CN113188540A - Inertia/astronomical self-adaptive filtering method based on star number and configuration - Google Patents

Inertia/astronomical self-adaptive filtering method based on star number and configuration Download PDF

Info

Publication number
CN113188540A
CN113188540A CN202110346872.3A CN202110346872A CN113188540A CN 113188540 A CN113188540 A CN 113188540A CN 202110346872 A CN202110346872 A CN 202110346872A CN 113188540 A CN113188540 A CN 113188540A
Authority
CN
China
Prior art keywords
matrix
astronomical
error
coordinate system
star
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110346872.3A
Other languages
Chinese (zh)
Other versions
CN113188540B (en
Inventor
安竞轲
熊智
王融
康骏
张新睿
李婉玲
李欣童
曹志国
聂庭宇
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN202110346872.3A priority Critical patent/CN113188540B/en
Publication of CN113188540A publication Critical patent/CN113188540A/en
Application granted granted Critical
Publication of CN113188540B publication Critical patent/CN113188540B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G01C21/025—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means with the use of startrackers
    • 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
    • G01C21/10—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
    • G01C21/18—Stabilised platforms, e.g. by gyroscope
    • 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
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/29—Graphical models, e.g. Bayesian networks
    • G06F18/295—Markov models or related models, e.g. semi-Markov models; Markov random fields; Networks embedding Markov models

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • General Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Evolutionary Biology (AREA)
  • Operations Research (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Astronomy & Astrophysics (AREA)
  • Evolutionary Computation (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Artificial Intelligence (AREA)
  • Computing Systems (AREA)
  • Probability & Statistics with Applications (AREA)
  • Navigation (AREA)

Abstract

The invention discloses an inertia/astronomical self-adaptive filtering method based on the number and configuration of stars, and belongs to the technical field of integrated navigation. The method comprises the following steps: s1, modeling astronomical attitude determination errors; s2, deducing an inertia/astronomical adaptive filtering method based on the star vector number and the configuration; and S3, verifying the effectiveness of the inertia/astronomical adaptive filtering method. The simulation result of the invention shows that the designed inertia/astronomical self-adaptive filtering method is utilized to realize the optimal utilization of the inertia navigation information and the astronomical navigation information compared with the traditional Kalman filtering fusion method, thereby effectively improving the output precision of the integrated navigation system.

Description

Inertia/astronomical self-adaptive filtering method based on star number and configuration
Technical Field
The invention relates to an inertia/astronomical self-adaptive filtering method based on the number and configuration of stars, and belongs to the technical field of integrated navigation.
Background
The astronomical navigation system has high output precision and errors are not accumulated along with time, so that the astronomical navigation system is very suitable to be used as an inertia/astronomical combined navigation system together with inertial navigation, and the inertia/astronomical combined navigation system is widely applied to spacecrafts, long-endurance airplanes and the like. However, the attitude accuracy of the astronomical navigation also changes dynamically along with the change of the star observation condition, the measurement noise of the kalman filter determines the trust degree of the filter on the measurement of the quantity, the fixed measurement noise cannot realize the optimal observation on the astronomical navigation attitude, and an adaptive kalman filter with the measurement noise dynamically adjusted along with the astronomical observation trust degree needs to be designed to realize the optimal fusion of the inertial navigation information and the astronomical navigation information.
Disclosure of Invention
The invention provides an inertia/astronomical adaptive filtering method based on star number and configuration.
The invention adopts the following technical scheme for solving the technical problems:
an inertial/astronomical adaptive filtering method based on star number and configuration comprises the following steps:
s1, collecting star light vectors through a star sensor, and carrying out astronomical attitude determination error modeling based on the number and configuration of the collected star light vectors;
s2, deducing an inertia/astronomical self-adaptive filtering method based on the star vector number and configuration according to the actual influence of the star light vector on the astronomical attitude determination error;
and S3, verifying the effectiveness of the inertial/astronomical adaptive filtering method by simulating a starlight vector.
