CN107655493A

CN107655493A - A kind of position system level scaling methods of optical fibre gyro SINS six

Info

Publication number: CN107655493A
Application number: CN201710795340.1A
Authority: CN
Inventors: 徐晓苏; 吴梅; 王捍兵
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2017-09-06
Filing date: 2017-09-06
Publication date: 2018-02-02
Anticipated expiration: 2037-09-06
Also published as: CN107655493B

Abstract

The invention discloses a kind of position system level scaling methods of optical fibre gyro SINS six, this is by analyzing inertia component erroi propagation law, the rotation in six-position of turntable is designed, system speed error and attitude error is calculated, estimation is filtered to every error by Kalman filter.Beneficial effects of the present invention are：The error of zero, scale factor error and the alignment error of the error of zero of optical fibre gyro, scale factor error, alignment error and accelerometer can be calibrated exactly based on system level approach；The present invention gives most easy position arrangement, while the reason for give calibration position layout, calibration principle is clear, can disposably demarcate.

Description

A kind of position system level scaling methods of optical fibre gyro SINS six

Technical field

The present invention relates to calibration technique field, especially a kind of position system level scaling methods of optical fibre gyro SINS six.

Background technology

Strapdown inertial navigation system is a kind of using gyro and the angular movement of accelerometer measures carrier and line motion, by product Partite transport is calculated and obtains carrier transient posture, speed and the navigation equipment of position, and it fully relies on the inertia component of itself and completes navigation Task, it is a kind of entirely autonomous navigation system without relying on any external information.SINS is due to its independence Height, good concealment, it is round-the-clock, stability is good and short-term accuracy is high the advantages that, be widely used in science and techniques of defence field.Strapdown is used to The characteristics of guiding systems is to substitute the physical platform of gimbaled inertial navigation with mathematical platform come analogue navigation coordinate system, due to it It is dead reckoning system in matter, its error can be increased over time and accumulated.

It can be seen from the principle of strapdown inertial navigation, its key technology includes inertia type instrument technology, inertia component erroi Compensation technique, Initial Alignment Technique and strap-down matrix more new algorithm.Inertia component erroi accounts for 90% of systematic error or so, inertia The method of component erroi compensation technique is exactly to demarcate.The purpose of demarcation is to determine the error of inertia component, and calibrated error is mended Repay in inertia component, improve the navigation accuracy of system.At present, used fiber-optic gyroscope calibration method is mainly discrete mark Fixed and systematic calibration.Discrete demarcation is usually to provide position and speed reference by high precision turntable；Systematic calibration master If by observing the anti-parameters released in error model of navigation error.This method is based on navigation calculation, to turntable Required precision it is very low, but this method principle is complicated, and the general nominal time is longer.

Optical fibre gyro is one kind of optical gyroscope, is the sensor for detecting angular speed.Optical fibre gyro is using Sagnac Principle of interference, it is coiled into annular light path with optical fiber and detects the phase with rotation and between the two-way laser beam of caused anti-phase rotation Potential difference, thus calculate the angular speed of rotation.Optical fibre gyro has the difference of essence with traditional mechanical gyro in principle, has The advantages of mechanical gyro is incomparable, it is used widely at present in inertial guidance and navigation field.

The content of the invention

The technical problems to be solved by the invention are, there is provided a kind of position system level demarcation sides of optical fibre gyro SINS six Method, the various errors of optical fibre gyro can be calibrated exactly, calibration principle is clear, can disposably demarcate.

In order to solve the above technical problems, the present invention provides a kind of position system level scaling methods of optical fibre gyro SINS six, bag Include following steps：

(1) inertia component is arranged on turntable, inertia component is initially oriented east-north-day；Inertia component is powered pre- Heat, set the sampling period；

(2) start to gather inertia module data and establish inertia component erroi model and SINS error model；

(3) initial position of inertia component setting in step (1) is stood 1 minute and carry out static navigational, then make to be used to Property component with 10 °/angular speed rotate forward 180 ° around X-axis, make inertia component is oriented Dong-south-ground, and stands 1 minute Carry out static navigational；

(4) inertia component is made to rotate forward 90 ° around X-axis, make inertia component is oriented east-ground-north, and stands 1 minute Carry out static navigational, followed by inertia component with 10 °/angular speed rotate forward 180 ° about the z axis, make being oriented for inertia component West-day-north, and stand 1 minute and carry out static navigational；

