CN108955671A - A kind of Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle - Google Patents
A kind of Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle Download PDFInfo
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- CN108955671A CN108955671A CN201810379122.4A CN201810379122A CN108955671A CN 108955671 A CN108955671 A CN 108955671A CN 201810379122 A CN201810379122 A CN 201810379122A CN 108955671 A CN108955671 A CN 108955671A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/04—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means
- G01C21/08—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means involving use of the magnetic field of the earth
Abstract
The embodiment of the invention discloses one kind to be based on magnetic declination, magnetic dip angle Kalman filtering air navigation aid.The described method includes: carrier construction coordinate system, and determine carrier coordinate system to NED navigational coordinate system transition matrix；Using quaternary number, three positions, three speed, three axis accelerometer zero bias, three axis accelerometer zero bias, a magnetic declination, a magnetic dip angle, totally 18 quantity of states are as system mode；Construct the state equation of the Kalman filtering system based on magnetic declination and magnetic dip angle；Speed and the position of carrier are calculated based on Kalman filtering.In addition, carrying out the sequential update of UD in Kalman filtering, change of scale is carried out to matrix D diagonal entry, calculates the scale before completing and then switching back to, can be avoided appearance and calculate error.The technical solution of the embodiment of the present invention fully considers the influence of magnetic declination and magnetic dip angle, robustness and scalability with higher.
Description
Technical field
The present embodiments relate to navigation field more particularly to a kind of Kalman filterings based on magnetic declination, magnetic dip angle angle
Air navigation aid.
Background technique
Modern unmanned plane is generally equipped with a variety of navigation equipments, such as inertial sensor IMU, GPS etc., generallys use Kalman
Filtering carries out the resolving of data fusion and speed, position.But in traditional integrated navigation, Kalman filtering is not accounted for
Magnetic declination and magnetic dip angle, and find in engineering practice, the influence if do not considered magnetic declination and magnetic dip angle, then it will lead to complete
There is larger difference in the navigation effect of ball different regions.In addition, in the sequential update of progress Kalman filtering UD, it may appear that square
The division calculation of battle array D diagonal entry, if differing greatly between diagonal entry, it is possible that biggish calculating misses
Difference.Factors above all constrains the precision and robustness of navigation significantly.
Summary of the invention
In view of this, the embodiment of the invention provides a kind of Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle,
To solve the problems, such as to ignore in the prior art that navigation accuracy caused by the influence of magnetic declination, magnetic dip angle is low, transplantability is poor.
The embodiment of the invention provides a kind of the Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle, the method
It comprises the steps of:
Step 1: setting carrier coordinate system, three axis of carrier coordinate system are expressed as being denoted as xyz；
Step 2: determining the attitude of carrier at current time by inertial sensor, is denoted as att=[φ θ ψ], wherein φ
Roll angle is represented, θ represents pitch angle, and ψ represents course angle；
Step 3: it determines transition matrix of the carrier coordinate system to navigational coordinate system, is denoted as
Simplifying transition matrix is following form
Step 4: quaternary number q=[q is used0 q1 q2 q3], three position p=[pn pe pd], three speed v=[vn
ve vd], three axis accelerometer zero bias ba=[bax bay baz], three axis accelerometer zero bias bω=[bωx bωy bωz], a magnetic biasing
Angle α, magnetic dip angle γ this 18 quantity of states are denoted as X=[q as system mode0 q1 q2 q3 pn pe pd vn ve vd
bax bay baz bωx bωy bωz α γ]T；
Step 5: Kalman filtering of the building based on magnetic declination, magnetic dip angle；
Step 6: the resolving of bearer rate, position is carried out according to the Kalman filtering based on magnetic declination, magnetic dip angle.
Preferably, the carrier coordinate system is connected firmly with carrier, and coordinate system meets right-hand rule, and origin is in carrier center of gravity, x
Axis is directed toward carrier direction of advance, and y-axis is directed toward on the right side of carrier by origin, and z-axis direction is determined according to xy axis by right-hand rule；It is described
Navigational coordinate system is NED navigational coordinate system.
