CN106403997A - Dynamic fine alignment method for inertial strapdown system - Google Patents
Dynamic fine alignment method for inertial strapdown system Download PDFInfo
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- CN106403997A CN106403997A CN201610780385.7A CN201610780385A CN106403997A CN 106403997 A CN106403997 A CN 106403997A CN 201610780385 A CN201610780385 A CN 201610780385A CN 106403997 A CN106403997 A CN 106403997A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
Abstract
The invention discloses a dynamic fine alignment method for an inertial strapdown system. The method comprises the following steps: a step 1, coordinates are defined; a step 2, an i system error angle phi i is calculated; a step 3, an attitude transformation matrix is calculated in order to complete a dynamic fine alignment process. The problems of low aligning precision and long aligning time in the prior aligning methods are solved.
Description
【Technical field】
The invention belongs to strap-down inertial technical field is and in particular to a kind of side of the dynamic fine alignment of inertia strapdown system
Method.
【Background technology】
In actual be aligned environment, rock because external interference produces to pedestal, lead to inertial sensor part measurement output letter
In number in addition to containing rotational-angular velocity of the earth component, also comprise carrier and rock constant angular velocity information so that the noise of signal
Than reduction.So the attitude that application coarse alignment method obtains in inertial coodinate system can have error, real by gyro output
When calculated posture changing matrix there is also error.The presence of these errors makes alignment precision reduce, and to punctual
Between extend.
【Content of the invention】
It is an object of the invention to provide a kind of method of the dynamic fine alignment of inertia strapdown system, to solve existing alignment methods
Alignment precision low, be aligned time length problem.
The present invention employs the following technical solutions:A kind of method of the dynamic fine alignment of inertia strapdown system, according to following steps
Implement:
Step one, definition coordinate:
1) geocentric inertial coordinate system, i.e. i system:Plane is interior under the line and points to the first point of Aries for X-axis, and Z axis point to earth rotation side
To three axles constitute right-handed coordinate system;
2) i' system:An error angle φ is contained between calculated i system, and true i systemi;
3) " right-front-on " coordinate system defining carrier is strapdown inertial measurement unit coordinate system, i.e. b system;
4) choosing " east-north-sky " coordinate system is navigational coordinate system, i.e. n system;
Step 2, calculating i system error angle φi:
If the attitude matrix of t i system isI' system attitude matrix isAnd calculate i' system with respect to i
The attitude error angle of system is φi;
Step 3, calculating posture changing matrixComplete dynamic fine alignment process:
Attitude matrix is obtained by following formula (11)Accurate estimation, that is,
In formula, t2For fine alignment finish time.
Further, calculating attitude error angle in step 2 is φiConcrete grammar be:
2.1) i system is with respect to the transformation matrix of coordinates of b systemThe differential equation be:
In formula,For the actual rotation angular velocity of carrier,
Due to the actual Output speed of gyroIn contain gyroscopic drift ε, that is,
2.2) Practical Calculation inertial coodinate system i' system is with respect to the transformation matrix of carrier coordinate system b systemThe differential equation
For:
2.3) according to above-mentionedWithThe differential equation, calculate the attitude error fastened of strapdown system inertial coordinate micro-
Divide equation, attitude error angular estimation value φ is updated with iterationi.
Further, step 2.3) concrete grammar be:
Order
Then have
Formula (1) is substituted into formula (4), and omits second order in a small amount, obtain:
Again by formula (3) both sides to time derivation, derivation obtainsBy in formulaSubstituted with (1) formula,
?:
Abbreviation is compared to upper facial (5) and formula (6),
?:
Take advantage of on above-mentioned formula (7) the both sides right sideObtain the attitude error equation that strapdown system inertial coordinate is fastened:
Because gyroscopic drift ε includes gyroscope constant value drift εbMeasure white noise with gyroAssumeFor Gauss white noise
Sound, then
Composite type (8), formula (9) two formula, obtain the differential equation at the attitude error angle that strapdown system inertial coordinate is fastened:
Further, the circular of step 3 is:
3.1) fine alignment finish time, n system with respect to the transformation matrix of coordinates of i system is:
Wherein, λ is t2 moment latitude, and L is t2 moment longitude, and dt is the fine alignment time, wieRepresent rotational-angular velocity of the earth;
3.2) i system with respect to the transformation matrix of coordinates of i' system is:
33) fine alignment finish time, i system with respect to the transformation matrix of coordinates of b system isAt the end of coarse alignment
ObtainAnd gyro output valve is asked for during fine alignment.