(5) inertia component is made to rotate forward 90 ° about the z axis, make inertia component is oriented day-east-north, and stands 1 minute Carry out static navigational, followed by inertia component with 10 °/angular speed rotate forward 180 ° around Y-axis, make being oriented for inertia component Ground-Dong-south, and stand 1 minute and carry out static navigational, number is adopted in stopping；

(6) offline navigation calculation, and computing system velocity error and attitude error are carried out to the data of inertia component collection；

(7) design Kalman filter is filtered estimation to inertia component erroi；

(8) step (1) is repeated to step (5), repeats all change different angular velocity of rotations every time；To every The secondary data that collect of repeating carry out navigation calculation and Kalman Filter Estimation, under the different angular speed that are calculated Inertia component erroi results averaged, as final result.

Preferably, in step (1), sampling period T=0.005s.

Preferably, in step (2), establishing inertia component erroi model is specially：By the alignment error of optical fibre gyro, scale System errors and constant value drift are built into gyroscope error model, obtain：

In formula, n is navigational coordinate system；B is carrier coordinate system；I is inertial coodinate system；ε^bFloated for constant value under carrier coordinate system Move；For the transformation matrix from carrier coordinate system to navigational coordinate system；For the output of gyro；[δK_G] be gyro scale system Number error,[δ G] is alignment error,

The alignment error of accelerometer, scale coefficient error and constant value drift are built into accelerometer error model, obtained：

In formula,For constant value drift under carrier coordinate system；f^bFor the output of accelerometer；[δK_A] be accelerometer scale system Number error,[δ A] is alignment error,

Establishing attitude error equations is：

In formula, φ is attitude error angle vector；Sat for the angular speed of navigational coordinate system relative inertness coordinate system in navigation Projection under mark system；For navigational coordinate system relative inertness coordinate system rotational angular velocity calculation error；Missed for gyroscope Projection of the difference under navigational coordinate system；

Establishing velocity error equation is：

In formula, φⁿFor attitude error angle under navigational coordinate system；fⁿFor the output of accelerometer under navigational coordinate system；For Projection of the accelerometer error under navigational coordinate system；δVⁿ=[δ V_E δV_N δV_U]^TFor east orientation, north orientation and sky orientation speed error；Follow projection of the geocyclic angular speed under navigational coordinate system；With respect to the earth caused by carrier movement Projection of the angular velocity of rotation under navigational coordinate system；Vⁿ=[V_E V_N V_U]^TFor east orientation, north orientation, sky orientation speed；With For corresponding error.

Preferably, in step (3), the initial position of inertia component setting in step (1) is stood 1 minute and carry out static state Navigation calculation, inertia component is rotated forward 180 ° around X-axis with 10 °/s angular speed, make inertia component be oriented east- South-ground, and stand 1 minute progress static navigational and be specially：

Under the conditions of turntable, attitude error equations are savedExpression；The attitude error only as caused by gyro error Equation can be written as form：

Velocity error equation can be written as form only as caused by accelerometer error：

East-north-day towards when：

Deploy：

Velocity error equation caused by accelerometer：

Deploy：

Rotated around X-axis, rotational angle is 180 °, and the rotational speed omega used during demarcation is about 10 °/s, and ω is much larger than earth rotation Component ω_ie(15 °/h) and gyro zero bias, so earth rotation component and gyro zero bias can be ignored, ω_x≈ ω, ω_y≈ 0, ω_z≈ 0, then have：

Deploy：

Various integrate above can be obtained：

After having rotated, Dong-south-ground towards when：

Velocity error equation caused by accelerometer：

Deploy：

Parsed to obtain accelerometer related excitation error term according to the velocity error in this step on two positions.

Preferably, in step (4), inertia component is rotated forward 90 ° around X-axis, make inertia component be oriented east-ground- North, and stand 1 minute and carry out static navigational, followed by inertia component rotates forward 180 ° about the z axis with 10 °/s angular speed, makes Inertia component is oriented west-day-north, and stands 1 minute progress static navigational and be specially：

East-ground-north towards when：

Deploy：

Rotate about the z axis, rotational angle is 180 °, ω_x≈ 0, ω_y≈ 0, ω_z≈ ω, then have：

Deploy：

Various integrate above can be obtained：

After having rotated, west-day-north towards when：

Velocity error equation caused by accelerometer：

Deploy：

It can be parsed to obtain accelerometer related excitation error term according to the velocity error in this step on two positions.

