CN107741240A - A kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving - Google Patents

A kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving Download PDF

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Publication number
CN107741240A
CN107741240A CN201710942241.1A CN201710942241A CN107741240A CN 107741240 A CN107741240 A CN 107741240A CN 201710942241 A CN201710942241 A CN 201710942241A CN 107741240 A CN107741240 A CN 107741240A
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mrow
msub
msup
msubsup
mtd
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CN201710942241.1A
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Chinese (zh)
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郭静
胡明武
刘荣
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成都国卫通信技术有限公司
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Priority to CN201710942241.1A priority Critical patent/CN107741240A/en
Publication of CN107741240A publication Critical patent/CN107741240A/en

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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

Abstract

The present invention relates to a kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving, including step:(1) each coordinate system is defined;(2) inertial coodinate system is sought to the transition matrix of navigational coordinate system;(3) pedestal relation coordinate system is sought to the transition matrix of inertial coodinate system;(4) carrier coordinate system is sought to the transition matrix of pedestal relation coordinate system;(5) multiple carrier coordinate system is sought to the average value of the transition matrix of pedestal relation coordinate system;(6) pedestal relation coordinate system is calculated to the error of the transition matrix of inertial coodinate system;(7) given threshold, threshold value and error size are compared;(8) seek to obtain carrier coordinate system to the transition matrix of navigational coordinate system according to step (2), (3) and (4), so as to realize the initial alignment of carrier.This method changes slow characteristic using projection of the acceleration of gravity in pedestal inertial system, while has merged the judgement to dynamic characteristic, the communication in moving being adapted under different conditions.

Description

A kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving

Technical field

The present invention relates to assembled gesture fields of measurement, and it is adaptive to relate generally to a kind of combined inertial nevigation system suitable for communication in moving Answer Initial Alignment Method.

Background technology

In the prior art, communication in moving inertial navigation system coarse alignment is typically realized using two ways, when analytic expression coarse alignment, Second, wave dynamic alignment.

Analytic expression coarse alignment requires that carrier must be totally stationary, even requires to close engine under automobile scenarios and avoids people Member walks about, nonetheless, it is still necessary to initial alignment precision is improved by extending the alignment time, and communication in moving is required to dynamic substantially Initially it is aligned under the conditions of state, therefore, analytic expression coarse alignment is not particularly suited for communication in moving.

The coarse alignment that dynamic alignment disclosure satisfy that communication in moving under dynamic condition, but this method alignment time length are waved, at least 1~2min times are needed to complete the coarse alignment of certain precision, therefore can extend the initial Alignment of Inertial Navigation System time, can not meet to use Family rapidity requirement.At present, for inertial navigation system, it is two conclusions runed counter to shorten the initial alignment time and improve precision, But for communication in moving system, the communication in moving of different application environment different series is different to the requirement being initially aligned.Must therefore, having A kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving is proposed, with suitable for different communication in moving.

The content of the invention

At the beginning of the technical problems to be solved by the invention are to provide a kind of combined inertial nevigation system self-adaption suitable for communication in moving Beginning alignment methods, this method changes slow characteristic using projection of the acceleration of gravity in pedestal inertial system, while merges Judgement to dynamic characteristic, the communication in moving being adapted under different conditions.

The technical scheme that the present invention solves above-mentioned technical problem is as follows:

A kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving, including step:

(1) inertial coodinate system, navigational coordinate system, carrier coordinate system and pedestal relation coordinate system are defined;

(2) positional information of carrier is obtained, try to achieve inertial coodinate system according to the positional information turns to navigational coordinate system Change matrix;

(3) acceleration of carrier is obtained, tries to achieve the projection of acceleration under carrier coordinate system in pedestal relation coordinate system, and it is right The projection is integrated to obtain speed, and pedestal relation coordinate system is tried to achieve to the transition matrix of inertial coodinate system according to speed;

