CN111121766A - Astronomical and inertial integrated navigation method based on starlight vector - Google Patents

Astronomical and inertial integrated navigation method based on starlight vector Download PDF

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CN111121766A
CN111121766A CN201911305233.1A CN201911305233A CN111121766A CN 111121766 A CN111121766 A CN 111121766A CN 201911305233 A CN201911305233 A CN 201911305233A CN 111121766 A CN111121766 A CN 111121766A
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error
inertial
astronomical
navigation
model
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CN111121766B (en
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范杰
颜斐
钱晨
陈庆伟
郭建
吴益飞
王潇
舒海洋
魏清华
张宇
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Nanjing University of Science and Technology
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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
    • 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
    • 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 star light vectors, which comprises the steps of establishing an inertial navigation attitude, speed and position updating model; establishing an astronomical and inertial combined navigation state quantity model; establishing an astronomical and inertial integrated navigation measurement model; discretizing an astronomical and inertial integrated 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; correcting the position, speed and attitude value according to the estimated value; outputting the attitude, speed and position results obtained by astronomical and inertial integrated 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 inertia and astronomical navigation state quantity model, so that the precision of astronomical and inertia combined navigation is improved.

Description

Astronomical and inertial integrated navigation method based on starlight vector
Technical Field
The invention relates to a combined navigation technology, in particular to an astronomical and inertial combined navigation method based on starlight vectors.
Background
In recent years, with the development and development of high-altitude long-endurance unmanned aerial vehicles, the requirements on navigation systems of the high-altitude long-endurance unmanned aerial vehicles are also increased, and the navigation systems are required to provide high-precision position values, high-precision speed values and high-precision attitude values for the high-altitude long-endurance unmanned aerial vehicles in all weather. The high-altitude long-endurance unmanned aerial vehicle mainly uses an inertia and astronomical combined navigation system to provide high-precision position, speed and attitude information for the high-altitude long-endurance unmanned aerial vehicle. The traditional astronomical and inertial integrated navigation method needs to carry out ground calibration on the installation error angle of the astronomical navigation sensor, and the ground calibration value of the installation error angle is used as the real value of the installation error angle of the astronomical navigation sensor to carry out derivation on 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 real value of the installation error angle, so that the precision of integrated navigation is reduced. In addition, in the traditional astronomical and inertial combined navigation method, error values in output positions, speeds and attitude values of inertial navigation can be corrected only by identifying at least 3 stars by the astronomical navigation sensor, but the astronomical navigation sensor is interfered by sunlight in the daytime, and the number of the identified stars cannot ensure 3 more stars, so that the precision and reliability of the astronomical and inertial combined navigation are further reduced.
Disclosure of Invention
The invention aims to provide an astronomical and inertial combined navigation method based on starlight vectors.
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 1, establishing an inertial navigation attitude, speed and position updating model according to Newton's law of mechanics and Euler's theorem of fixed-point rotation of a rigid body;
step 2, establishing an astronomical and inertial combined navigation state quantity model according to the error characteristic of the inertial navigation sensor and the installation error angle characteristic of the astronomical navigation sensor;
step 3, establishing an astronomical and inertial integrated navigation measurement model according to the starlight vector in the inertial coordinate system and the starlight vector in the star sensitive coordinate system;
step 4, discretizing the astronomical and inertial integrated navigation state quantity model and the measurement model, and estimating a position error value, a speed error value and an attitude error value contained in an output value of the 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 estimation values in the step 4;
and 6, outputting attitude, speed and position results obtained by astronomical and inertial integrated navigation calculation, judging whether navigation is finished or not, 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) the star light vector is used for constructing the measurement model, and the astronomical and inertial integrated navigation can be completed under the condition that less than 3 stars are identified by the astronomical navigation sensor, so that the reliability of the astronomical and inertial integrated navigation is improved.
Drawings
FIG. 1 is a flow chart of an astronomical and inertial integrated navigation method based on star light vectors according to the present invention.
Fig. 2 is a flight path diagram of an embodiment of the invention.
FIG. 3 is a schematic diagram showing the comparison of the roll angle error results between the method of the present invention and the conventional method.