Preferably, in step (5), inertia component is rotated forward 90 ° about the z axis, make inertia component be oriented day-east- North, and stand 1 minute and carry out static navigational, followed by inertia component rotates forward 180 ° with 10 °/s angular speed around Y-axis, makes Inertia component is oriented ground-Dong-south, and stands 1 minute and carry out static navigational, and stopping adopts number and is specially：

Day-east-north towards when：

Deploy：

Rotated around Y-axis, rotational angle is 180 °, ω_x≈ 0, ω_y≈ ω, ω_z≈ 0, then have：

Deploy：

Various integrate above can be obtained：

After having rotated, on ground-Dong-south towards when：

Velocity error equation caused by accelerometer：

Deploy：

Preferably, in step (6), offline navigation calculation, and computing system speed are carried out to the data of inertia component collection Error and attitude error are specially；First according to gyro in above-mentioned steps and accelerometer measures obtain relative to inertial coordinate The angular speed and specific force of system fasten projection in carrier；Afterwards, changed by coordinate system, obtain carrier angular speed and specific force and navigating Projected on coordinate system, by once integrating, carrier can be obtained relative to the transient posture angle of navigational coordinate system and linear velocity；Attitude angle True value can be provided by turntable, and speed true value is set to 0.

Preferably, in step (7), design Kalman filter is filtered estimation to inertia component erroi and is specially：

Establish optical fibre gyro system level demarcation Kalman filtering state equation：

In formula,

A₁=[A₁₁ A₁₂ A₁₃ A₁₄]

In formula,For random disturbances caused by gyro；T_ij(i,j =1,2,3) it is attitude matrixCorresponding element.

Establish corresponding measurement equation：

Z₁(t)=H₁X₁(t)+V(t)

In formula,

In formula, θ_I、γ_I、ψ_IThe angle of pitch, roll angle and the course angle information that respectively navigation calculation obtains；θ_z、γ_Z、ψ_ZPoint Wei not turntable posture true value；δ θ, δ γ, δ ψ are respectively the error between navigation calculation and turntable true value；V (t) makes an uproar for system measurements Sound；

Establish accelerometer system level demarcation Kalman filtering state equation：

In formula,

A₂=[A₂₁ A₂₂ A₂₃ A₂₄]

In formula,For random disturbances caused by accelerometer； T_ij(i, j=1,2,3) is attitude matrixCorresponding element；

Establish corresponding measurement equation：

Z₂(t)=Vⁿ(t) -0=H₂X₂(t)+V(t)

In formula,

Z₂(t)=[δ V_E δV_N δV_U]^T

In formula, δ V_E、δV_N、δV_UError between navigation calculation and true value；V (t) is system measurements noise；With step (3) SYSTEM ERROR MODEL establishes 24 dimension Kalman filter in, and inertia component items error is demarcated；Filtered using Kalman Ripple device principle, every error parameter in quantity of state is estimated, complete the identification to inertia component items error parameter.

Preferably, in step (8), the span of angular velocity of rotation for 10 °/- 30 °/.

Beneficial effects of the present invention are：The error of zero of optical fibre gyro can be calibrated exactly based on system level approach, carved Spend the error of zero, scale factor error and the alignment error of factor error, alignment error and accelerometer；The present invention gives most Easy position arrangement, while the reason for give calibration position layout, calibration principle is clear, can disposably demarcate.

Brief description of the drawings

Fig. 1 is the scaling method intermediate station rotating path layout schematic diagram of the present invention.