(4) in multi-period lower repeat step (3), according to the pedestal relation coordinate system tried to achieve is repeated several times to inertial coodinate system Transition matrix averaged, obtain final pedestal relation coordinate system to the transition matrix of inertial coodinate system;

(5) angular speed of carrier is obtained, acceleration is in pedestal relation coordinate under the carrier coordinate system tried to achieve according to step (3) The projection of system, gyro drift estimate is calculated, and gyro drift estimate is fed back into angular speed and carries out drift compensation, according to benefit Angular speed after repaying tries to achieve carrier coordinate system to the transition matrix of pedestal relation coordinate system;

(6) pedestal relation coordinate system is calculated to the error of the transition matrix of inertial coodinate system;

(7) given threshold, threshold value and error size are compared, when error is less than threshold value, then into step (8);Work as error During more than threshold value, return to step (3);

(8) by the transition matrix of inertial coodinate system to navigational coordinate system, turn of pedestal relation coordinate system to inertial coodinate system Change matrix and carrier coordinate system and carry out product to the transition matrix of pedestal relation coordinate system, obtain carrier coordinate system and sat to navigation The transition matrix of system is marked, so as to realize the initial alignment of carrier.

The beneficial effects of the invention are as follows:

(1) whether this method judges the environment of now system application in height according to step (6) and the error of step (7) Dynamically, under the precision conditions for meeting system requirements, the initial alignment time is constantly adjusted according to application environment, so, full Under conditions of pedal system required precision, initially it is aligned with the shortest time, to meet the requirement of system rapidity.

(2) this method has used multi-period average value in step (4) and gyro drift estimation is added in step (5) Value complement is repaid, it will and it is higher than the dynamic alignment precision of prior art, if the initial alignment of same precision, the inventive method need to be completed Time used also can be more shorter than the time used in the dynamic alignment of prior art.

(3) the initial alignment of this method is dynamic alignment, it is not required that equipment is in static state, is so also more suitable for The actual use of communication in moving equipment.

On the basis of above-mentioned technical proposal, the present invention can also do following improvement.

Further, the inertial coodinate system is i systems, is specifically defined as:Origin is located at earth center, and z-axis is pointed to along the earth's axis North, x, y-axis are respectively directed to two fixed stars in space on earth;

The navigational coordinate system is n systems, is specifically defined as:Origin is located at carrier center of gravity, and x-axis points to east, and y-axis points to north, z Axle points to day, i.e. northeast day coordinate system;

The carrier coordinate system is b systems, is specifically defined as:Origin is located at carrier center of gravity, and x-axis points to right, y along carrier transverse axis Before axle points to along the carrier longitudinal axis, in z-axis sensing;

The pedestal relation coordinate system is b0 systems, is specifically defined as:The carrier coordinate system of initial time.

Further, the positional information, acceleration and angular speed are passed by GPS, acceleration transducer and gyroscope respectively Sensor obtains, and the positional information includes longitude and latitude.

Further, the inertial coodinate system in the step (2) is to the transition matrix of navigational coordinate system:

Wherein, λ is the latitude of carrier,For the longitude of carrier.

Further, the detailed process of the step (3) is:

Acceleration is projected as in pedestal relation coordinate system under carrier coordinate system:

Wherein, gbFor acceleration,Transition matrix for carrier coordinate system to pedestal relation coordinate system;

The projection is integrated to obtain speed:

Wherein, ForInverse matrix,

Transition matrix for inertial coodinate system to pedestal relation coordinate system,

If

Then,

Wherein,It isInverse matrix.

Further, acceleration is in pedestal relation coordinate under the carrier coordinate system tried to achieve in the step (5) according to step (3) The projection of system, gyro drift estimate is calculated, and gyro drift estimate is fed back into angular speed and carries out drift compensation, its is specific Process is:

Acceleration is projected as in pedestal relation coordinate system under carrier coordinate system:

Take two t at different momentsk1And tk2Projection, i.e.,:

Then, gyro drift estimate is:

It is using the above-mentioned further beneficial effect of scheme:The precision being initially aligned further is improved, makes low performance index Inertial navigation system initial alignment precision can reach high performance index inertial navigation system initial alignment precision.

