CN111121766B - Astronomical and inertial integrated navigation method based on starlight vector - Google Patents
Astronomical and inertial integrated navigation method based on starlight vector Download PDFInfo
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- CN111121766B CN111121766B CN201911305233.1A CN201911305233A CN111121766B CN 111121766 B CN111121766 B CN 111121766B CN 201911305233 A CN201911305233 A CN 201911305233A CN 111121766 B CN111121766 B CN 111121766B
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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
- G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention discloses an astronomical and inertial integrated navigation method based on a starlight vector, which comprises the steps of establishing an inertial navigation attitude, speed and position updating model; establishing an astronomical and inertial integrated navigation state quantity model; establishing an astronomical and inertial integrated navigation measurement model; a discretized astronomical and inertial integrated navigation state quantity model and a measurement model are used for estimating a position error value, a speed error value and an attitude error value contained in an output value of an inertial navigation update model on line by using Kalman filtering; correcting the position, speed and attitude values according to the estimated values; outputting the gesture, speed and position results obtained by combining astronomical and inertial navigation, judging whether the navigation is finished, and repeating the steps if the navigation is not finished. According to the method, the installation error angle of the astronomical navigation sensor is added into the inertial and astronomical navigation state quantity model, so that the precision of astronomical and inertial integrated navigation is improved.
Description
Technical Field
The invention relates to a combined navigation technology, in particular to an astronomical and inertial combined navigation method based on a starlight vector.
Background
In recent years, along with development and development of high-altitude long-endurance unmanned aerial vehicles, requirements on a navigation system of the high-altitude long-endurance unmanned aerial vehicle are also improved, and the navigation system is required to provide high-precision position values, speed values and attitude values for the high-altitude long-endurance unmanned aerial vehicle all-weather. The unmanned aerial vehicle with high altitude and long endurance mostly uses an inertial and astronomical combined navigation system to provide high-precision position, speed and gesture information for the unmanned aerial vehicle. The traditional astronomical and inertial integrated navigation method needs to perform ground calibration on the installation error angle of the astronomical navigation sensor, the ground calibration value of the installation error angle is used as the true value of the installation error angle of the astronomical navigation sensor to deduce the astronomical and inertial integrated navigation method, but a certain difference still exists between the ground calibration value of the installation error angle and the true value of the installation error angle, which reduces the accuracy of integrated navigation. In addition, the traditional astronomical and inertial integrated navigation method needs that an astronomical navigation sensor at least identifies 3 satellites to correct error values in inertial navigation output position, speed and attitude values, but the astronomical navigation sensor is disturbed by sunlight in the daytime, and the number of the identified satellites cannot guarantee more than 3, so that the precision and reliability of astronomical and inertial integrated navigation are further reduced.
Disclosure of Invention
The invention aims to provide an astronomical and inertial integrated navigation method based on a starlight vector.
The technical solution for realizing the purpose of the invention is as follows: an astronomical and inertial integrated navigation method based on starlight vectors comprises the following steps:
step 3, establishing an astronomical and inertial integrated navigation measurement model according to the starlight vector under the inertial coordinate system and the starlight vector under the star-sensitive coordinate system;
and 6, outputting the gesture, speed and position results obtained by combining astronomical and inertial navigation, judging whether the navigation is finished, and if not, performing the step 1.
Compared with the prior art, the invention has the remarkable advantages that: 1) The installation error angle of the astronomical navigation sensor is introduced to construct a state model, so that the precision of astronomical and inertial integrated navigation is improved; 2) And a measurement model is constructed by using the starlight vector, so that the combined navigation of astronomy and inertia can be completed under the condition that fewer than 3 stars are identified by the astronomical navigation sensor, and the reliability of the combined navigation of astronomy and inertia is improved.
Drawings
FIG. 1 is a flow chart of an astronomical and inertial integrated navigation method based on starlight vectors.
Fig. 2 is a flight trajectory diagram of an embodiment of the present invention.
FIG. 3 is a graph showing the comparison of the roll angle error results of the method of the present invention and the conventional method.