Step S1 includes the following steps:
s11, astronomical navigation pose determination;
and calculating the position information of the fixed star unit vector in the star sensor coordinate system according to the image point position, wherein the calculation formula is as follows:
Figure BDA0003000997770000021
in the formula, skIs the unit vector coordinate, u, of the kth fixed star in the star sensor coordinate systemkProjecting the x-direction coordinate, v, of the image point for the star vectorkProjecting the y-direction coordinate of an image point for the fixed star vector, wherein f is a focal length;
denote the vector coordinate system as Ob-xbybzbAbbreviated as "b" and the centroid inertial coordinate system is "Oi-xiyiziThe coordinate system s of the star sensor is regarded as coincidence with the coordinate system b of the carrier, and the star sensor obtains the coordinate s of the fixed star relative to the carrier coordinate system1、s2、…snWherein s isk＝[xsk ysk zsk]T(k ═ 1,2, … n); meanwhile, the coordinates v of the fixed stars relative to the geocentric inertial coordinate system are calculated through the navigation ephemeris1、v2、…vnWherein v isk＝[xik yik zik]TThen skAnd vkThe relationship of (a) to (b) is as follows:
Figure BDA0003000997770000022
in the formula, vkIs the coordinate vector, s, of the kth satellite relative to the Earth's center inertial framekAs a coordinate vector, matrix, of the kth satellite relative to the carrier coordinate system
Figure BDA0003000997770000023
Is an attitude transformation matrix from a star sensor coordinate system s system to a geocentric inertial coordinate system i system
Figure BDA0003000997770000024
The attitude transformation matrix from a carrier coordinate system b to a geocentric inertial coordinate system i is used, the s system is superposed with the b system, and the two matrixes are equivalent;
note the book
Figure BDA0003000997770000025
Then, according to the formula:
Figure BDA0003000997770000026
therefore, when the number n of stars observed by the star sensor is more than or equal to 3, the attitude transformation matrix of the carrier system relative to the inertial system is obtained by least square fitting of each star observation vector
Figure BDA0003000997770000027
Namely, it is
Figure BDA0003000997770000028
Wherein the content of the first and second substances,
Q＝(VTV)-1VT
q is a conversion coefficient matrix;
s12, modeling astronomical attitude determination errors;
the actual vector information of the star relative to the star sensor coordinate system should be:
Figure BDA0003000997770000031
wherein, Delta S is astronomical attitude determination observation error,
Figure BDA0003000997770000032
the actual coordinate vector of the fixed star relative to the star sensor coordinate system is shown, and S is an ideal coordinate vector of the fixed star relative to the star sensor coordinate system;
the attitude transformation matrix thus solved is:
Figure BDA0003000997770000033
wherein the content of the first and second substances,
Figure BDA0003000997770000034
taking a carrier coordinate system b as a reference coordinate system, and recording an astronomical attitude determination error vector as
Figure BDA0003000997770000035
Figure BDA0003000997770000036
When the astronomical attitude determination error angles are all small, the attitude transformation matrix
Figure BDA0003000997770000037
Expressed as:
Figure BDA0003000997770000038
wherein b' is expressed as a calculation carrier coordinate system with errors,
Figure BDA0003000997770000039
for the reality of the carrier coordinate system relative to the inertial coordinate systemA matrix of the attitude transformation is generated,
Figure BDA00030009977700000310
is the actual attitude transformation matrix variation of the carrier coordinate system relative to the inertial coordinate system,
Figure BDA00030009977700000311
is an attitude transformation matrix from an actual carrier coordinate system to an ideal carrier coordinate system,
Figure BDA00030009977700000312
for an error angle of rotation in the x-axis direction,
Figure BDA00030009977700000313
for an error angle of rotation in the y-axis direction,
Figure BDA00030009977700000314
is an error angle of rotation in the z-axis direction;
further obtaining:
Figure BDA00030009977700000315
wherein the content of the first and second substances,
Figure BDA00030009977700000316
error matrix is recorded
Figure BDA00030009977700000317
Has a covariance matrix of PΔAnd then:
Figure BDA0003000997770000041
let the covariance matrix of matrix M be PMAnd then:
Figure BDA0003000997770000042
astronomical attitude determination error vector
Figure BDA0003000997770000043
Has a covariance matrix of
Figure BDA0003000997770000044
Then:
Figure BDA0003000997770000045
further obtaining:
Figure BDA0003000997770000046
wherein, PMCovariance matrix as matrix M
Figure BDA0003000997770000047
Is a covariance matrix of the attitude determination error vector, and tr () is a trace of a matrix;
when the measurement noise delta S of the star sensor is certain and is Gaussian white noise, the following results are obtained:
Figure BDA0003000997770000048
wherein, PΔIs an error matrix
Figure BDA0003000997770000051
E () is expressed as a mean value,
Figure BDA0003000997770000052
variance of the observed noise Δ S;
thus, the astronomical attitude determination error variance is:
Figure BDA0003000997770000053
wherein A ═ VTV)*Is a 3 × 3 square matrix, is a matrix VTThe companion matrix of V is the matrix of V,
Figure BDA0003000997770000054
for the mean square error coefficient of astronomical attitude determination errors, det () represents determinant;
and S13, linearly fitting the astronomical attitude determination mean square error and the attitude determination error mean square error coefficient ξ.