Further, the carrier coordinate system in the step (5) is to the transition matrix of pedestal relation coordinate system, its detailed process For:

The differential equation be:

Wherein, Ω is the skew symmetric matrix that forms of element by angular velocity omega, ωx、ωy、ωzRespectively include gyroscope Three axis angular rates and gyro drift estimate of sensor measurement;

Take sampling period T time interval to be calculated, then:

Angular velocity omega keeps constant in whole sampling period T, then:

It can obtain:

Further, the error calculation formula of the step (6) is:

Wherein, For acceleration gbProjection in carrier coordinate system.

It is using the above-mentioned further beneficial effect of scheme:Whether decision-making system is in high dynamic state, is meeting system Under the conditions of permissible accuracy, the initial alignment time is constantly adjusted according to application environment.

Further, the step (8) is:

Wherein,For the transition matrix of inertial coodinate system to navigational coordinate system,Sat for pedestal relation coordinate system to inertia The transition matrix of system is marked,Transition matrix for carrier coordinate system to pedestal relation coordinate system.

It is using the above-mentioned further beneficial effect of scheme:Realize still can carry out degree of precision in a dynamic condition Initial alignment.

Brief description of the drawings

Fig. 1 is the inventive method flow chart.

Embodiment

The principle and feature of the present invention are described below in conjunction with accompanying drawing, the given examples are served only to explain the present invention, and It is non-to be used to limit the scope of the present invention.

As shown in figure 1, it is the combined inertial nevigation system self-adaption Initial Alignment Method provided by the invention suitable for communication in moving Flow chart, mainly for the coarse alignment that waves dynamic alignment at present and disclosure satisfy that communication in moving under dynamic condition, but this method is aligned Time is grown, the problem of can not meeting user's rapidity requirement.

A kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving, acceleration make use of to be used in pedestal Property the projection fastened change slow characteristic, while merged the judgement to dynamic characteristic, it is dynamic under different conditions for adapting to In lead to, including step:

(1) inertial coodinate system, navigational coordinate system, carrier coordinate system and pedestal relation coordinate system are defined;It is specifically defined as Under:

The inertial coodinate system is i systems, is specifically defined as:Origin is located at earth center, and z-axis points to north, x, y-axis along the earth's axis Two fixed stars in space are respectively directed on earth;

The navigational coordinate system is n systems, is specifically defined as:Origin is located at carrier center of gravity, and x-axis points to east, and y-axis points to north, z Axle points to day, i.e. northeast day coordinate system;

The carrier coordinate system is b systems, is specifically defined as:Origin is located at carrier center of gravity, and x-axis points to right, y along carrier transverse axis Before axle points to along the carrier longitudinal axis, in z-axis sensing;

The pedestal relation coordinate system is b0 systems, is specifically defined as:The carrier coordinate system of initial time.

(2) positional information of carrier is obtained, the positional information is obtained by the GPS on airborne, the position Information includes longitude and latitude, and inertial coodinate system is tried to achieve to the transition matrix of navigational coordinate system according to the positional information;

Wherein, λ is the latitude of carrier,For the longitude of carrier.

(3) acceleration of carrier is obtained, acceleration is obtained by acceleration transducer, tries to achieve acceleration under carrier coordinate system Integrated to obtain speed in the projection of pedestal relation coordinate system, and to the projection, pedestal relation coordinate is tried to achieve according to speed It is the transition matrix to inertial coodinate system, detailed process is:

Acceleration is projected as in pedestal relation coordinate system under carrier coordinate system:

Wherein, gbFor acceleration,Transition matrix for carrier coordinate system to pedestal relation coordinate system;

The projection is integrated to obtain speed:

Wherein, ForInverse matrix,

Transition matrix for inertial coodinate system to pedestal relation coordinate system,

If

Then,

Wherein,It isInverse matrix.