FIG. 4 is a graph showing the pitch angle error results of the method of the present invention compared to the conventional method.
FIG. 5 is a graph showing the comparison of yaw angle error results of the method of the present invention and the conventional method.
FIG. 6 is a graph showing the comparison of the east speed error results of the method of the present invention and the conventional method.
FIG. 7 is a graph showing the comparison of the north velocity error results of the method of the present invention and the conventional method.
FIG. 8 is a graph showing the comparison of the results of the tangential velocity error in the method of the present invention and the conventional method.
FIG. 9 is a graph showing the comparison of longitude error results of the method of the present invention and the conventional method.
FIG. 10 is a graph showing comparison of latitude error results of the method of the present invention and conventional methods.
FIG. 11 is a comparison of the results of the height error of the method of the present invention and the conventional method.
Detailed Description
The present invention will be further described with reference to the drawings and the specific embodiments.
As shown in fig. 1, the astronomical and inertial integrated navigation method based on the starlight vector comprises the following steps:
According to Newton's law of mechanics and Euler's theorem of fixed point rotation of rigid body, the attitude, speed and position updating model of inertial navigation is established under a local geographic coordinate system, namely an east-north-sky coordinate system, as follows:
and (3) updating a model by the gesture:
wherein, the liquid crystal display device comprises a liquid crystal display device,
posture transformation matrix representing carrier coordinate system to local geographic coordinate system, < >>
Representation->
Is used for the purpose of determining the derivative of (c),
representing the angular velocity of the inertial frame relative to the carrier frame, measured by the inertial navigation sensor gyroscope,
the angular velocity of the inertial coordinate system relative to the local geographic coordinate system is represented, x being the inverse of this matrix representation.
And (3) updating a model by speed:
wherein v represents the speed of the carrierValues in the form of v= [ v ] E v N v U ] T Respectively representing the east and north speeds and the sky speed of the carrier under a local geographic coordinate system,
for v derivative, < >>
Posture transformation matrix representing carrier coordinate system to local geographic coordinate system, < >>
The specific force value of the carrier in the carrier system is represented and is measured by an inertial navigation sensor accelerometer; />
Expressed as the angular velocity of rotation of the earth->
Represents the angular velocity, g, of the local geographic coordinate system relative to the geocentric fixed coordinate system n The x represents the inverse of this matrix representation for the gravitational acceleration of the position of the carrier.
A location update model:
in the formula (3), r= [ lambda L h ]] T The longitude, latitude and altitude values respectively representing the position of the carrier,
represents the derivative of R, R M And R is N The meridian radius and the mortise unitary radius of the position, v E 、v N And v U The east and north and sky speeds in the local geographic coordinate system are represented, respectively.
Firstly, establishing a model of gyro noise epsilon and accelerometer noise
Model of (2)
Wherein ε b And
the random constant zero drift representing the gyroscope and the accelerometer is a constant value; epsilon g And->
Is white gaussian noise.
Then the triaxial gyroscope error model epsilon x ε y ε z Triaxial accelerometer error model
The method comprises the following steps:
wherein [ epsilon ] x ε y ε z ] T Respectively representing the total measurement error of the x, y and z axis gyroscopes, [ epsilon ] bx ε by ε bz ] T Representing the random constant zero drift error component of the x, y and z axis gyroscopes [ epsilon ] gx ε gy ε gz ] T Representing gaussian white noise error components of the x-, y-, z-axis gyroscopes,
indicating the total measurement error of the x, y and z-axis accelerometer, < >>
Representing random constant zero drift error component of x, y and z axis accelerometer, +.>
Representing the white gaussian noise error components of the x, y, z axis accelerometer.