Preferably, if the state equation of Kalman filtering system are as follows:
Wherein,For the derivative of system mode, f (x) is the function of system mode, and w is system noise, and Z is the amount of system
Survey state, h (x) are the state quantity measurement function of system, and v is to measure noise；
NoteAbove formula is embodied as:
Wherein,It is body to the transition matrix of quaternary number；
If position Z in metric datap=[Zpn Zpe Zpd]T, speed Zv=[Zvn Zve Zvd]T, the three-axle magnetic field of body
Intensity is Zm=[Zmx Zmy Zmz]T, BeIt and, is constant known to one for magnetic-field vector of the earth；
Then the measurement vector of system can be expressed as
Z=[Zpn Zpe Zpd Zvn Zve Zvd Zmx Zmy Zmz]T (6)
To f (x) and h (x), it solves Jacobian matrix and obtains matrix F and H, the state equation after can obtaining system linearization
Preferably, the Kalman filtering includes the time updating and measuring amendment；
The specific steps that time updates include:
Wherein, vectorFor the one-step prediction value of system mode vector, vectorFor the estimated value of last moment,
Matrix Φ is the discrete form of matrix F, Φk/k-1For Matrix of shifting of a step, matrix Pk/k-1For the one-step prediction side of state vector
Poor matrix, matrix Pk/k-1For the last moment variance matrix of state vector, matrix QkFor system noise variance matrix；
It is described to measure modified specific steps and include:
Wherein, vectorFor the current maximum likelihood estimate of system mode vector, matrix KkFor gain matrix, matrix HkFor amount
Survey matrix, matrix RkTo measure noise sequence variance matrix, matrix I is unit matrix.
Preferably, when carrying out Kalman filtering, in order to eliminate the influence of numerical error, nonnegative definite variance matrix is sat such as
Lower decomposition:
If matrix D is n rank square matrix, there was only diagonal entry is non-zero element, by using normalized method, by square
The data of battle array D element are limited in [0,1], are prevented because the difference of data scale causes to dissipate, specific method for normalizing is as follows:
Matrix D completes change of scale at this time.
The Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle that the embodiment of the invention provides a kind of, uses improvement
Kalman filter method, fully consider the influence of magnetic declination and magnetic dip angle, have higher robustness and scalability；And it is directed to
The Kalman filter of the sequential update of UD, it is contemplated that in the sequential update of progress UD, it may appear that removed to matrix D diagonal entry
Method calculates, if differing greatly between diagonal entry, it is possible that calculating error, therefore carries out ruler to diagonal entry
Degree transformation, calculates the scale before completing and then switching back to.The method has operand small, and extension is convenient, calculation accuracy
The advantages that high.
Detailed description of the invention
Fig. 1 is a kind of Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle that the embodiment of the present invention one provides
Flow chart；
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawing to of the invention specific real
Example is applied to be described in further detail.It is understood that specific embodiment described herein is used only for explaining the present invention,
Rather than limitation of the invention.
It also should be noted that only the parts related to the present invention are shown for ease of description, in attached drawing rather than
Full content.It should be mentioned that some exemplary embodiments are described before exemplary embodiment is discussed in greater detail
At the processing or method described as flow chart.Although operations (or step) are described as the processing of sequence by flow chart,
It is that many of these operations can be implemented concurrently, concomitantly or simultaneously.In addition, the sequence of operations can be by again
It arranges.The processing can be terminated when its operations are completed, it is also possible to have the additional step being not included in attached drawing.
The processing can correspond to method, function, regulation, subroutine, subprogram etc..
Embodiment one
The embodiment of the present invention one can specifically be applied in the product for needing high-precision navigation, if unmanned plane positions, be driven automatically
It sails, digital city, robot navigation etc..Fig. 1 is a kind of karr based on magnetic declination, magnetic dip angle that the embodiment of the present invention one provides
The flow chart of graceful filtering air navigation aid.The method of the present embodiment specifically includes:
110, carrier coordinate system is set, and three axis of carrier coordinate system is expressed as being denoted as xyz.
In this city example, the carrier coordinate system is connected firmly with carrier, and coordinate system meets right-hand rule, and origin is in carrier weight
At the heart, x-axis is directed toward carrier direction of advance, and y-axis is directed toward on the right side of carrier by origin, and z-axis direction is determined according to xy axis by right-hand rule.
120, the attitude of carrier that current time is determined by inertial sensor is denoted as att=[φ θ ψ], and wherein φ is represented
Roll angle, θ represent pitch angle, and ψ represents course angle.