The invention has the beneficial effects as follows:SINS for swaying base gives a kind of accurate alignment method, makes
With the method, so that SINS can be aligned in traveling, improve mobility and the alignment precision of system, subtract
Lack the system alignment time.
【Specific embodiment】
Below by embodiment, technical scheme is described in further detail.
The invention provides a kind of method of the dynamic fine alignment of inertia strapdown system, implement according to following steps:
Step one, definition coordinate:
1) geocentric inertial coordinate system (i system):Plane is interior under the line and points to the first point of Aries for X-axis, and Z axis point to earth rotation side
To three axles constitute right-handed coordinate system;
2) i' system is to contain an error angle φ between calculated i system, and true i systemi;
3) " right-front-on " coordinate system defining carrier is strapdown inertial measurement unit coordinate system (b system);
4) choosing " east-north-sky " coordinate system is navigational coordinate system (n system);
Step 2, calculating i system error angle φi:
Wherein, φiIt is the error angle between i' system and true i system.
If the attitude matrix of t i system isI' system attitude matrix isAnd calculate i' system with respect to i
The attitude error angle of system is φi.T is coarse alignment finish time, fine alignment start time.
Attitude error angle is φiCircular be:
2.1) i system is with respect to the transformation matrix of coordinates of b systemThe differential equation be:
In formula,For the actual rotation angular velocity of carrier,
Due to the actual Output speed of gyroIn contain gyroscopic drift ε, that is,
2.2) Practical Calculation inertial coodinate system i' system is with respect to the transformation matrix of carrier coordinate system b systemThe differential equation
For:
2.3) according to above-mentionedWithThe differential equation, calculate the attitude error fastened of strapdown system inertial coordinate micro-
Divide equation, attitude error angular estimation value φ is updated with iterationi:
This attitude error differential equation circular is:
Order
Then have
Formula (1) is substituted into formula (4), and omits second order in a small amount, obtain:
Again by formula (3) both sides to time derivation, derivation obtainsBy in formulaSubstituted with (1) formula,
?:
Abbreviation is compared to upper facial (5) and formula (6),
?:
Take advantage of on above-mentioned formula (7) the both sides right sideObtain the attitude error equation that strapdown system inertial coordinate is fastened:
Because gyroscopic drift ε includes gyroscope constant value drift εbMeasure white noise with gyroAssumeFor Gauss white noise
Sound, then
Composite type (8), formula (9) two formula, obtain the differential equation at the attitude error angle that strapdown system inertial coordinate is fastened:
Step 3, calculating posture changing matrix
Attitude matrix is obtained by following formula (11)Accurate estimation, that is,:
In formula, t2For fine alignment finish time,
3.1) fine alignment finish time, n system with respect to the transformation matrix of coordinates of i system is:
Wherein, λ is t2 moment latitude, and L is t2 moment longitude, and dt is the fine alignment time, wieRepresent rotational-angular velocity of the earth;
3.2) i system with respect to the transformation matrix of coordinates of i' system is:
3.3) fine alignment finish time, i system with respect to the transformation matrix of coordinates of b system isAt the end of coarse alignment
ObtainAnd gyro output valve is asked for during fine alignment:It is coarse alignment finish timeMatrix,It isThe differential equation;It is gyro sampled data;By runge kutta method or complete card update algorithm
All can iteration obtainRunge kutta method or complete card update algorithm are the classical derivation algorithms of the differential equation.
In existing alignment methods, general fine alignment is all carried out in the quiescent state, and time-consuming, now system can not do right
Thing beyond standard.And the dynamic fine alignment of the present invention, with inertial coodinate system as basis reference, by pose transformation matrix's
Calculating is converted into i system error angle φiCalculating, system can be allowed to be aligned in traveling, increased maneuverability.For rocking
The SINS of pedestal gives a kind of accurate alignment method, using the method, makes SINS in traveling
It is aligned, improve mobility and the alignment precision of system, decrease the system alignment time.Solve existing alignment methods
Alignment precision low, be aligned time length problem.