According to the inertial navigation system update model and the error model of the gyroscope and the accelerometer, an astronomical and inertial combined navigation state quantity model can be obtained, and the method comprises the following steps:
misalignment angle error model
Wherein phi = [ phi ] E φ N φ U ] T Referred to as a misalignment angle error,
is the derivative of phi, δv= [ δv ] E δv N δv U ] T Respectively represent east-direction speed error, north-direction speed error and sky-direction speed error, δr= [ δlδλδh ]] T Representing latitude, longitude and altitude errors, respectively. [ epsilon ] x ε y ε z ]Representing the measurement errors contained in the measurements from the tri-axial gyroscopes,
representing the measurement error, ω, contained in the measurement by the triaxial accelerometer ie The rotational angular velocity of the earth is represented,
representing a pose transformation matrix of a carrier coordinate system to a local geographic coordinate system, R M And R is N The radius of the meridian and the radius of the mortise unitary circle at the position are respectively, L and h are latitude value and height value of the position of the carrier, v E And v N The east and north velocities in the local geographic coordinate system are represented, respectively, and x represents the inverse of this matrix representation.
Speed error model
Wherein phi = [ phi ] E φ N φ U ] T As misalignment angle error δv= [ δv ] E δv N δv U ] T Respectively represent an east speed error value, a north speed error value and an sky speed error value,
is the derivative of δv, δr= [ δlδλδh] T Respectively represent latitude error value, longitude error value and altitude error value, [ epsilon ] x ε y ε z ]Representing the measurement errors contained in the measurements from the tri-axial gyroscopes,
representing the measurement error, ω, contained in the measurement by the triaxial accelerometer ie Indicating the rotation angular velocity of the earth as a constant value, < ->
Representing a pose transformation matrix of a carrier coordinate system to a local geographic coordinate system, R M And R is N The meridian radius and the mortise unitary radius of the position are respectively,is uniquely determined by the position of the carrier, L and h are latitude value and altitude value of the position of the carrier, v E 、v N And v U The east and north and sky speeds under the local geographic coordinate system are represented, respectively, x represents the inverse of this matrix representation.
Position error model:
δr＝[δL δλ δh] T to represent the latitude error value, the longitude error value and the altitude error value respectively,
is the derivative of δr, R M And R is N The radius of the meridian and the radius of the mortise circle at the position are respectively determined uniquely by the position of the carrier, L and h are the latitude value and the height value of the position of the carrier, v E 、v N And v U The east and north and sky speeds in the local geographic coordinate system are represented, respectively.
Gyroscope error model
Wherein 0 is 3*3 For a matrix of 3*3 zero values, [ epsilon ] bx ε by ε bz ] T Represents the random constant zero drift of the three-axis gyroscope,
is [ epsilon ] bx ε by ε bz ] T Is a derivative of (a).
Accelerometer error model:
wherein 0 is 3*3 Is a matrix of zeros of 3*3,
representing the random constant zero drift of the triaxial accelerometer,
is->
Is a derivative of (a).
Since the three-axis installation error angle of the astronomical navigation sensor is constant, the symbol representation mode is assumed to be δa= [ δa ] x δA y δA z ] T An installation error angle error model can be obtained:
wherein 0 is 3*3 A matrix of values of 3*3, representing δa= [ δa ] x δA y δA z ] T The astronomical navigation sensor is mounted with a three-axis error angle,
is [ delta A ] x δA y δA z ] T Is a derivative of (a).
And (3) sorting and combining the formulas (7) to (12) to obtain an astronomical and inertial combined navigation state quantity model as follows:
Step 3, establishing an astronomical and inertial integrated navigation measurement model
Assuming that an astronomical navigation sensor recognizes n stars, the starlight vectors of the n stars under an inertial coordinate system are
And a star vector in the star-sensitive coordinate system of +.>
Wherein the starlight vector of the ith star in the inertial coordinate system +.>
Star vector in star-sensitive coordinate system>
Column vectors of 3*1, will first be +.>
And->
Unifying to a local geographic coordinate system to get +.>
And->
The process is as follows:
wherein, therein
Represents the coordinate transformation from the inertial system to the geocentric fixed coordinate system, which is uniquely determined by the current time t,
coordinate transformation matrix representing geocentric-geodetic coordinate system given by inertial navigation to local-geodetic coordinate system,/v>
Coordinate transformation representing star-sensitive system to aircraft carrier system, as fixed value, +.>
Representing the gesture conversion matrix given by inertial navigation, I 3*3 Representing 3*3, δa represents the three-axis installation error angle of the astronomical navigation sensor.