FIG. 4 is a schematic diagram showing the comparison of the pitch angle error results between the method of the present invention and the conventional method.
FIG. 5 is a schematic diagram showing the comparison of the yaw angle error results between the method of the present invention and the conventional method.
FIG. 6 is a schematic diagram showing the comparison of east-direction velocity error results between the method of the present invention and the conventional method.
FIG. 7 is a diagram showing the comparison of the results of the error in the north speed between the method of the present invention and the conventional method.
FIG. 8 is a schematic diagram showing the comparison of the results of the errors of the speed in the direction of the day between the method of the present invention and the conventional method.
FIG. 9 is a diagram illustrating the longitude error results of the present invention method compared with the conventional method.
FIG. 10 is a schematic diagram showing the comparison of the latitude error results of the method of the present invention and the conventional method.
FIG. 11 is a schematic diagram showing the comparison of the height error results of the method of the present invention and the conventional method.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings.
As shown in fig. 1, the astronomical and inertial combined navigation method based on starlight vectors includes the following steps:
step 1, establishing an inertial navigation attitude, speed and position updating model
According to the Newton's law of mechanics and the Euler's theorem of fixed point rotation of rigid bodies, the attitude, speed and position updating model of inertial navigation is established under the local geographic coordinate system, namely the east-north-sky coordinate system, as follows:
and (3) updating the model by the posture:
Figure BDA0002322902400000021
wherein the content of the first and second substances,
Figure BDA0002322902400000022
a pose transformation matrix representing the carrier coordinate system to the local geographic coordinate system,
Figure BDA0002322902400000023
to represent
Figure BDA0002322902400000024
The derivative of (a) of (b),
Figure BDA0002322902400000031
representing the angular velocity of the inertial frame relative to the carrier frame, measured by the inertial navigation sensor gyroscope,
Figure BDA0002322902400000032
representing the angular velocity of the inertial frame relative to the local geographic frame, and x represents the inverse of this matrix representation.
And (3) updating the model by the speed:
Figure BDA0002322902400000033
wherein v represents the velocity value of the vector, and its development form is v ═ vEvNvU]TRespectively representing the east and north speeds and the sky speed of the carrier under the local geographic coordinate system,
Figure BDA0002322902400000034
is the derivative of v and is,
Figure BDA0002322902400000035
a pose transformation matrix representing the carrier coordinate system to the local geographic coordinate system,
Figure BDA0002322902400000036
the specific force value of the carrier in the carrier system is represented and measured by an inertial navigation sensor accelerometer;
Figure BDA0002322902400000037
expressed as the rotational angular velocity of the earth,
Figure BDA0002322902400000038
representing the angle of the local geographical coordinate system relative to the geocentric geostationary coordinate systemVelocity, gnThe acceleration of gravity at the position of the carrier is represented by x, which is expressed against this matrix.
And (3) updating the model by the position:
Figure BDA00023229024000000313
in the formula (3), r ═ λ L h]TRespectively representing longitude, latitude and altitude values of the location of the carrier,
Figure BDA0002322902400000039
denotes the derivative of R, RMAnd RNRespectively the radius of the meridian and the radius of the unitary mortise, vE、vNAnd vURepresenting east and north speeds and a sky speed, respectively, in a local geographic coordinate system.
Step 2, establishing an astronomical and inertial combined navigation state quantity model
In step 1 of formula (1)
Figure BDA00023229024000000310
And in formula (2)
Figure BDA00023229024000000311
The state quantity model of the astronomical and inertial integrated navigation is established on the basis of error analysis of output results of an inertial navigation updating model if the measurement values of the gyroscope and the accelerometer are noisy.
Firstly, a model of gyro noise epsilon and accelerometer noise are established
Figure BDA00023229024000000312
Model (2)
Figure BDA0002322902400000041
Wherein epsilonbAnd
Figure BDA0002322902400000042
the random constant zero drift of the gyroscope and the accelerometer is a constant value; epsilongAnd
Figure BDA0002322902400000043
is gaussian white noise.