(4) in multi-period lower repeat step (3), according to the pedestal relation coordinate system tried to achieve is repeated several times to inertial coodinate system Transition matrix averaged, obtain final pedestal relation coordinate system to the transition matrix of inertial coodinate system;

(5) angular speed of carrier is obtained, angular speed is obtained using the gyro sensor of airborne upper installation, due to initial right Standard need to use gyro angular speed, and gyro drift will influence the precision that is initially aligned, therefore during initial alignment, carry out gyro Drift is estimated.Gyro drift estimation is theoretical using mahony, and the drift of gyro is estimated using the value of accelerometer, utilizes process The gyro angular speed of drift compensation, the precision that raising is initially aligned.Accelerate under the carrier coordinate system tried to achieve according to step (3) The projection in pedestal relation coordinate system is spent, calculates gyro drift estimate, and gyro drift estimate is fed back into angular speed and entered Row drift compensates, and tries to achieve carrier coordinate system to the transition matrix of pedestal relation coordinate system according to the angular speed after compensation, its is specific Process is:

Acceleration is projected as in pedestal relation coordinate system under carrier coordinate system:

Take two t at different momentsk1And tk2Projection, i.e.,:

Then, gyro drift estimate is:

To the transition matrix of pedestal relation coordinate system, its detailed process is carrier coordinate system:

The differential equation be:

Wherein, Ω is the skew symmetric matrix that forms of element by angular velocity omega, ωx、ωy、ωzRespectively include gyroscope Three axis angular rates and gyro drift estimate of sensor measurement;

Take sampling period T time interval to be calculated, then:

Angular velocity omega keeps constant in whole sampling period T, then:

It can obtain:

(6) pedestal relation coordinate system is calculated to the error of the transition matrix of inertial coodinate system;Error calculation formula is:

Wherein, For acceleration gbProjection in carrier coordinate system.

(7) given threshold, threshold value and error size are compared, when error is less than threshold value, then into step (8);Work as error During more than threshold value, return to step (3);

(8) by the transition matrix of inertial coodinate system to navigational coordinate systemPedestal relation coordinate system is to inertial coodinate system Transition matrixAnd carrier coordinate system is to the transition matrix of pedestal relation coordinate systemProduct is carried out, obtains carrier coordinate system To the transition matrix of navigational coordinate system:So as to realize the initial alignment of carrier.

In summary, the present invention has advantages below using the above method:

(1) whether this method judges the environment of now system application in height according to step (6) and the error of step (7) Dynamically, under the precision conditions for meeting system requirements, the initial alignment time is constantly adjusted according to application environment, so, full Under conditions of pedal system required precision, initially it is aligned with the shortest time, to meet the requirement of system rapidity.

(2) this method has used multi-period average value in step (4) and gyro drift estimation is added in step (5) Value complement is repaid, it will and it is higher than the dynamic alignment precision of prior art, if the initial alignment of same precision, the inventive method need to be completed Time used also can be more shorter than the time used in the dynamic alignment of prior art.

(3) the initial alignment of this method is dynamic alignment, it is not required that equipment is in static state, is so also more suitable for The actual use of communication in moving equipment.

The foregoing is only presently preferred embodiments of the present invention, be not intended to limit the invention, it is all the present invention spirit and Within principle, any modification, equivalent substitution and improvements made etc., it should be included in the scope of the protection.

Claims (9)