Linearly fitting the astronomical attitude determination mean square error and the attitude determination error mean square error coefficient xi to obtain the approximate linear relation of the astronomical attitude determination mean square error and the attitude determination error mean square error coefficient xi
δc＝3.32ξ+1.36
Wherein, deltacAnd the astronomical attitude determination mean square error is obtained, observation noise is adjusted in real time through a fitted linear relation, and the combined navigation precision is improved.
The specific process of step S2 is as follows:
the linear Kalman filter is used for combination, and the state equation and the observation equation of the inertia and astronomical integrated navigation system are as follows:
Figure BDA0003000997770000055
wherein, X (t) is a system state variable;
Figure BDA0003000997770000056
is the derivative of the system state variable; f (t) is a system matrix; g (t) is a system noise coefficient matrix; w (t) is a system noise matrix; z (t) is an observed quantity; h (t) is an observation matrix; v (t) is observation noise;
the inertial/astronomical integrated navigation system adopts a Kalman filtering mode to perform information fusion, and the state equation is as follows:
Figure BDA0003000997770000061
wherein the state variable X (t) is:
Figure BDA0003000997770000062
the state transition matrix is:
Figure BDA0003000997770000063
Figure BDA0003000997770000064
Figure BDA0003000997770000065
the noise matrix is:
Figure BDA0003000997770000066
the system noise vector is:
W(t)9×1＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz]T
wherein: phi is aE、φN、φUFor roll, pitch and roll angle errors, δ vE、δvN、δvURepresenting the speed errors of the inertial navigation system in the east, north and sky directions under the geographic coordinate system; delta L, delta lambda and delta h represent errors of longitude, latitude and height of the inertial navigation system in a ground-interior coordinate system; epsilonbx、εby、εbzRepresenting a gyro random constant error; epsilonrx、εry、εrzRepresenting a random error of a gyro first-order Markov process;
Figure BDA0003000997770000067
representing a first order markov process random error of the accelerometer; a (t)18×18A state transition matrix for the system; g (t)18×9Is a noise coefficient matrix; w (t)9×1Is the white noise vector of the system;
FNtransformation matrix for corresponding state quantities of gyro and accelerometer, FSTransforming the state quantities of the gyro and the accelerometer into a matrix of error quantities, FMIs an error amount transformation matrix, O is a null matrix with all elements being 0, O3×3Is an empty matrix of 3 rows and 3 columns, O9×3Is an empty matrix of 9 rows and 3 columns,
Figure BDA0003000997770000071
for transformation of the carrier coordinate system into the geographic coordinate system, I3×3In an identity matrix of three rows and three columns, Trx、Try、TrzComponents of gyro error-related time in three axes, Tax、Tay、TazFor the time of accelerometer correlation, the component in three axes, ωgx、ωgy、ωgzDriving white noise, omega, for a first order Markov process for three axes of a gyroscoperx、ωry、ωrzWhite noise, omega, in three axes of the gyroscopeax、ωay、ωazDriving white noise for a first order markov process for three axes of the accelerometer;
defining the observed quantity as the difference between the attitude angle of the carrier measured by astronomical navigation and the attitude angle of inertial navigation, wherein the observation equation is as follows:
ZC(t)＝HC(t)X(t)+vC(t)
at small platform error angles, the observation matrix is represented by the following formula:
Figure BDA0003000997770000072
in the formula, HC(t) the observation matrixes gamma, theta and psi are respectively roll angle, pitch angle and course angle;
thus, the observation equation is expressed as:
Figure BDA0003000997770000073
in the formula, gammaI、θI、ψI，γCNS、θCNS、ψCNSRespectively outputting roll, pitch and yaw angles of inertial navigation and astronomical navigation,
Figure BDA0003000997770000074
representing the east, north and sky direction platform error angle v of inertial navigation in the geographic coordinate systemC(t) is attitude error angle observation noise, vC(t) will adapt the size, v, as the observed star vector changesC(t) is represented as follows:
Figure BDA0003000997770000075
wherein, deltacIs the noise coefficient and alpha is the adaptive coefficient.