Error model epsilon of three-axis gyroscopexεyεzAnd a triaxial accelerometer error model
Figure BDA0002322902400000044
Comprises the following steps:
Figure BDA0002322902400000045
wherein, [ epsilon ]xεyεz]TRespectively represents the total measurement error of the x-axis gyroscope, the y-axis gyroscope and the z-axis gyroscope, [ epsilon ]bxεbyεbz]TRepresents the random constant zero drift error component of the x, y and z axis gyroscope, [ epsilon ]gxεgyεgz]TRepresenting the white gaussian noise error component of the x, y and z axis gyroscopes,
Figure BDA0002322902400000046
represents the total measurement error of the accelerometer with x, y and z axes,
Figure BDA0002322902400000047
representing the random constant zero drift error components of the accelerometer of the x, y and z axes,
Figure BDA0002322902400000048
representing the gaussian white noise error component of the accelerometer of the x, y and z axes.
According to the inertial navigation system updating 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
Figure BDA0002322902400000049
Wherein phi is [ phi ]EφNφU]TReferred to as the misalignment angle error,
Figure BDA0002322902400000051
is the derivative of phi, δ v ═ δ vEδvNδvU]TRespectively indicate east-direction speed error, north-direction speed error and sky-direction speed error, and δ r ═ δ L δ λ δ h]TRespectively, a latitude error, a longitude error, and an altitude error. [ epsilon ]xεyεz]Indicating the measurement errors contained in the measurements made by the three-axis gyroscope,
Figure BDA0002322902400000052
representing the measurement error, ω, contained in the measurement by the three-axis accelerometerieThe angular velocity of rotation of the earth is represented,
Figure BDA0002322902400000053
an attitude transformation matrix, R, representing the transformation from the carrier coordinate system to the local geographic coordinate systemMAnd RNRespectively the meridian radius and the unitary radius of the position, L and h are the latitude value and the height value of the position of the carrier, vEAnd vNRespectively representing east and north speeds in the local geographical coordinate system, x representing the inverse of this matrix representation.
Velocity error model
Figure BDA0002322902400000054
Wherein phi is [ phi ]EφNφU]TFor misalignment angle error, δ v ═ δ vEδvNδvU]TRespectively representing an east speed error value, a north speed error value, and a sky speed error value,
Figure BDA0002322902400000055
is the derivative of δ v，δr＝[δL δλ δh]TRespectively representing a latitude error value, a longitude error value and an altitude error value, [ epsilon ]xεyεz]Indicating the measurement errors contained in the measurements made by the three-axis gyroscope,
Figure BDA0002322902400000056
representing the measurement error, ω, contained in the measurement by the three-axis accelerometerieRepresents the rotational angular velocity of the earth, is a constant value,
Figure BDA0002322902400000061
an attitude transformation matrix, R, representing the transformation from the carrier coordinate system to the local geographic coordinate systemMAnd RNThe radius of the meridian and the radius of the unitary mortise are respectively determined by the position of the carrier, L and h are the latitude value and the height value of the position of the carrier, vE、vNAnd vURepresenting east and north speeds and a day speed, respectively, in the local geographical coordinate system, x representing the inverse of this matrix representation.
Position error model:
Figure BDA0002322902400000062
δr＝[δL δλ δh]Tto represent a latitude error value, a longitude error value and an altitude error value respectively,
Figure BDA0002322902400000063
is the derivative of δ R, RMAnd RNThe radius of the meridian and the radius of the unitary mortise are respectively determined by the position of the carrier, L and h are the latitude value and the height value of the position of the carrier, vE、vNAnd vURepresenting east and north speeds and a sky speed, respectively, in a local geographic coordinate system.
Gyroscope error model
Figure BDA0002322902400000064
Wherein 03*3Zero value matrix of 3 x 3, [ epsilon ]bxεbyεbz]TRepresents the random constant null shift of the three-axis gyroscope,
Figure BDA0002322902400000065
is [ epsilon ]bxεbyεbz]TThe derivative of (c).
An accelerometer error model:
Figure BDA0002322902400000066
wherein 03*3A matrix of zero values of 3 x 3,
Figure BDA0002322902400000071
represents a random constant null shift of the tri-axial accelerometer,
Figure BDA0002322902400000072
is composed of
Figure BDA0002322902400000073
The derivative of (c).