1. a kind of combined inertial nevigation system self-adaption Initial Alignment Method suitable for communication in moving, it is characterised in that including step:
(1) inertial coodinate system, navigational coordinate system, carrier coordinate system and pedestal relation coordinate system are defined;
(2) positional information of carrier is obtained, inertial coodinate system is tried to achieve to the conversion square of navigational coordinate system according to the positional information Battle array;
(3) acceleration of carrier is obtained, tries to achieve the projection of acceleration under carrier coordinate system in pedestal relation coordinate system, and to described Projection is integrated to obtain speed, and pedestal relation coordinate system is tried to achieve to the transition matrix of inertial coodinate system according to speed;
(4) in multi-period lower repeat step (3), according to turn of the pedestal relation coordinate system tried to achieve to inertial coodinate system is repeated several times Matrix averaged is changed, obtains final pedestal relation coordinate system to the transition matrix of inertial coodinate system;
(5) angular speed of carrier is obtained, acceleration is in pedestal relation coordinate system under the carrier coordinate system tried to achieve according to step (3) Projection, gyro drift estimate is calculated, and gyro drift estimate is fed back into angular speed and carries out drift compensation, after compensation Angular speed try to achieve carrier coordinate system to the transition matrix of pedestal relation coordinate system;
(6) pedestal relation coordinate system is calculated to the error of the transition matrix of inertial coodinate system;
(7) given threshold, threshold value and error size are compared, when error is less than threshold value, then into step (8);When error is more than During threshold value, return to step (3);
(8) by the transition matrix of inertial coodinate system to navigational coordinate system, the conversion square of pedestal relation coordinate system to inertial coodinate system Battle array and carrier coordinate system carry out product to the transition matrix of pedestal relation coordinate system, obtain carrier coordinate system to navigational coordinate system Transition matrix, so as to realize the initial alignment of carrier.
2. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 1 suitable for communication in moving, its feature It is, the inertial coodinate system is i systems, is specifically defined as:Origin is located at earth center, and z-axis points to north along the earth's axis, and x, y-axis exist Two fixed stars in space are respectively directed on the earth;
The navigational coordinate system is n systems, is specifically defined as:Origin is located at carrier center of gravity, and x-axis points to east, and y-axis points to north, and z-axis refers to Xiang Tian, i.e. northeast day coordinate system;
The carrier coordinate system is b systems, is specifically defined as:Origin is located at carrier center of gravity, and x-axis points to right, y-axis edge along carrier transverse axis Before the carrier longitudinal axis points to, in z-axis sensing;
The pedestal relation coordinate system is b0 systems, is specifically defined as:The carrier coordinate system of initial time.
3. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 2 suitable for communication in moving, its feature It is, the positional information, acceleration and angular speed are obtained by GPS, acceleration transducer and gyro sensor respectively, institute Stating positional information includes longitude and latitude.
4. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 3 suitable for communication in moving, its feature It is, the inertial coodinate system in the step (2) is to the transition matrix of navigational coordinate system:
Wherein, λ is the latitude of carrier,For the longitude of carrier.
5. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 4 suitable for communication in moving, its feature It is, the detailed process of the step (3) is:
Acceleration is projected as in pedestal relation coordinate system under carrier coordinate system:
<mrow> <msup> <mover> <mi>f</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mo>=</mo> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mo>*</mo> <msup> <mi>g</mi> <mi>b</mi> </msup> <mo>;</mo> </mrow>
Wherein, gbFor acceleration,Transition matrix for carrier coordinate system to pedestal relation coordinate system;
The projection is integrated to obtain speed:
<mrow> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <msub> <mi>t</mi> <mi>k</mi> </msub> </msubsup> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mo>*</mo> <msup> <mi>g</mi> <mi>b</mi> </msup> <mi>d</mi> <mi>t</mi> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <msub> <mi>t</mi> <mi>k</mi> </msub> </msubsup> <mo>-</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mo>*</mo> <msup> <mi>g</mi> <mi>i</mi> </msup> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mo>-</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mo>*</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <msub> <mi>t</mi> <mi>k</mi> </msub> </msubsup> <msup> <mi>g</mi> <mi>i</mi> </msup> <mi>d</mi> <mi>t</mi> </mrow>
Wherein, ForInverse matrix,
Transition matrix for inertial coodinate system to pedestal relation coordinate system,