Then subjecting the mixture obtained in the formula (14)
And->
And taking difference, taking measurement, and establishing a measurement model of astronomical and inertial integrated navigation on the ith star to obtain:
Z i ＝h i (X(t),t)+V i (t) A (15)
h i (X (t), t) represents the measurement function of the ith star of astronomical and inertial integrated navigation, V i And (t) represents the measurement noise contained in the star vector measurement value of the ith star at time t.
And (3) combining the measurement models of the n stars to obtain a whole astronomical and inertial integrated navigation measurement model:
Discretizing the astronomical and inertial integrated navigation state quantity model obtained in the step 2 and the astronomical and inertial integrated navigation measurement model obtained in the step 3:
i.e.
Discretizing to obtain
Wherein X is K At t K Moment astronomical and inertial combined navigation state quantity X K-1 At t K-1 Time astronomical and inertial combined navigation state quantity phi K,K-1 At t K-1 From time to t K Moment astronomical and inertial combined navigation state transition matrix, w K-1 At t K-1 Time state noise matrix, Z K At t K Time measurement matrix, H K At t K Measurement coefficient matrix of time, V K At t K And measuring a noise matrix at the moment.
Then, estimating the astronomical and inertial combined navigation state quantity by adopting Kalman filtering:
wherein X is k|k-1 Is the state quantity X K-1 Is one-step predictive estimate of P k-1|k-1 At t K-1 Time filtering state estimation covariance matrix, Q k-1 At t K-1 Time state noise w K-1 Covariance matrix, P k|k-1 At t K-1 From time to t K State one-step prediction covariance matrix of moment, R k Representing t K Time measurement noise V K Covariance matrix, K k At t K Time filtering gain matrix, P k|k At t K Time instant filter state estimationCovariance matrix, X k|k Is the state quantity X K Is a Kalman filter estimate; x is X k|k The deployment format is as follows:
Using the attitude error estimated value phi obtained in step 5 k|k ＝φ[ E,k|k φ N,k|k φ U,k|k ] T Position error estimation δr k|k ＝[δL k|k δλ k|k δh k|k ] T And a velocity error estimate δv k|k ＝[δv E,k|k δv N,k|k δv U,k|k ] T Correcting the attitude conversion matrix obtained by updating inertial navigation by the model in the step 1
The speed value v and the position value r are used for obtaining a combined navigation output result gesture conversion matrix +.>
Velocity value v Combination of two or more kinds of materials And a position value r Combination of two or more kinds of materials
The correction process is as follows:
Output step 5Position r after correction Combination of two or more kinds of materials Velocity v Combination of two or more kinds of materials And gesture conversion matrix
And judging whether the navigation needs to be continued, if so, returning to the step 1, otherwise, ending the navigation.
The method needs the astronomical navigation sensor to have a measured value, if no measured value is output, the attitude conversion matrix determined in the step 1 is directly output
A velocity value v and a position value r.
Examples
To verify the performance of the method of the present invention, simulation experiments were performed using the trajectories of fig. 2. The errors of the traditional method and the method in the attitude, the speed and the position are compared with those shown in fig. 3-11, so that the method is smaller than the traditional method, and the precision of combined astronomical and inertial navigation is obviously improved.