Since the three-axis installation error angle of the astronomical navigation sensor is a constant value, the symbolic representation mode is assumed to be that delta A is ═ delta AxδAyδAz]TAnd obtaining an installation error angle error model:
Figure BDA0002322902400000074
wherein 03*3A zero value matrix of 3 x 3, representing δ a ═ δ axδAyδAz]TThe three-axis installation error angle of the astronomical navigation sensor,
Figure BDA0002322902400000075
is [ delta A ]xδAyδAz]TThe derivative of (c).
After the equations (7) to (12) are arranged and combined, the astronomical and inertial combined navigation state quantity model can be obtained as follows:
Figure BDA0002322902400000076
Figure BDA0002322902400000077
attitude error, speed error, position error, gyroscope triaxial null shift, accelerometer triaxial null shift, and astronomical navigation triaxial installation error angle of astronomical and inertial combined navigation,
Figure BDA00023229024000000717
is the derivative of the state quantity X, f (X (t), t) is the astronomical and inertial combined navigation state transfer function, w is the process noise, and w (t) is w at the time t.
Step 3, establishing an astronomical and inertial integrated navigation measurement model
Suppose that the astronomical navigation sensor identifies n stars, and the star light vector of the n stars under the inertial coordinate system is
Figure BDA0002322902400000078
And the star light vector in the star sensitive coordinate system is
Figure BDA0002322902400000079
Wherein the starlight vector of the ith star in the inertial coordinate system
Figure BDA00023229024000000710
And the star light vector under the star sensitive coordinate system
Figure BDA00023229024000000711
Column vectors of 3 x 1 each, first of all
Figure BDA00023229024000000712
And
Figure BDA00023229024000000713
unified to local geographic coordinate system
Figure BDA00023229024000000714
And
Figure BDA00023229024000000715
the process is as follows:
Figure BDA00023229024000000716
wherein, therein
Figure BDA0002322902400000081
Represents the coordinate transformation from the inertial system to the geocentric coordinate system, is uniquely determined by the current time t,
Figure BDA0002322902400000082
a coordinate transformation matrix representing the geocentric-geostationary coordinate system to the local geographic coordinate system given by inertial navigation,
Figure BDA0002322902400000083
the coordinate transformation from the star sensor system to the aircraft carrier system is expressed as a fixed value,
Figure BDA0002322902400000084
representing the attitude transformation matrix given by inertial navigation, I3*33 x 3 of the unit matrix, and delta A of the unit matrix represents a three-axis installation error angle of the astronomical navigation sensor.
Then subjecting the compound obtained in formula (14)
Figure BDA0002322902400000085
And
Figure BDA0002322902400000086
and performing difference measurement, and establishing a measurement model of the astronomical and inertial integrated navigation about the ith satellite to obtain:
Zi＝hi(X(t),t)+Vi(t) formula (15)
hi(X (t), t) is a measurement function of the ith star of the combined astronomical and inertial navigation, Vi(t) represents the measurement noise contained in the measured value of the star vector of the ith star at time t.
The measurement models of n stars are connected to obtain the whole astronomical and inertial integrated navigation measurement model:
Figure BDA0002322902400000087
step 4, discretizing an astronomical and inertial integrated navigation state quantity model and a measurement model, and estimating the state quantity by using Kalman filtering
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:
that is to say, the
Figure BDA0002322902400000088
Discretizing to obtain
Figure BDA0002322902400000089
Wherein, XKIs tKTime astronomical and inertial combined navigation state quantity, XK-1Is tK-1Navigation state quantity phi of combination of time astronomical and inertiaK,K-1Is tK-1Time to tKTime astronomical and inertial combined navigation state transition matrix, wK-1Is tK-1Time of day state noise matrix, ZKIs tKMeasurement matrix of time of day, HKIs tKMeasurement coefficient matrix of time, VKIs tKA measured noise matrix at a time.
