub> </mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>r</mi> </msub> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>v</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>g</mi> <msub> <mi>&phi;</mi> <mi>N</mi> </msub> </mrow> </math>
<math> <mrow> <mi>&delta;</mi> <mover> <mi>&lambda;</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <msub> <mi>&delta;v</mi> <mi>E</mi> </msub> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <mi>cos</mi> <mi>L</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>
taking Laplace transform for equations (9) and (10), the block diagram is shown in FIG. 1, the gyro constant drift is regarded as step signal <math> <mrow> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> <mo>&CenterDot;</mo> <mn>1</mn> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&DoubleLeftRightArrow;</mo> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> <mi>s</mi> </mfrac> <mo>.</mo> </mrow> </math>
Obtaining a rotating system error analytic expression from a block diagram:
<math> <mrow> <msub> <mi>&delta;v</mi> <mi>E</mi> </msub> <mo>=</mo> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> <mfrac> <mrow> <msub> <mi>R</mi> <mi>E</mi> </msub> <msubsup> <mi>&omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <msubsup> <mi>&omega;</mi> <mi>r</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>&omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>[</mo> <mfrac> <mn>1</mn> <msub> <mi>&omega;</mi> <mi>s</mi> </msub> </mfrac> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>s</mi> </msub> <mi>t</mi> <mo>)</mo> </mrow> <mfrac> <mn>1</mn> <msub> <mi>&omega;</mi> <mi>r</mi> </msub> </mfrac> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>r</mi> </msub> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </math>
<math> <mrow> <mi>&delta;&lambda;</mi> <mo>=</mo> <mfrac> <msub> <mi>&epsiv;</mi> <mi>N</mi> </msub> <mrow> <mi>cos</mi> <mi>L</mi> </mrow> </mfrac> <mo>&CenterDot;</mo> <mfrac> <msubsup> <mi>&omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> <mrow> <msubsup> <mi>&omega;</mi> <mi>r</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>&omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>[</mo> <mfrac> <mrow> <msubsup> <mi>&omega;</mi> <mi>r</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>&omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mrow> <msubsup> <mi>&omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&omega;</mi> <mi>s</mi> <mn>2</mn> </msubsup> </mfrac> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>s</mi> </msub> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>&omega;</mi> <mi>r</mi> <mn>2</mn> </msubsup> </mfrac> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mi>r</mi> </msub> <mi>t</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>
whereinThe Schuler frequency. As can be seen from equation (11), the longitude error caused by the equivalent north gyro changes from the divergent type to the oscillatory type, indicating that the position accuracy can be improved after rotation.
According to the rotational symmetry requirement, the uniaxial rotation scheme realizes the modulation of the deviation of the inertial device by adopting a cycle method of IMU unit positive and negative rotation stop.
The single axis rotary mechanism periodically sequences fixed points to each perform a 360 ° periodic indexing at a rotational angular velocity about the IMU zenith axis OZS.
The entire one modulation period scheme is as follows:
procedure 1 (stop): the optical IMU stays at the zero position for 60 s; as shown in fig. 2A.
Procedure 2 (run): the optical IMU rotates one revolution clockwise at an angular rate of 6 °/s; as shown in fig. 2B.
Procedure 3 (stop): the optical IMU stays at the zero position for 60 s; as shown in fig. 2C.
Procedure 4 (run): the optical IMU rotates one revolution counter-clockwise at an angular rate of 6 °/s; as shown in fig. 2D.
The spin-stop sequence is one full cycle as shown in fig. 2 below, after which the above process is cycled.
From the above analysis, it can be known that each order attitude matrix is recorded as if only the gyro constant drift is consideredThe modulation of the rotation on the gyro output error caused by the constant drift error is then obtained as:
<math> <mrow> <msubsup> <munder> <mi>C</mi> <mo>&OverBar;</mo> </munder> <mi>p</mi> <mi>b</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <munder> <mi>&epsiv;</mi> <mo>&OverBar;</mo> </munder> <mi>b</mi> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>bx</mi> </msub> <mi>cos</mi> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&epsiv;</mi> <mi>by</mi> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>bs</mi> </msub> <mi>sin</mi> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&epsiv;</mi> <mi>by</mi> </msub> <mi>cos</mi> <mi>&theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&epsiv;</mi> <mi>bz</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> </math>
it can be seen that the rotation mode is the rotation speed when the positive and negative rotation stops in a fixed periodThe constant drift on the vertical plane of the rotating shaft can be completely modulated within one rotating period, and the constant drift on the rotating shaft can not be modulated and still can be propagated according to the original rule.