Claims (5)
1. The astronomical and inertial integrated navigation method based on the starlight vector is characterized by comprising the following steps of:
step 1, establishing an inertial navigation attitude, speed and position updating model according to Newton's law of mechanics and Euler theorem of fixed point rotation of a rigid body;
step 2, establishing an astronomical and inertial combined navigation state quantity model according to error characteristics of the inertial navigation sensor and installation error angle characteristics of the astronomical navigation sensor;
step 3, establishing an astronomical and inertial integrated navigation measurement model according to the starlight vector under the inertial coordinate system and the starlight vector under the star-sensitive coordinate system;
step 4, discretizing an astronomical and inertial combined navigation state quantity model and a measurement model, and estimating a position error value, a speed error value and an attitude error value contained in an output value of an inertial navigation updating model on line by using Kalman filtering;
step 5, correcting the position, speed and attitude values obtained in the step 1 according to the estimated value in the step 4;
step 6, outputting the gesture, speed and position results obtained by combining astronomical and inertial navigation, judging whether the navigation is finished, and if not, performing step 1;
in the step 2, the specific method for constructing the astronomical and inertial combined navigation state quantity model is as follows:
firstly, establishing a model of gyro noise epsilon and accelerometer noise
Model of (2)
Wherein ε b And
the random constant zero drift representing the gyroscope and the accelerometer is a constant value; epsilon g And->
Is Gaussian white noise;
then determining the error model epsilon of the triaxial gyroscope x ε y ε z Triaxial accelerometer error model
The method comprises the following steps:
wherein [ epsilon ] x ε y ε z ] T Respectively representing the total measurement error of the x, y and z axis gyroscopes, [ epsilon ] bx ε by ε bz ] T Representing the random constant zero drift error component of the x, y and z axis gyroscopes [ epsilon ] gx ε gy ε gz ] T Representing gaussian white noise error components of the x-, y-, z-axis gyroscopes,
indicating the total measurement error of the x, y and z-axis accelerometer, < >>
Representing random constant zero drift error component of x, y and z axis accelerometer, +.>
Representing Gaussian white noise error components of the x, y and z-axis accelerometers;
finally, according to the inertial navigation system updating model and the error model of the gyroscope and the accelerometer, obtaining an astronomical and inertial combined navigation state quantity model, comprising:
misalignment angle error model
Wherein phi = [ phi ] E φ N φ U ] T Referred to as a misalignment angle error,
is the derivative of phi, δv= [ δv ] E δv N δv U ] T Respectively represent east-direction speed error, north-direction speed error and sky-direction speed error, δr= [ δlδλδh ]] T Respectively representing latitude error, longitude error and altitude error, [ epsilon ] x ε y ε z ]Representing the measurement error contained in the measurement by the triaxial gyroscope,/->
Representing the measurement error, ω, contained in the measurement by the triaxial accelerometer ie Indicating the rotational angular velocity of the earth>
Representing a pose transformation matrix of a carrier coordinate system to a local geographic coordinate system, R M And R is N The radius of the meridian and the radius of the mortise unitary circle at the position are respectively, L and h are latitude value and height value of the position of the carrier, v E And v N Respectively representing the east and north speeds in the local geographic coordinate system, x representing the inverse of this matrix representation;
speed error model
Wherein phi = [ phi ] E φ N φ U ] T As misalignment angle error δv= [ δv ] E δv N δv U ] T Respectively represent an east speed error value, a north speed error value and an sky speed error value,
is the derivative of δv, δr= [ δlδλδh] T Respectively represent latitude error value, longitude error value and altitude error value, [ epsilon ] x ε y ε z ]Representing the measurement errors contained in the measurements from the tri-axial gyroscopes,
representing the measurement error, ω, contained in the measurement by the triaxial accelerometer ie Indicating the rotation angular velocity of the earth as a constant value, < ->
Representing a pose transformation matrix of a carrier coordinate system to a local geographic coordinate system, R M And R is N The radius of the meridian and the radius of the mortise circle at the position are respectively determined uniquely by the position of the carrier, L and h are the latitude value and the height value of the position of the carrier, v E 、v N And v U Respectively representing the east and north and the sky speeds in a local geographic coordinate system, x representing the inverse matrix representation;
position error model:
δr＝[δL δλ δh] T to represent the latitude error value, the longitude error value and the altitude error value respectively,
is the derivative of δr, R M And R is N The radius of the meridian and the radius of the mortise circle at the position are respectively determined uniquely by the position of the carrier, L and h are the latitude value and the height value of the position of the carrier, v E 、v N And v U The east and north and sky speeds in the local geographic coordinate system are represented, respectively;