The invention has the following beneficial effects:
according to the inertia/astronomical self-adaptive filtering method based on the star number and the configuration, when the star number is small, the noise matrix value measured by Kalman filtering is increased, so that the reliability of astronomical attitude information is reduced; and when the number of stars is large, reducing the noise matrix value measured by Kalman filtering to increase the reliability of the astronomical attitude information. The noise matrix value measured by Kalman filtering is adjusted in real time according to the star number and the attitude determination error mean square error coefficient xi, so that the stability and the integrated navigation precision of the system can be improved to a great extent. Therefore, the studied adaptive filtering method has rationality and correctness.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a method simulation track graph.
FIG. 3(a) is a graph showing the accuracy analysis of the roll angle under the three-star condition; FIG. 3(b) is a graph of accuracy analysis of the pitch angle under the three-star condition; FIG. 3(c) is a diagram of the accuracy analysis of the course angle under the three-star condition.
FIG. 4(a) is a diagram of an analysis of accuracy of a roll angle under a six-star condition; FIG. 4(b) is a diagram of accuracy analysis of the pitch angle under six-star condition; fig. 4(c) is a diagram of the accuracy analysis of the course angle under the six-star condition.
FIG. 5(a) is a view showing an accuracy analysis of a roll angle under a ten-star condition; FIG. 5(b) is a diagram of accuracy analysis of the pitch angle under ten-star condition; FIG. 5(c) is a diagram of the accuracy analysis of the course angle under the condition of ten stars.
FIG. 6(a) is a plot of adaptive filtered versus non-adaptive filtered roll angle error; FIG. 6(b) is a plot of pitch error versus adaptive filtering and non-adaptive filtering; FIG. 6(c) is a plot of a comparison of adaptively filtered and non-adaptively filtered course angle error.
FIG. 7(a) is a graph comparing east position error with adaptive and non-adaptive filtering; FIG. 7(b) is a graph comparing adaptive filtered and non-adaptive filtered north position error; FIG. 7(c) is a graph comparing adaptive filtered and non-adaptive filtered spatial position error.
FIG. 8(a) is a graph comparing east-direction velocity error with adaptive and non-adaptive filtering; FIG. 8(b) is a graph comparing adaptive filtered and non-adaptive filtered northbound speed errors; FIG. 8(c) is a plot of adaptive filtered versus non-adaptive filtered antenna direction velocity error.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
As shown in fig. 1, the inertia/astronomical combination filtering method based on star number and configuration of the present invention comprises the following steps:
s11, astronomical navigation pose determination;
the star sensor can be regarded as an information processing system, input information is a starlight direction vector, and output information is the attitude of the aircraft under an inertial coordinate system. The input information comes from two aspects, on the one hand from the navigation star catalogue and on the other hand from the real-time measurement of the star sensor. O iss-xsyszsIs the star sensor coordinate system (abbreviated as s system), OUvw is a CCD array plane imaging coordinate system; o issO is the direction of the optical axis, OsysShaft, OwThe axes are all consistent with the direction of the optical axis; (u)k,vk) The position information of the image point of a certain star on the CCD array surface is obtained. According to the image point position, the position information of the star unit vector in the star sensor coordinate system can be obtained through calculation. The calculation formula is as follows:
Figure BDA0003000997770000091
in the formula, skIs the unit vector coordinate of the kth fixed star in the star sensor coordinate system, f is the focal length of the optical lens, ukProjecting the x-direction coordinate, v, of the image point for the star vectorkAnd projecting the y-direction coordinate of the image point for the star vector.