Embodiment

Turntable rotating path layout schematic diagram as shown in Figure 1, the rotation in six-position of the invention by designing turntable, calculate System speed error is obtained, inertia component erroi parameter is estimated by Kalman filter, in order to ensure final calibration result Accuracy, turntable carry out rotation in six-position in triplicate, and using the inertia component erroi being calculated three times carry out it is average as Final calibration result, specific scaling method are as follows：

Step 1：Inertia component is arranged on turntable, inertia component is initially oriented east-north-day；Inertia component is powered Preheating, set the sampling period；

Step 2：Start to gather inertia module data and establish inertia component erroi model and SINS error mould Type；

The alignment error of optical fibre gyro, scale coefficient error and constant value drift are built into gyroscope error model, obtained：

In formula,For constant value drift under carrier coordinate system；f^bFor the output of accelerometer；[δK_A] be accelerometer scale System errors,[δ A] is alignment error,

Establishing attitude error equations is：

Establishing velocity error equation is：

In formula, φⁿFor attitude error angle under navigational coordinate system；fⁿFor the output of accelerometer under navigational coordinate system；For Projection of the accelerometer error under navigational coordinate system；δVⁿ=[δ V_E δV_N δV_U]^TFor east orientation, north orientation and sky orientation speed error；Follow projection of the geocyclic angular speed under navigational coordinate system；With respect to the earth caused by carrier movement Projection of the angular velocity of rotation under navigational coordinate system；Vⁿ=[V_E V_N V_U]^TFor east orientation, north orientation, sky orientation speed；With For corresponding error；

Under the conditions of only considering turntable, now, the accurate geographic position information of SINS be it is knowable, therefore We only need to settle accounts stance loop, it is not necessary to speed and position loop are resolved, and attitude algorithm error is only It is relevant with gyro error.Simultaneously because turntable can provide accurate attitude information, and therefore, when considering velocity error equation, The aceleration of transportation can be ignored.

Step 3：The initial position for making inertia component be set in step 1 stands 1 minute and carries out static navigational resolving, so Make afterwards inertia component with 10 °/angular speed rotate forward 180 ° around X-axis, make inertia component is oriented Dong-south-ground, and stands Carry out static navigational within 1 minute；

Due to being under the conditions of turntable, analyze for convenience, attitude error equations are savedExpression.

Attitude error equations can be written as form only as caused by gyro error：

East-north-day towards when：

Deploy：

Velocity error equation caused by accelerometer：

Deploy：

Being rotated around X-axis, rotational angle is 180 °, the rotational speed omega used during demarcation is about 10 °/, ω is much larger than earth rotation Component ω_ie(15 °/h) and gyro zero bias, so earth rotation component and gyro zero bias can be ignored, ω_x≈ ω, ω_y≈ 0, ω_z≈ 0, then have：

Deploy：

Various integrate above can be obtained：

After having rotated, Dong-south-ground towards when：

Velocity error equation caused by accelerometer：

Deploy：

Step 4：Inertia component is set to rotate forward 90 ° around X-axis, make inertia component is oriented east-ground-north, and stands 1 Minute carry out static navigational, followed by inertia component with 10 °/angular speed rotate forward 180 ° about the z axis, make the court of inertia component Xiang Weixi-day-north, and stand 1 minute and carry out static navigational；

East-ground-north towards when：

Deploy：

Various integrate above can be obtained：

After having rotated, west-day-north towards when：

Velocity error equation caused by accelerometer：

Deploy：

Step 5：Inertia component is set to rotate forward 90 ° about the z axis, make inertia component is oriented day-east-north, and stands 1 Minute carry out static navigational, followed by inertia component with 10 °/angular speed rotate forward 180 ° around Y-axis, make the court of inertia component To for ground-Dong-south, and stand 1 minute and carry out static navigational, number is adopted in stopping.

Day-east-north towards when：

Deploy：

Various integrate above can be obtained：

After having rotated, on ground-Dong-south towards when：

Velocity error equation caused by accelerometer：

Deploy：

Step 6：Offline navigation calculation, and computing system velocity error and posture are carried out to the data of inertia component collection Error；

First according to gyro in above-mentioned steps and accelerometer measures obtain relative to inertial coodinate system angular speed and Specific force fastens projection in carrier.Afterwards, changed by coordinate system, obtain carrier angular speed and specific force in navigational coordinate system upslide Shadow, by once integrating, carrier can be obtained relative to the transient posture angle of navigational coordinate system and linear velocity.Attitude angle true value can be by turning Platform provides, and speed true value is set to 0.

Step 7：Design Kalman filter is filtered estimation to inertia component erroi；

In formula,

A₁=[A₁₁ A₁₂ A₁₃ A₁₄]

Establish corresponding measurement equation：

Z₁(t)=H₁X₁(t)+V(t)

In formula,

In formula, θ_i、γ_I、ψ_IThe angle of pitch, roll angle and the course angle information that respectively navigation calculation obtains；θ_z、γ_z、ψ_ZPoint Wei not turntable posture true value；δ θ, δ γ, δ ψ are respectively the error between navigation calculation and turntable true value；V (t) makes an uproar for system measurements Sound.