gyroscope error model
Wherein 0 is 3*3 For a matrix of 3*3 zero values, [ epsilon ] bx ε by ε bz ] T Represents the random constant zero drift of the three-axis gyroscope,
is [ epsilon ] bx ε by ε bz ] T Is a derivative of (2);
accelerometer error model:
wherein 0 is 3*3 Is a matrix of zeros of 3*3,
representing the random constant zero drift of the triaxial accelerometer,
is->
Is a derivative of (2);
installing an error angle error model:
wherein 0 is 3*3 A matrix of values of 3*3, representing δa= [ δa ] x δA y δA z ] T The astronomical navigation sensor is mounted with a three-axis error angle,
is [ delta A ] x δA y δA z ] T Is a derivative of (2);
the astronomical and inertial combined navigation state quantity models obtained by arranging and combining the formulas (7) to (12) are as follows:
2. The astronomical and inertial integrated navigation method based on starlight vector according to claim 1, wherein in step 1, the inertial navigation gesture, speed and position update model is specifically:
according to Newton's law of mechanics and Euler's theorem of fixed point rotation of rigid body, the attitude, speed and position updating model of inertial navigation is established under a local geographic coordinate system, namely an east-north-sky coordinate system, as follows:
and (3) updating a model by the gesture:
wherein, the liquid crystal display device comprises a liquid crystal display device,
posture transformation matrix representing carrier coordinate system to local geographic coordinate system, < >>
Representation->
Derivative of>
Representing the angular velocity of the inertial frame relative to the carrier frame, measured by the inertial navigation sensor gyro,/->
Representing the angular velocity of the inertial coordinate system relative to the local geographic coordinate system, x representing the inverse of this matrix representation;
and (3) updating a model by speed:
wherein v represents the velocity value of the carrier in the form of v= [ v ] E v N v U ] T Respectively representing the east and north speeds and the sky speed of the carrier under a local geographic coordinate system,
for v derivative, < >>
Posture transformation matrix representing carrier coordinate system to local geographic coordinate system, < >>
The specific force value of the carrier in the carrier system is represented and is measured by an inertial navigation sensor accelerometer; />
Expressed as the angular velocity of rotation of the earth->
Represents the angular velocity, g, of the local geographic coordinate system relative to the geocentric fixed coordinate system n The x represents the gravitational acceleration of the carrier at the position opposite to the matrix representation;
a location update model:
in the formula (3), r= [ lambda L h ]] T The longitude, latitude and altitude values respectively representing the position of the carrier,
represents the derivative of R, R M And R is N The meridian radius and the mortise unitary radius of the position, v E 、v N And v U The east and north and sky speeds in the local geographic coordinate system are represented, respectively.
3. The astronomical and inertial integrated navigation method based on the starlight vector according to claim 1, wherein in step 3, the specific method for establishing the astronomical and inertial integrated navigation measurement model is as follows:
assuming that an astronomical navigation sensor recognizes n stars, the starlight vectors of the n stars under an inertial coordinate system are
And a star vector in the star-sensitive coordinate system of +.>
Wherein the starlight vector of the ith star in the inertial coordinate system +.>
Star vector in star-sensitive coordinate system>
Column vectors of 3*1, will first be +.>
And->
Unifying to a local geographic coordinate system to get +.>
And->
The process is as follows:
wherein, therein
Representing the coordinate transformation from the inertial system to the geocentric geodetic system, which is uniquely determined by the current time t,/->
Representing geocentric coordinates given by inertial navigationCoordinate transformation matrix tied to local geographic coordinate system,/->
Coordinate transformation representing star-sensitive system to aircraft carrier system, as fixed value, +.>
Representing the gesture conversion matrix given by inertial navigation, I 3*3 Representing a 3*3 identity matrix, and delta A representing an astronomical navigation sensor triaxial installation error angle;
then subjecting the mixture obtained in the formula (14)
And->
And taking difference, taking measurement, and establishing a measurement model of astronomical and inertial integrated navigation on the ith star to obtain:
Z i ＝h i (X(t),t)+V i (t) A (15)
h i (X (t), t) represents the measurement function of the ith star of astronomical and inertial integrated navigation, V i (t) represents the measurement noise contained in the star vector measurement value of the ith star at time t;
and (3) combining the measurement models of the n stars to obtain a whole astronomical and inertial integrated navigation measurement model:
4. the astronomical and inertial integrated navigation method based on the starlight vector according to claim 1, wherein the specific process of step 4 is as follows:
discretizing the astronomical and inertial integrated navigation state quantity model obtained in the step 2 and the astronomical and inertial integrated navigation measurement model obtained in the step 3:
i.e.