Then, estimating the astronomical and inertial integrated navigation state quantity by adopting Kalman filtering:
Figure BDA0002322902400000091
wherein, Xk|k-1Is a state quantity XK-1One-step predictive estimate of, Pk-1|k-1Is tK-1Time-of-day filtering state estimation covariance matrix, Qk-1Is tK-1Time of day state noise wK-1Of the covariance matrix, Pk|k-1Is tK-1Time to tKState one-step prediction covariance matrix, R, for a time instantkRepresents tKTime measurement noise VKCovariance matrix of, KkIs tKTime of day filter gain matrix, Pk|kIs tKTime-of-day filtering state estimation covariance matrix, Xk|kIs a state quantity XK(iii) a kalman filter estimate; xk|kThe expanded form is as follows:
Figure BDA0002322902400000092
wherein the attitude error estimate is: phi is ak|k＝[φE,k|kφN,k|kφU,k|k]TThe velocity error estimate is: delta vk|k＝[δvE,k|kδvN,k|kδvU,k|k]TPosition error estimate δ rk|k＝[δLk|kδλk|kδhk|k]T
Step 5, correcting the output result of the inertial navigation updating model according to the Kalman filtering estimated value
Utilizing the attitude error estimated value phi obtained in the step 5k|k＝φ[E,k|kφN,k|kφU,k|k]TPosition error estimated value δ rk|k＝[δLk|kδλk|kδhk|k]TAnd velocity error estimate δ vk|k＝[δvE,k|kδvN,k|kδvU,k|k]TCorrecting the attitude transformation matrix obtained by inertial navigation updating of the model in step 1
Figure BDA0002322902400000093
Obtaining a posture conversion matrix of the combined navigation output result by the velocity value v and the position value r
Figure BDA0002322902400000094
Velocity value vCombination ofAnd positionValue rCombination of
The correction process is as follows:
Figure BDA0002322902400000095
step 6, outputting the position, speed and attitude information of the carrier
Outputting the corrected position r in the step 5Combination ofVelocity vCombination ofAnd attitude transformation matrix
Figure BDA0002322902400000101
And judging whether the navigation is needed 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, and if no measured value is output, the attitude conversion matrix determined in the step 1 is directly output
Figure BDA0002322902400000102
Velocity value v and position value r.
Examples
To verify the performance of the method of the present invention, a simulation experiment was performed using the trace of fig. 2. The error ratio of the traditional method and the method of the invention in attitude, speed and position is shown in fig. 3-11, and it can be seen that the method of the invention is smaller than the traditional method, and the precision of astronomical and inertial combined navigation is obviously improved.

Claims (6)

1. An astronomical and inertial integrated navigation method based on starlight vectors is characterized by comprising the following steps:
step 1, establishing an inertial navigation attitude, speed and position updating model according to Newton's law of mechanics and Euler's theorem of fixed-point rotation of a rigid body;
step 2, establishing an astronomical and inertial combined navigation state quantity model according to the error characteristic of the inertial navigation sensor and the installation error angle characteristic of the astronomical navigation sensor;
step 3, establishing an astronomical and inertial integrated navigation measurement model according to the starlight vector in the inertial coordinate system and the starlight vector in the star sensitive coordinate system;
step 4, discretizing the astronomical and inertial integrated navigation state quantity model and the measurement model, and estimating a position error value, a speed error value and an attitude error value contained in an output value of the 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 estimation values in the step 4;
and 6, outputting attitude, speed and position results obtained by astronomical and inertial integrated navigation calculation, judging whether navigation is finished or not, and if not, performing the step 1.