130, it determines transition matrix of the carrier coordinate system to navigational coordinate system, is denoted as
Simplifying transition matrix is following form
140, the Kalman filtering based on magnetic declination, magnetic dip angle is constructed.
In the present embodiment, using quaternary number q=[q0 q1 q2 q3], three position p=[pn pe pd], three speed v
=[vn ve vd], three axis accelerometer zero bias ba=[bax bay baz], three axis accelerometer zero bias bω=[bωx bωy bωz], one
A magnetic declination α, magnetic dip angle γ this 18 quantity of states are denoted as X=[q as system mode0 q1 q2 q3 pn pe pd vn
ve vd bax bay baz bωx bωy bωz α γ]T。
If the state equation of Kalman filtering system are as follows:
Wherein,For the derivative of system mode, f (x) is the function of system mode, and w is system noise, and Z is the amount of system
Survey state, h (x) are the state quantity measurement function of system, and v is to measure noise；
NoteAbove formula is embodied as:
Wherein,It is body to the transition matrix of quaternary number；
If position Z in metric datap=[Zpn Zpe Zpd]T, speed Zv=[Zvn Zve Zvd]T, the three-axle magnetic field of body
Intensity is Zm=[Zmx Zmy Zmz]T, BeIt and, is constant known to one for magnetic-field vector of the earth；
Then the measurement vector of system can be expressed as
Z=[Zpn Zpe Zpd Zvn Zve Zvd Zmx Zmy Zmz]T (6)
To f (x) and h (x), it solves Jacobian matrix and obtains matrix F and H, the state equation after can obtaining system linearization
150, the resolving of bearer rate, position is carried out according to the Kalman filtering based on magnetic declination, magnetic dip angle.
In the present embodiment, the Kalman filtering includes the time updating and measuring amendment；
The specific steps that time updates include:
Wherein, vectorFor the one-step prediction value of system mode vector, vectorFor the estimated value of last moment,
Matrix Φ is the discrete form of matrix F, Φk/k-1For Matrix of shifting of a step, matrix Pk/k-1For the one-step prediction side of state vector
Poor matrix, matrix Pk/k-1For the last moment variance matrix of state vector, matrix QkFor system noise variance matrix；
It is described to measure modified specific steps and include:
Wherein, vectorFor the current maximum likelihood estimate of system mode vector, matrix KkFor gain matrix, matrix HkFor amount
Survey matrix, matrix RkTo measure noise sequence variance matrix, matrix I is unit matrix.
Preferably, when carrying out Kalman filtering, in order to eliminate the influence of numerical error, nonnegative definite variance matrix is sat such as
Lower decomposition:
If matrix D is n rank square matrix, there was only diagonal entry is non-zero element, by using normalized method, by square
The data of battle array D element are limited in [0,1], are prevented because the difference of data scale causes to dissipate, specific method for normalizing is as follows:
Matrix D completes change of scale at this time.
The Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle that the embodiment of the invention provides a kind of, uses improvement
Kalman filter method, fully consider the influence of magnetic declination and magnetic dip angle, have higher robustness and scalability；And it is directed to
The Kalman filter of the sequential update of UD, it is contemplated that in the sequential update of progress UD, it may appear that removed to matrix D diagonal entry
Method calculates, if differing greatly between diagonal entry, it is possible that calculating error, therefore carries out ruler to diagonal entry
Degree transformation, calculates the scale before completing and then switching back to.The method has operand small, and extension is convenient, calculation accuracy
The advantages that high.
It should also be noted that the above is only a better embodiment of the present invention and the applied technical principle.Those skilled in the art
It will be appreciated that the invention is not limited to the specific embodiments described herein, it is able to carry out for a person skilled in the art various obvious
Variation, readjustment and substitution without departing from protection scope of the present invention.Therefore, although by above embodiments to this hair
It is bright to be described in further detail, but the present invention is not limited to the above embodiments only, in the feelings for not departing from present inventive concept
It can also include more other equivalent embodiments under condition, and the scope of the invention is determined by the scope of the appended claims.