Discretizing to obtain
Wherein X is K At t K Moment astronomical and inertial combined navigation state quantity X K-1 At t K-1 Time astronomical and inertial combined navigation state quantity phi K,K-1 At t K-1 From time to t K Moment astronomical and inertial combined navigation state transition matrix, w K-1 At t K-1 Time state noise matrix, Z K At t K Time measurement matrix, H K At t K Measurement coefficient matrix of time, V K At t K Measuring a noise matrix at the moment;
then, estimating the astronomical and inertial combined navigation state quantity by adopting Kalman filtering:
wherein X is kk-1 Is the state quantity X K-1 Is one-step predictive estimate of P k-1k-1 At t K-1 Time filtering state estimation covariance matrix, Q k-1 At t K-1 Time state noise w K-1 Covariance matrix, P kk-1 At t K-1 From time to t K State one-step prediction covariance matrix of moment, R k Representing t K Time measurement noise V K Covariance matrix, K k At t K Time filtering gain matrix, P kk At t K Time filtering state estimation covariance matrix X kk Is the state quantity X K Is a Kalman filter estimate; x is X kk The deployment format is as follows:
wherein the attitude error estimation value is: phi (phi) k|k ＝[φ E,k|k φ N,k|k φ U,k|k ] T The speed error estimate is: δv k|k ＝[δv E,k|k δv N,k|k δv U,k|k ] T Position error estimate δr k|k ＝[δL k|k δλ k|k δh k|k ] T 。
5. The astronomical and inertial integrated navigation method based on the starlight vector according to claim 1, wherein the specific process of the step 5 is as follows:
using the attitude error estimated value phi obtained in step 5 k|k ＝[φ E,k|k φ N,k|k φ U,k|k ] T Position error estimation δr k|k ＝[δL k|k δλ k|k δh k|k ] T And a velocity error estimate δv k|k ＝[δv E,k|k δv N,k|k δv U,k|k ] T Correcting the attitude conversion matrix obtained by updating inertial navigation by the model in the step 1
The speed value v and the position value r are used for obtaining a combined navigation output result gesture conversion matrix +.>
Velocity value v Combination of two or more kinds of materials And a position value r Combination of two or more kinds of materials The correction process is as follows:
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| CN111947653A (en) * | 2020-08-13 | 2020-11-17 | 北京航空航天大学 | Dual-mode inertial/visual/astronomical navigation method for lunar surface inspection tour detector |
| CN111947652B (en) * | 2020-08-13 | 2022-09-20 | 北京航空航天大学 | Inertia/vision/astronomy/laser ranging combined navigation method suitable for lunar lander |
| CN113218390B (en) * | 2021-05-27 | 2022-09-27 | 西北工业大学 | Rotation inertia astronomy combined navigation method based on attitude and star altitude angle fusion |
| CN113252029B (en) * | 2021-06-04 | 2021-10-22 | 华中光电技术研究所（中国船舶重工集团公司第七一七研究所） | Astronomical navigation attitude transfer method based on optical gyroscope measurement information |
| CN113551667A (en) * | 2021-07-21 | 2021-10-26 | 北京航空航天大学 | Spacecraft inertia/fixed star light vector/sun Doppler velocity combined navigation method |
| CN113551668A (en) * | 2021-07-21 | 2021-10-26 | 北京航空航天大学 | Spacecraft inertia/fixed star light vector/star light refraction combined navigation method |
| CN117606474B (en) * | 2024-01-24 | 2024-03-29 | 北京神导科技股份有限公司 | Inertial astronomical combined navigation time synchronization method based on quaternion second-order interpolation |
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