In formula,

A₂=[A₂₁ A₂₂ A₂₃ A₂₄]

In formula,For random disturbances caused by accelerometer； T_ij(i, j=1,2,3) is attitude matrixCorresponding element.

Establish corresponding measurement equation：

Z₂(t)=Vⁿ(t) -0=H₂X₂(t)+V(t)

In formula,

Z₂(t)=[δ V_E δV_N δV_U]^T

In formula, δ V_E、δV_N、δV_UError between navigation calculation and true value；V (t) is system measurements noise.

24 dimension Kalman filter are established with SYSTEM ERROR MODEL in step 3, inertia component items error is demarcated

Using Kalman filter principle, every error parameter in quantity of state is estimated, completed each to inertia component The identification of item error parameter.

Step 8：Step 1 is repeated to step 5, repeats all change different angular velocity of rotations every time；It is right The data collected are repeated every time carries out navigation calculation and Kalman Filter Estimation, method and step 6 and step 7 phase Together；To the inertia component erroi results averaged under the different angular speed that are calculated, as final result.

Although the present invention is illustrated and described with regard to preferred embodiment, it is understood by those skilled in the art that Without departing from scope defined by the claims of the present invention, variations and modifications can be carried out to the present invention.

Claims

1. a kind of position system level scaling methods of optical fibre gyro SINS six, it is characterised in that comprise the following steps：

(1) inertia component is arranged on turntable, inertia component is initially oriented east-north-day；Inertia component, which is powered, to be preheated, if Determine the sampling period；

(3) initial position of inertia component setting in step (1) is stood 1 minute and carry out static navigational, then make inertia group Part with 10 °/angular speed rotate forward 180 ° around X-axis, make inertia component is oriented Dong-south-ground, and stands 1 minute and carry out Static navigational；

(4) inertia component is made to rotate forward 90 ° around X-axis, make inertia component is oriented east-ground-north, and stands 1 minute and carry out Static navigational, followed by inertia component with 10 °/angular speed rotate forward 180 ° about the z axis, make inertia component be oriented west- My god-north, and stand 1 minute and carry out static navigational；

(5) inertia component is made to rotate forward 90 ° about the z axis, make inertia component is oriented day-east-north, and stands 1 minute and carry out Static navigational, followed by inertia component with 10 °/angular speed rotate forward 180 ° around Y-axis, make inertia component be oriented ground- Dong-south, and stand 1 minute and carry out static navigational, number is adopted in stopping；

(7) design Kalman filter is filtered estimation to inertia component erroi；

(8) step (1) is repeated to step (5), repeats all change different angular velocity of rotations every time；To weight every time The data that collect are performed again and carry out navigation calculation and Kalman Filter Estimation, to used under the different angular speed that are calculated Property component erroi results averaged, as final result.

2. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (1), Sampling period is T=0.005s.

3. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (2), Establishing inertia component erroi model is specially：The alignment error of optical fibre gyro, scale coefficient error and constant value drift are built into top Spiral shell error model, is obtained：

In formula, n is navigational coordinate system；B is carrier coordinate system；I is inertial coodinate system；ε^bFor constant value drift under carrier coordinate system；For the transformation matrix from carrier coordinate system to navigational coordinate system；For the output of gyro；[δK_G] be gyro calibration factor Error,[δ G] is alignment error,

In formula,For constant value drift under carrier coordinate system；f^bFor the output of accelerometer；[δK_A] be accelerometer calibration factor Error,[δ A] is alignment error,

Establishing attitude error equations is：

In formula, φ is attitude error angle vector；For navigational coordinate system relative inertness coordinate system angular speed in navigational coordinate system Under projection；For navigational coordinate system relative inertness coordinate system rotational angular velocity calculation error；Exist for gyro error Projection under navigational coordinate system；

Establishing velocity error equation is：

In formula, φⁿFor attitude error angle under navigational coordinate system；fⁿFor the output of accelerometer under navigational coordinate system；To accelerate Projection of the degree meter error under navigational coordinate system；δVⁿ=[δ V_E δV_N δV_U]^TFor east orientation, north orientation and sky orientation speed error；With With projection of the geocyclic angular speed under navigational coordinate system；Relative to the rotation of the earth caused by carrier movement Projection of the angular speed under navigational coordinate system；Vⁿ=[V_E V_N V_U]^TFor east orientation, north orientation, sky orientation speed；WithFor phase The error answered.

4. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (3), The initial position of inertia component setting in the step (1) is stood 1 minute and carry out static navigational resolving, then make inertia component with 10 °/s angular speed rotates forward 180 ° around X-axis, and make inertia component is oriented Dong-south-ground, and stands 1 minute and carry out static state Navigation is specially：

Under the conditions of turntable, attitude error equations are savedExpression；The attitude error equations only as caused by gyro error Form can be written as：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi>&phi;</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>G</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>G</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>G</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&omega;</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&omega;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&omega;</mi> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>f</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>f</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>f</mi> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

East-north-day towards when：

Deploy：

Velocity error equation caused by accelerometer：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </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> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>g</mi> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

Deploy：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>&delta;</mi> <msub> <mi>A</mi> <mi>y</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> <mo>=</mo> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

Rotated around X-axis, rotational angle is 180 °, and the rotational speed omega used during demarcation is about 10 °/s, and ω is much larger than earth rotation component ω_ie(15 °/h) and gyro zero bias, so earth rotation component and gyro zero bias can be ignored, ω_x≈ ω, ω_y≈ 0, ω_z ≈ 0, then have：

Deploy：

Various integrate above can be obtained：

After having rotated, Dong-south-ground towards when：

Velocity error equation caused by accelerometer：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>g</mi> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

Deploy：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mi>&delta;</mi> <msub> <mi>A</mi> <mi>y</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> <mo>=</mo> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

5. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (4), Inertia component is set to rotate forward 90 ° around X-axis, make inertia component is oriented east-ground-north, and stands 1 minute progress static state and lead Boat, followed by inertia component rotates forward 180 ° about the z axis with 10 °/s angular speed, make inertia component is oriented west-day-north, And stand 1 minute progress static navigational and be specially：

East-ground-north towards when：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>g</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

Deploy：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>&delta;</mi> <msub> <mi>A</mi> <mi>z</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

Deploy：

Various integrate above can be obtained：

After having rotated, west-day-north towards when：

Velocity error equation caused by accelerometer：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>g</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

Deploy：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>&delta;</mi> <msub> <mi>A</mi> <mi>y</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> <mo>=</mo> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

6. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (5), Inertia component is set to rotate forward 90 ° about the z axis, make inertia component is oriented day-east-north, and stands 1 minute progress static state and lead Boat, followed by inertia component rotates forward 180 ° with 10 °/s angular speed around Y-axis, make inertia component is oriented ground-Dong-south, And stand 1 minute and carry out static navigational, stopping adopts number and is specially：

Day-east-north towards when：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>g</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

Deploy：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mi>&delta;</mi> <msub> <mi>G</mi> <mi>y</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

Deploy：

Various integrate above can be obtained：

After having rotated, on ground-Dong-south towards when：

Velocity error equation caused by accelerometer：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>(</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&delta;G</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mo>-</mo> <mi>g</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <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> <mo>)</mo> </mrow> </mrow>

Deploy：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>E</mi> </msub> <mo>=</mo> <mi>&delta;</mi> <msub> <mi>G</mi> <mi>y</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>N</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>+</mo> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&delta;</mi> <msub> <mover> <mi>V</mi> <mo>&CenterDot;</mo> </mover> <mi>U</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> <mo>&CenterDot;</mo> <mi>g</mi> <mo>-</mo> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

7. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (6), Offline navigation calculation is carried out to the data of inertia component collection, and computing system velocity error and attitude error are specially；First The angular speed and specific force relative to inertial coodinate system obtained according to gyro in above-mentioned steps and accelerometer measures is in carrier system Upper projection；Afterwards, changed by coordinate system, obtain carrier angular speed and specific force projects in navigational coordinate system, process is once accumulated Point, carrier can be obtained relative to the transient posture angle of navigational coordinate system and linear velocity；Attitude angle true value can be provided by turntable, and speed is true Value is set to 0.

8. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (7), Design Kalman filter is filtered estimation to inertia component erroi and is specially：

<mrow> <msub> <mover> <mi>X</mi> <mo>&CenterDot;</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>G</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>W</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>

In formula,A₁ =[A₁₁ A₁₂ A₁₃ A₁₄]

<mrow> <msub> <mi>A</mi> <mn>11</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>sin</mi> <mi>L</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>cos</mi> <mi>L</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>sin</mi> <mi>L</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>cos</mi> <mi>L</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <msub> <mi>A</mi> <mn>13</mn> </msub> <mo>=</mo> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>11</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>x</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>12</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>y</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>13</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>z</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>21</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>x</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>22</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>y</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>23</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>z</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>31</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>x</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>32</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>y</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>33</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>z</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <msub> <mi>A</mi> <mn>14</mn> </msub> <mo>=</mo> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>12</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>z</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>13</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>x</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>11</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>y</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>22</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>z</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>23</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>x</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>21</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>y</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>32</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>z</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>33</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>x</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>31</mn> </msub> <msubsup> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> <mi>y</mi> </mrow> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

In formula,For random disturbances caused by gyro；T_ij(i, j=1, 2,3) it is attitude matrixCorresponding element.

Establish corresponding measurement equation：

Z₁(t)=H₁X₁(t)+V(t)

In formula,

<mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&theta;</mi> <mi>I</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&gamma;</mi> <mi>I</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&psi;</mi> <mi>I</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&theta;</mi> <mi>Z</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&gamma;</mi> <mi>Z</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&psi;</mi> <mi>Z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>&delta;</mi> <mi>&theta;</mi> </mrow> </mtd> <mtd> <mrow> <mi>&delta;</mi> <mi>&gamma;</mi> </mrow> </mtd> <mtd> <mrow> <mi>&delta;</mi> <mi>&psi;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow>

<mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>cos&psi;</mi> <mi>I</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>sin&psi;</mi> <mi>I</mi> </msub> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>1</mn> <mo>&times;</mo> <mn>9</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>sin&psi;</mi> <mi>I</mi> </msub> <mo>/</mo> <msub> <mi>cos&theta;</mi> <mi>I</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>cos&psi;</mi> <mi>I</mi> </msub> <mo>-</mo> <mn>2</mn> <msub> <mi>sin&theta;</mi> <mi>I</mi> </msub> <msub> <mi>sin&gamma;</mi> <mi>I</mi> </msub> <msub> <mi>cos&gamma;</mi> <mi>I</mi> </msub> <msub> <mi>sin&psi;</mi> <mi>I</mi> </msub> <mo>)</mo> </mrow> <mrow> <msub> <mi>cos&theta;</mi> <mi>I</mi> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>1</mn> <mo>&times;</mo> <mn>9</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>sin&psi;</mi> <mi>I</mi> </msub> <msub> <mi>cos&theta;</mi> <mi>I</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>cos&psi;</mi> <mi>I</mi> </msub> <msub> <mi>tan&theta;</mi> <mi>I</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>1</mn> <mo>&times;</mo> <mn>9</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

In formula, θ_I、γ_I、ψ_IThe angle of pitch, roll angle and the course angle information that respectively navigation calculation obtains；θ_Z、γ_Z、ψ_ZRespectively Turntable posture true value；δ θ, δ γ, δ ψ are respectively the error between navigation calculation and turntable true value；V (t) is system measurements noise；

<mrow> <msub> <mover> <mi>X</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>X</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>G</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>W</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>

In formula,

<mrow> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&delta;V</mi> <mi>E</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;V</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;V</mi> <mi>U</mi> </msub> </mrow> </mtd> <mtd> <msub> <mo>&dtri;</mo> <mi>x</mi> </msub> </mtd> <mtd> <msub> <mo>&dtri;</mo> <mi>y</mi> </msub> </mtd> <mtd> <msub> <mo>&dtri;</mo> <mi>z</mi> </msub> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>y</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;K</mi> <mrow> <mi>A</mi> <mi>z</mi> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>x</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&delta;A</mi> <mi>z</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>;</mo> </mrow>

A₂=[A₂₁ A₂₂ A₂₃ A₂₄]