Claims (4)
1. a kind of method of the dynamic fine alignment of inertia strapdown system is it is characterised in that implement according to following steps:
Step one, definition coordinate:
1) geocentric inertial coordinate system, i.e. i system:X-axis is under the line in plane and point to the first point of Aries, and Z axis point to earth rotation direction, and three
Axle constitutes right-handed coordinate system;
2) i' system:An error angle φ is contained between calculated i system, and true i systemi;
3) " right-front-on " coordinate system defining carrier is strapdown inertial measurement unit coordinate system, i.e. b system;
4) choosing " east-north-sky " coordinate system is navigational coordinate system, i.e. n system;
Step 2, calculating i system error angle φi:
If the attitude matrix of t i system isI' system attitude matrix isAnd calculate the appearance that i' system is with respect to i system
State error angle is φi;
Step 3, calculating posture changing matrixComplete dynamic fine alignment process:
Attitude matrix is obtained by following formula (11)Accurate estimation, that is,
In formula, t2For fine alignment finish time.
2. the method for the dynamic fine alignment of inertia strapdown system as claimed in claim 1 is it is characterised in that described step 2 is fallen into a trap
Calculating attitude error angle is φiConcrete grammar be:
2.1) i system is with respect to the transformation matrix of coordinates of b systemThe differential equation be:
In formula,For the actual rotation angular velocity of carrier,
Due to the actual Output speed of gyroIn contain gyroscopic drift ε, that is,
2.2) Practical Calculation inertial coodinate system i' system is with respect to the transformation matrix of carrier coordinate system b systemThe differential equation be:
2.3) according to above-mentionedWithThe differential equation, calculate the attitude error differential side that fastens of strapdown system inertial coordinate
Journey, updates attitude error angular estimation value φ with iterationi.
3. the method for the dynamic fine alignment of inertia strapdown system as claimed in claim 2 is it is characterised in that described step 2.3)
Concrete grammar is:
Order
Then have
Formula (1) is substituted into formula (4), and omits second order in a small amount, obtain:
Again by formula (3) both sides to time derivation, derivation obtainsBy in formulaWith
(1) formula substitutes,
?:
Abbreviation is compared to upper facial (5) and formula (6),
?:
Take advantage of on above-mentioned formula (7) the both sides right sideObtain the attitude error equation that strapdown system inertial coordinate is fastened:
Because gyroscopic drift ε includes gyroscope constant value drift εbMeasure white noise with gyroAssumeFor white Gaussian noise, then
Composite type (8), formula (9) two formula, obtain the differential equation at the attitude error angle that strapdown system inertial coordinate is fastened:
4. the method for the dynamic fine alignment of inertia strapdown system as claimed in claim 1 is it is characterised in that the tool of described step 3
Body computational methods are:
3.1) fine alignment finish time, n system with respect to the transformation matrix of coordinates of i system is:
Wherein, λ is t2 moment latitude, and L is t2 moment longitude, and dt is the fine alignment time, wieRepresent rotational-angular velocity of the earth;
3.2) i system with respect to the transformation matrix of coordinates of i' system is:
3.3) fine alignment finish time, i system with respect to the transformation matrix of coordinates of b system isObtained by the end of coarse alignment
'sAnd gyro output valve is asked for during fine alignment.
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Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN103245360A (en) * | 2013-04-24 | 2013-08-14 | 北京工业大学 | Autocollimation method of carrier aircraft rotating type strapdown inertial navigation system under shaking base |
CN103557871A (en) * | 2013-10-22 | 2014-02-05 | 北京航空航天大学 | Strap-down inertial navigation air initial alignment method for floating aircraft |
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Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN103245360A (en) * | 2013-04-24 | 2013-08-14 | 北京工业大学 | Autocollimation method of carrier aircraft rotating type strapdown inertial navigation system under shaking base |
CN103557871A (en) * | 2013-10-22 | 2014-02-05 | 北京航空航天大学 | Strap-down inertial navigation air initial alignment method for floating aircraft |
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Application publication date: 20170215 |