Through the uniaxial rotation modulation, navigation errors caused by constant errors of the east-direction inertial element and the north-direction inertial element are modulated, and the constant errors of the sky-direction inertial element are still propagated according to the original rule. Therefore, the position precision is doubled, and the modulation effect of the attitude and the heading is obvious.
As shown in fig. 3, the single-axis rotational inertial navigation system of the marine optical gyroscope is composed of an inertial device, a display control device and a power supply device.
The rotary modulation technology can eliminate the influence of constant and slowly varying errors, thereby greatly improving the system precision.
FIG. 4 is a block diagram of a system strap-down solution, where s is an IMU sensitive system, n is a geographic system, and b is a machine system. Compared with the common strapdown resolving process, the system-level rotation modulation strapdown inertial navigation resolving process increases attitude demodulation, the real attitude of the carrier can be obtained only after the attitude demodulation of the IMU, and the relative angular motion of the IMU and the carrier is measured by an angular position sensor on a rotating shaft.
As shown in fig. 5, the structural diagram of a single-axis rotational optical inertial navigation system is shown, and the system mainly includes an IMU and a single-axis indexing mechanism, where an IMU vertical axis and an indexing mechanism rotation axis coincide.
The single-shaft rotating mechanism is used for periodically sequencing fixed points and respectively conducting 360-degree transposition around an azimuth axis OZS of the IMU at a certain rotating angular velocity, so that the constant errors of the IMU horizontal axial inertial device can be effectively modulated, the single-shaft rotating modulation strapdown inertial navigation resolving process is similar to the traditional strapdown inertial navigation resolving process, only three-degree-of-freedom attitude demodulation is added, the installation errors caused by rotation are eliminated on software by using a new transposition mode, and therefore the errors of error sources caused by system introduction are effectively modulated. The attitude of the IMU is demodulated to obtain the true attitude of the carrier, and the relative angular motion of the IMU (inertial measurement unit) and the carrier is measured by an angular position sensor on the rotating shaft.
And the system simulation verification is carried out by combining the overall design flow and thought of the system and matching with the new transposition scheme in the invention.
Simulation conditions are as follows: taking the gyro constant drift valuex,y,z]=[0.01,0.01,0.01]V [. v ] constant value of accelerometerx,▽y,▽z]=[100,100,100]μ g, other errors are zero. The rotation stopping scheme is adopted, the rotation speed is 6 degrees/s, and the stopping time Th is 60 s. The sampling period is 0.1s, and the simulation time is 24 h. A comparison of the navigation error caused by the constant error in the non-rotating system and the rotating system is shown in fig. 6 and 7.
The simulation results are shown in fig. 6 and 7.
Simulation results show that the navigation output precision, especially the very important positioning precision index, of the long-endurance navigation system is obviously superior to the optical inertial navigation output index under the traditional non-rotation condition under the same condition by adopting a rotation scheme of unit-position positive and negative rotation stop, and the feasibility of the technology is verified.

Claims (1)

1. A system-level compensation method for marine optical inertial navigation long-endurance precision-preserving navigation is characterized by comprising the following steps: comprises the following steps: firstly, determining a ship coordinate system, identifying the system heading, and determining the pitch and roll coordinates of the system; secondly, mounting an optical gyroscope and an adder table on the high-strength and high-precision hexahedron, and ensuring the planeness, parallelism and verticality by using three coordinates; debugging a single-shaft rotating mechanism control system, designing a transposition scheme by using a mature PID control algorithm, and ensuring positioning precision and low-speed stability by using an optical means; step four, the IMU is installed and fixed on a table board of the indexing mechanism, and the table board is provided with a calibrated horizontal base plane and a head-to-head leaning plane, so that the installation of the table board is ensured to have certain repeatability; acquiring and processing original data of the strapdown inertial navigation system, and processing the data, such as temperature compensation, course effect compensation, system-level calibration and other tests; sixthly, attitude updating, speed and position resolving in pure inertial system algorithm design in the single-axis rotation modulation system; and seventhly, carrying out real-time demodulation processing of single-axis rotation.
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