If
Then,
<mrow> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mo>*</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mo>*</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> <mi>i</mi> </msubsup> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mi>i</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> </mtable> </mfenced> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>*</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msup> <mover> <mi>V</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein,It isInverse matrix.
6. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 5 suitable for communication in moving, its feature Be, under the carrier coordinate system tried to achieve in the step (5) according to step (3) acceleration pedestal relation coordinate system projection, Gyro drift estimate is calculated, and gyro drift estimate is fed back into angular speed and carries out drift compensation, its detailed process is:
Acceleration is projected as in pedestal relation coordinate system under carrier coordinate system:
<mrow> <msup> <mover> <mi>f</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mo>=</mo> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mo>*</mo> <msup> <mi>g</mi> <mi>b</mi> </msup> </mrow>
Take two t at different momentsk1And tk2Projection, i.e.,:
<mrow> <msup> <mover> <mi>f</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>g</mi> <mi>b</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msup> <mover> <mi>f</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>g</mi> <mi>b</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
Then, gyro drift estimate is:
<mrow> <mi>G</mi> <mi>y</mi> <mi>r</mi> <mi>o</mi> <mo>_</mo> <mi>b</mi> <mi>i</mi> <mi>a</mi> <mo>=</mo> <msup> <mover> <mi>f</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msup> <mover> <mi>f</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
7. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 6 suitable for communication in moving, its feature It is, the transition matrix of the carrier coordinate system in the step (5) to pedestal relation coordinate system, its detailed process is:
The differential equation be:
<mrow> <mover> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mi>o</mi> </mrow> </msubsup> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mi>o</mi> </mrow> </msubsup> <mo>*</mo> <mi>&amp;Omega;</mi> </mrow>
<mrow> <mi>&amp;Omega;</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein, Ω is the skew symmetric matrix that forms of element by angular velocity omega, ωx、ωy、ωzRespectively include gyro sensors Three axis angular rates and gyro drift estimate of device measurement;
Take sampling period T time interval to be calculated, then:
<mrow> <msub> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mi>o</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <msub> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mi>o</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msub> <mo>*</mo> <mi>e</mi> <mi>x</mi> <mi>p</mi> <munder> <mo>&amp;Integral;</mo> <mi>T</mi> </munder> <mi>&amp;Omega;</mi> <mi>d</mi> <mi>t</mi> </mrow>
Angular velocity omega keeps constant in whole sampling period T, then:
<mrow> <munder> <mo>&amp;Integral;</mo> <mi>T</mi> </munder> <mi>&amp;Omega;</mi> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>*</mo> <mi>T</mi> <mo>=</mo> <mo>&amp;lsqb;</mo> <mi>&amp;sigma;</mi> <mo>&amp;times;</mo> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow>
It can obtain:
<mrow> <msub> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mi>o</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <msub> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mi>o</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msub> <mo>*</mo> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mi>&amp;sigma;</mi> <mo>&amp;times;</mo> <mo>&amp;rsqb;</mo> <mo>.</mo> </mrow>
8. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 7 suitable for communication in moving, its feature It is, the error calculation formula of the step (6) is:
<mrow> <mi>E</mi> <mi>r</mi> <mi>r</mi> <mi>o</mi> <mi>r</mi> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mi>g</mi> <mi>i</mi> </msup> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>*</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> <mi>i</mi> </msubsup> <mo>*</mo> <msup> <mover> <mi>f</mi> <mo>~</mo> </mover> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msup> <mo>;</mo> </mrow>
Wherein,For acceleration gbProjection in carrier coordinate system.
9. the combined inertial nevigation system self-adaption Initial Alignment Method according to claim 8 suitable for communication in moving, its feature It is, the step (8) is:
<mrow> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <mo>=</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mi>n</mi> </msubsup> <mo>*</mo> <msubsup> <mi>C</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> <mi>i</mi> </msubsup> <mo>*</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mrow> <mi>b</mi> <mn>0</mn> </mrow> </msubsup> </mrow>
Wherein,For the transition matrix of inertial coodinate system to navigational coordinate system,For pedestal relation coordinate system to inertial coodinate system Transition matrix,Transition matrix for carrier coordinate system to pedestal relation coordinate system.
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