2. The astronomical and inertial combined navigation method based on the starlight vector as claimed in claim 1, wherein in step 1, the inertial navigation attitude, velocity and position update model specifically comprises:
according to the Newton's law of mechanics and the Euler's theorem of fixed point rotation of rigid bodies, the attitude, speed and position updating model of inertial navigation is established under the local geographic coordinate system, namely the east-north-sky coordinate system, as follows:
and (3) updating the model by the posture:
Figure FDA0002322902390000011
wherein the content of the first and second substances,
Figure FDA0002322902390000012
a pose transformation matrix representing the carrier coordinate system to the local geographic coordinate system,
Figure FDA0002322902390000013
to represent
Figure FDA0002322902390000014
The derivative of (a) of (b),
Figure FDA0002322902390000015
representing the angular velocity of the inertial frame relative to the carrier frame, measured by the inertial navigation sensor gyroscope,
Figure FDA0002322902390000016
representing the angular velocity of the inertial frame relative to the local geographic frame, x representing the inverse of this matrix representation;
and (3) updating the model by the speed:
Figure FDA0002322902390000017
wherein v represents the velocity value of the vector, and its development form is v ═ vEvNvU]TRespectively representing the east and north speeds and the sky speed of the carrier under the local geographic coordinate system,
Figure FDA0002322902390000018
is the derivative of v and is,
Figure FDA0002322902390000019
a pose transformation matrix representing the carrier coordinate system to the local geographic coordinate system,
Figure FDA0002322902390000021
the specific force value of the carrier in the carrier system is represented and measured by an inertial navigation sensor accelerometer;
Figure FDA0002322902390000022
expressed as the rotational angular velocity of the earth,
Figure FDA0002322902390000023
representing the angular velocity, g, of the local geographical coordinate system relative to the geocentric geostationary coordinate systemnThe gravity acceleration of the position of the carrier is shown, and x represents the inverse matrix representation;
and (3) updating the model by the position:
Figure FDA0002322902390000024
in the formula (3), r ═ λ L h]TRespectively representing longitude, latitude and altitude values of the location of the carrier,
Figure FDA0002322902390000025
denotes the derivative of R, RMAnd RNRespectively the radius of the meridian and the radius of the unitary mortise, vE、vNAnd vURepresenting east and north speeds and a sky speed, respectively, in a local geographic coordinate system.
3. The astronomical and inertial combined navigation method based on the starlight vector as claimed in claim 1, wherein in step 2, the specific method for constructing the astronomical and inertial combined navigation state quantity model is as follows:
firstly, a model of gyro noise epsilon and accelerometer noise are established
Figure FDA0002322902390000026
Model (2)
Figure FDA0002322902390000027
Wherein epsilonbAnd
Figure FDA0002322902390000028
the random constant zero drift of the gyroscope and the accelerometer is a constant value; epsilongAnd
Figure FDA0002322902390000029
is white gaussian noise;
then determining an error model epsilon of the three-axis gyroscopexεyεzAnd a triaxial accelerometer error model
Figure FDA00023229023900000210
Comprises the following steps:
Figure FDA00023229023900000211
wherein, [ epsilon ]xεyεz]TRespectively represents the total measurement error of the x-axis gyroscope, the y-axis gyroscope and the z-axis gyroscope, [ epsilon ]bxεbyεbz]TRepresents the random constant zero drift error component of the x, y and z axis gyroscope, [ epsilon ]gxεgyεgz]TRepresenting the white gaussian noise error component of the x, y and z axis gyroscopes,
Figure FDA0002322902390000031
represents the total measurement error of the accelerometer with x, y and z axes,
Figure FDA0002322902390000032
representing the random constant zero drift error components of the accelerometer of the x, y and z axes,
Figure FDA0002322902390000033
representing Gaussian white noise error components of the accelerometer of the x axis, the y axis and the z axis;
and finally, updating the model and error models of a gyroscope and an accelerometer according to the inertial navigation system to obtain an astronomical and inertial combined navigation state quantity model, wherein the model comprises the following steps:
misalignment angle error model
Figure FDA0002322902390000034
Wherein phi is [ phi ]EφNφU]TReferred to as the misalignment angle error,
Figure FDA0002322902390000035
is the derivative of phi, δ v ═ δ vEδvNδvU]TRespectively representing east direction speed error, north direction speed error and dayTo speed error, δ r ═ δ L δ λ δ h]TRespectively, a latitude error, a longitude error, and an altitude error. [ epsilon ]xεyεz]Indicating the measurement errors contained in the measurements made by the three-axis gyroscope,
Figure FDA0002322902390000036
representing the measurement error, ω, contained in the measurement by the three-axis accelerometerieThe angular velocity of rotation of the earth is represented,
Figure FDA0002322902390000037
an attitude transformation matrix, R, representing the transformation from the carrier coordinate system to the local geographic coordinate systemMAnd RNRespectively the meridian radius and the unitary radius of the position, L and h are the latitude value and the height value of the position of the carrier, vEAnd vNRespectively representing east and north speeds in a local geographical coordinate system, and x represents the inverse of this matrix representation;
velocity error model
Figure FDA0002322902390000041
Wherein phi is [ phi ]EφNφU]TFor misalignment angle error, δ v ═ δ vEδvNδvU]TRespectively representing an east speed error value, a north speed error value, and a sky speed error value,
Figure FDA0002322902390000042
is the derivative of δ v, [ δ L δ λ δ h ═ δ r]TRespectively representing a latitude error value, a longitude error value and an altitude error value, [ epsilon ]xεyεz]Indicating the measurement errors contained in the measurements made by the three-axis gyroscope,
Figure FDA0002322902390000043
representing the measurement error, ω, contained in the measurement by the three-axis accelerometerieShowing groundThe rotation angular velocity of the ball is a fixed value,
Figure FDA0002322902390000044
an attitude transformation matrix, R, representing the transformation from the carrier coordinate system to the local geographic coordinate systemMAnd RNThe radius of the meridian and the radius of the unitary mortise are respectively determined by the position of the carrier, L and h are the latitude value and the height value of the position of the carrier, vE、vNAnd vURespectively representing east-oriented speed, north-oriented speed and sky-oriented speed under a local geographic coordinate system, and x represents the inverse of the matrix representation;
position error model:
Figure FDA0002322902390000045
δr＝[δL δλ δh]Tto represent a latitude error value, a longitude error value and an altitude error value respectively,
Figure FDA0002322902390000051
is the derivative of δ R, RMAnd RNThe radius of the meridian and the radius of the unitary mortise are respectively determined by the position of the carrier, L and h are the latitude value and the height value of the position of the carrier, vE、vNAnd vURespectively representing east and north speeds and a sky speed under a local geographic coordinate system;
gyroscope error model
Figure FDA0002322902390000052
Wherein 03*3Zero value matrix of 3 x 3, [ epsilon ]bxεbyεbz]TRepresents the random constant null shift of the three-axis gyroscope,
Figure FDA0002322902390000053
is [ epsilon ]bxεbyεbz]TA derivative of (a);
an accelerometer error model:
Figure FDA0002322902390000054
wherein 03*3A matrix of zero values of 3 x 3,
Figure FDA0002322902390000055
represents a random constant null shift of the tri-axial accelerometer,
Figure FDA0002322902390000056
is composed of
Figure FDA0002322902390000057
A derivative of (a);
installation error angle error model:
Figure FDA0002322902390000058
wherein 03*3A zero value matrix of 3 x 3, representing δ a ═ δ axδAyδAz]TThe three-axis installation error angle of the astronomical navigation sensor,
Figure FDA0002322902390000059
is [ delta A ]xδAyδAz]TA derivative of (a);
after the equations (7) to (12) are arranged and combined, the astronomical and inertial combined navigation state quantity model is obtained as follows:
Figure FDA0002322902390000061
Figure FDA0002322902390000062
astronomical and inertial combined navigation attitude error, speed error and position errorA gyroscope triaxial null shift, an accelerometer triaxial null shift and an astronomical navigation triaxial installation error angle,
Figure FDA0002322902390000063
is the derivative of the state quantity X, f (X (t), t) is the astronomical and inertial combined navigation state transfer function, w is the process noise, and w (t) is w at the time t.