<mrow> <msub> <mi>A</mi> <mn>21</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mfrac> <msub> <mi>V</mi> <mi>N</mi> </msub> <msub> <mi>R</mi> <mi>N</mi> </msub> </mfrac> <mi>tan</mi> <mi> </mi> <mi>L</mi> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mi>U</mi> </msub> <msub> <mi>R</mi> <mi>N</mi> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi> </mi> <mi>L</mi> <mo>+</mo> <mfrac> <msub> <mi>V</mi> <mi>E</mi> </msub> <msub> <mi>R</mi> <mi>N</mi> </msub> </mfrac> <mi>tan</mi> <mi> </mi> <mi>L</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> <mo>+</mo> <mfrac> <msub> <mi>V</mi> <mi>E</mi> </msub> <msub> <mi>R</mi> <mi>N</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi> </mi> <mi>L</mi> <mo>+</mo> <mfrac> <msub> <mi>V</mi> <mi>E</mi> </msub> <msub> <mi>R</mi> <mi>N</mi> </msub> </mfrac> <mi>tan</mi> <mi> </mi> <mi>L</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mi>U</mi> </msub> <msub> <mi>R</mi> <mi>M</mi> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>V</mi> <mi>N</mi> </msub> <msub> <mi>R</mi> <mi>M</mi> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>&omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> <mo>+</mo> <mfrac> <msub> <mi>V</mi> <mi>E</mi> </msub> <msub> <mi>R</mi> <mi>N</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mfrac> <mrow> <mn>2</mn> <msub> <mi>V</mi> <mi>N</mi> </msub> </mrow> <msub> <mi>R</mi> <mi>M</mi> </msub> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>

<mrow> <msub> <mi>A</mi> <mn>23</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>12</mn> </msub> <msubsup> <mi>f</mi> <mi>z</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>13</mn> </msub> <msubsup> <mi>f</mi> <mi>y</mi> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>13</mn> </msub> <msubsup> <mi>f</mi> <mi>x</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <msubsup> <mi>f</mi> <mi>z</mi> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>11</mn> </msub> <msubsup> <mi>f</mi> <mi>y</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>12</mn> </msub> <msubsup> <mi>f</mi> <mi>x</mi> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>22</mn> </msub> <msubsup> <mi>f</mi> <mi>z</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>23</mn> </msub> <msubsup> <mi>f</mi> <mi>y</mi> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>23</mn> </msub> <msubsup> <mi>f</mi> <mi>x</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>21</mn> </msub> <msubsup> <mi>f</mi> <mi>z</mi> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>21</mn> </msub> <msubsup> <mi>f</mi> <mi>y</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>22</mn> </msub> <msubsup> <mi>f</mi> <mi>x</mi> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>32</mn> </msub> <msubsup> <mi>&omega;f</mi> <mi>z</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>33</mn> </msub> <msubsup> <mi>f</mi> <mi>y</mi> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>33</mn> </msub> <msubsup> <mi>f</mi> <mi>x</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>31</mn> </msub> <msubsup> <mi>f</mi> <mi>z</mi> <mi>b</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>31</mn> </msub> <msubsup> <mi>f</mi> <mi>y</mi> <mi>b</mi> </msubsup> <mo>-</mo> <msub> <mi>T</mi> <mn>32</mn> </msub> <msubsup> <mi>f</mi> <mi>x</mi> <mi>b</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

In formula,For random disturbances caused by accelerometer；T_ij(i,j =1,2,3) it is attitude matrixCorresponding element；

Establish corresponding measurement equation：

Z₂(t)=Vⁿ(t) -0=H₂X₂(t)+V(t)

In formula,

Z₂(t)=[δ V_E δV_N δV_U]^T

<mrow> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>1</mn> <mo>&times;</mo> <mn>9</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>1</mn> <mo>&times;</mo> <mn>9</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>1</mn> <mo>&times;</mo> <mn>9</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

In formula, δ V_E、δV_N、δV_UError between navigation calculation and true value；V (t) is system measurements noise；With in step (3) SYSTEM ERROR MODEL establishes 24 dimension Kalman filter, and inertia component items error is demarcated；Utilize Kalman filter Principle, every error parameter in quantity of state is estimated, complete the identification to inertia component items error parameter.

9. the position system level scaling methods of optical fibre gyro SINS six as claimed in claim 1, it is characterised in that in step (8), The span of angular velocity of rotation is 10 °/s-30 °/s.