Claims (5)
1. a kind of Kalman filtering air navigation aid based on magnetic declination, magnetic dip angle, which is characterized in that the method includes following step
It is rapid:
Step 1: setting carrier coordinate system, three axis of carrier coordinate system are expressed as being denoted as xyz；
Step 2: determining the attitude of carrier at current time by inertial sensor, is denoted as att=[φ θ ψ], and wherein φ is represented
Roll angle, θ represent pitch angle, and ψ represents course angle；
Step 3: it determines transition matrix of the carrier coordinate system to navigational coordinate system, is denoted as
Simplifying transition matrix is following form
Step 4: quaternary number q=[q is used0 q1 q2 q3], three position p=[pn pe pd], three speed v=[vn ve
vd], three axis accelerometer zero bias ba=[bax bay baz], three axis accelerometer zero bias bω=[bωx bωy bωz], a magnetic declination α,
One magnetic dip angle γ this 18 quantity of state is denoted as X=[q as system mode0 q1 q2 q3 pn pe pd vn ve vd bax bay
baz bωx bωy bωz α γ]T；
Step 5: Kalman filtering of the building based on magnetic declination, magnetic dip angle；
Step 6: the resolving of bearer rate, position is carried out according to the Kalman filtering based on magnetic declination, magnetic dip angle.
2. coordinate system meets the method according to claim 1, wherein the carrier coordinate system is connected firmly with carrier
Right-hand rule, for origin in carrier center of gravity, x-axis is directed toward carrier direction of advance, and y-axis is directed toward on the right side of carrier by origin, z-axis direction root
It is determined according to xy axis by right-hand rule；The navigational coordinate system is NED navigational coordinate system.
3. the method according to claim 1, wherein setting the state equation of Kalman filtering system are as follows:
Wherein,For the derivative of system mode, f (x) is the function of system mode, and w is system noise, and Z is the measurement shape of system
State, h (x) are the state quantity measurement function of system, and v is to measure noise；
NoteAbove formula is embodied as:
Wherein,It is body to the transition matrix of quaternary number；
If position Z in metric datap=[Zpn Zpe Zpd]T, speed Zv=[Zvn Zve Zvd]T, the three-axle magnetic field intensity of body
For Zm=[Zmx Zmy Zmz]T, BeIt and, is constant known to one for magnetic-field vector of the earth；
Then the measurement vector of system can be expressed as
Z=[Zpn Zpe Zpd Zvn Zve Zvd Zmx Zmy Zmz]T (6)
To f (x) and h (x), it solves Jacobian matrix and obtains matrix F and H, the state equation after can obtaining system linearization
4. according to the method described in claim 3, it is characterized in that, the Kalman filtering includes that time update and measurement are repaired
Just；
The specific steps that time updates include:
Wherein, vectorFor the one-step prediction value of system mode vector, vectorFor the estimated value of last moment, matrix Φ
For the discrete form of matrix F, Φk/k-1For Matrix of shifting of a step, matrix Pk/k-1For the one-step prediction variance square of state vector
Battle array, matrix Pk/k-1For the last moment variance matrix of state vector, matrix QkFor system noise variance matrix；
It is described to measure modified specific steps and include:
Wherein, vectorFor the current maximum likelihood estimate of system mode vector, matrix KkFor gain matrix, matrix HkTo measure square
Battle array, matrix RkTo measure noise sequence variance matrix, matrix I is unit matrix.
5. according to the method described in claim 4, it is characterized in that, when carrying out Kalman filtering, in order to eliminate numerical error
Influence, following decompose is sat to nonnegative definite variance matrix:
If matrix D is n rank square matrix, there was only diagonal entry is non-zero element, by using normalized method, by matrix D member
The data of element are limited in [0,1], are prevented because the difference of data scale causes to dissipate, specific method for normalizing is as follows:
Matrix D completes change of scale at this time.
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| CN112833917A (en) * | 2021-01-27 | 2021-05-25 | 北京航空航天大学 | Three-axis magnetic sensor calibration method based on magnetic course angle and least square method |
| CN115900770A (en) * | 2023-02-14 | 2023-04-04 | 北京理工大学前沿技术研究院 | Online correction method and system for magnetic sensor in airborne environment |
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| CN115900770A (en) * | 2023-02-14 | 2023-04-04 | 北京理工大学前沿技术研究院 | Online correction method and system for magnetic sensor in airborne environment |
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