4. The integrated astronomical and inertial navigation method based on starlight vectors as claimed in claim 1, wherein the specific method for establishing the integrated astronomical and inertial navigation measurement model in step 3 comprises:
suppose that the astronomical navigation sensor identifies n stars, and the star light vector of the n stars under the inertial coordinate system is
Figure FDA0002322902390000064
And the star light vector in the star sensitive coordinate system is
Figure FDA0002322902390000065
Wherein the starlight vector of the ith star in the inertial coordinate system
Figure FDA0002322902390000066
And the star light vector under the star sensitive coordinate system
Figure FDA0002322902390000067
Column vectors of 3 x 1 each, first of all
Figure FDA0002322902390000068
And
Figure FDA0002322902390000069
unified to local geographic coordinate system
Figure FDA00023229023900000610
And
Figure FDA00023229023900000611
the process is as follows:
Figure FDA00023229023900000612
wherein, therein
Figure FDA00023229023900000613
Represents the coordinate transformation from the inertial system to the geocentric coordinate system, is uniquely determined by the current time t,
Figure FDA00023229023900000614
a coordinate transformation matrix representing the geocentric-geostationary coordinate system to the local geographic coordinate system given by inertial navigation,
Figure FDA00023229023900000615
the coordinate transformation from the star sensor system to the aircraft carrier system is expressed as a fixed value,
Figure FDA00023229023900000616
representing the attitude transformation matrix given by inertial navigation, I3*33, expressing a unit matrix of 3 x 3, wherein delta A expresses a three-axis installation error angle of the astronomical navigation sensor;
then subjecting the compound obtained in formula (14)
Figure FDA00023229023900000617
And
Figure FDA00023229023900000618
and performing difference measurement, and establishing a measurement model of the astronomical and inertial integrated navigation about the ith satellite to obtain:
Zi＝hi(X(t),t)+Vi(t) formula (15)
hi(X (t), t) is a measurement function of the ith star of the combined astronomical and inertial navigation, Vi(t) the measured value of the star vector of the ith star at time t is included in theThe measurement noise of (2);
the measurement models of n stars are connected to obtain the whole astronomical and inertial integrated navigation measurement model:
Figure FDA0002322902390000071
5. the astronomical and inertial combined navigation method based on starlight vectors as claimed in 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:
that is to say, the
Figure FDA0002322902390000072
Discretizing to obtain
Figure FDA0002322902390000073
Wherein, XKIs tKTime astronomical and inertial combined navigation state quantity, XK-1Is tK-1Navigation state quantity phi of combination of time astronomical and inertiaK,K-1Is tK-1Time to tKTime astronomical and inertial combined navigation state transition matrix, wK-1Is tK-1Time of day state noise matrix, ZKIs tKMeasurement matrix of time of day, HKIs tKMeasurement coefficient matrix of time, VKIs tKMeasuring a noise matrix at a moment;
then, estimating the astronomical and inertial integrated navigation state quantity by adopting Kalman filtering:
Figure FDA0002322902390000074
wherein, Xk|k-1Is a state quantity XK-1The one-step prediction of the estimated value of,Pk-1|k-1is tK-1Time-of-day filtering state estimation covariance matrix, Qk-1Is tK-1Time of day state noise wK-1Of the covariance matrix, Pk|k-1Is tK-1Time to tKState one-step prediction covariance matrix, R, for a time instantkRepresents tKTime measurement noise VKCovariance matrix of, KkIs tKTime of day filter gain matrix, Pk|kIs tKTime-of-day filtering state estimation covariance matrix, Xk|kIs a state quantity XK(iii) a kalman filter estimate; xk|kThe expanded form is as follows:
Figure FDA0002322902390000081
wherein the attitude error estimate is: phi is ak|k＝[φE,k|kφN,k|kφU,k|k]TThe velocity error estimate is: delta vk|k＝[δvE,k|kδvN,k|kδvU,k|k]TPosition error estimate δ rk|k＝[δLk|kδλk|kδhk|k]T。
6. The integrated astronomical and inertial navigation method based on starlight vectors as claimed in claim 1, wherein the specific process of step 5 is as follows:
utilizing the attitude error estimated value phi obtained in the step 5k|k＝[φE,k|kφN,k|kφU,k|k]TPosition error estimated value δ rk|k＝[δLk|kδλk|kδhk|k]TAnd velocity error estimate δ vk|k＝[δvE,k|kδvN,k|kδvU,k|k]TCorrecting the attitude transformation matrix obtained by inertial navigation updating of the model in step 1
Figure FDA0002322902390000082
Obtaining a combined navigation output node by the velocity value v and the position value rFruit posture conversion matrix
Figure FDA0002322902390000083
Velocity value vCombination ofAnd a position value rCombination ofThe correction process is as follows:
Figure FDA0002322902390000084
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