Denote the vector coordinate system as Ob-xbybzb(abbreviated as "b" system), the centroid inertial coordinate system is Oi-xiyizi(abbreviated as i series). The star sensor coordinate system s and the carrier coordinate system b are regarded as coincidence, and the star sensor can obtain the coordinate s of the fixed star relative to the carrier coordinate system1、s2、…snWherein s isk＝[xsk ysk zsk]T(k ═ 1,2, … n); meanwhile, the coordinates v of the fixed stars relative to the geocentric inertial coordinate system can be calculated through the navigation ephemeris1、v2、…vnWherein v isk＝[xik yikzik]TThen skAnd vkThe relationship of (a) to (b) is as follows:
Figure BDA0003000997770000092
in the formula, vkIs the coordinate vector, s, of the kth satellite relative to the Earth's center inertial framekAs a coordinate vector, matrix, of the kth satellite relative to the carrier coordinate system
Figure BDA0003000997770000093
Is an attitude transformation matrix from a star sensor coordinate system s system to a geocentric inertial coordinate system i system
Figure BDA0003000997770000094
The attitude transformation matrix from a carrier coordinate system b to a geocentric inertial coordinate system i is adopted, the s system is superposed with the b system, and the two matrixes are equivalent.
Note the book
Figure BDA0003000997770000095
Then, according to the formula:
Figure BDA0003000997770000101
therefore, when the number n of stars observed by the star sensor is more than or equal to 3, the attitude transformation matrix of the carrier system relative to the inertial system can be obtained by least square fitting of each star observation vector
Figure BDA0003000997770000102
Namely, it is
Figure BDA0003000997770000103
Wherein the content of the first and second substances,
Q＝(VTV)-1VT
q is a conversion coefficient matrix.
S12, modeling astronomical attitude determination errors;
due to the existence of observation errors of the star sensor, errors of a star observation vector are caused, and the actual vector information of the star relative to the star sensor coordinate system is as follows:
Figure BDA0003000997770000104
wherein, Delta S is astronomical attitude determination observation error,
Figure BDA0003000997770000105
the coordinate vector of the fixed star relative to the star sensor coordinate system is S, and the coordinate vector of the fixed star relative to the star sensor coordinate system is S.
The attitude transformation matrix thus solved is:
Figure BDA0003000997770000106
wherein the content of the first and second substances,
Figure BDA0003000997770000107
taking a carrier coordinate system b as a reference coordinate system, and recording an astronomical attitude determination error vector as
Figure BDA0003000997770000108
Figure BDA0003000997770000109
When the astronomical attitude determination error angles are all small, the attitude transformation matrix
Figure BDA00030009977700001010
Can be expressed as:
Figure BDA00030009977700001011
wherein the content of the first and second substances,
Figure BDA00030009977700001012
is the actual attitude transformation matrix of the carrier coordinate system relative to the inertial coordinate system,
Figure BDA00030009977700001013
is the actual attitude transformation matrix variation of the carrier coordinate system relative to the inertial coordinate system,
Figure BDA00030009977700001014
is an attitude transformation matrix from an actual carrier coordinate system to an inertial coordinate system,
Figure BDA00030009977700001015
is an attitude transformation matrix from an actual carrier coordinate system to an ideal carrier coordinate system,
Figure BDA00030009977700001016
for an error angle of rotation in the x-axis direction,
Figure BDA00030009977700001017
for an error angle of rotation in the y-axis direction,
Figure BDA00030009977700001018
is the error angle of rotation in the z-axis direction.
Further, it is possible to obtain:
Figure BDA0003000997770000111
wherein the content of the first and second substances,
Figure BDA0003000997770000112
wherein:
Figure BDA0003000997770000113
an attitude transformation matrix from an inertial coordinate system to a carrier coordinate system;
error matrix is recorded
Figure BDA0003000997770000114
Has a covariance matrix of PΔAnd then:
Figure BDA0003000997770000115
let the covariance matrix of matrix M be PMAnd then:
Figure BDA0003000997770000116
astronomical attitude determination error vector
Figure BDA0003000997770000117
Has a covariance matrix of
Figure BDA0003000997770000118
Then:
Figure BDA0003000997770000119
further, it is possible to obtain:
Figure BDA00030009977700001110
wherein: pMCovariance matrix as matrix M
Figure BDA00030009977700001111
Is the covariance matrix of the attitude determination error vector, tr () is the trace of the fetch matrix.
When the measurement noise delta S of the star sensor is certain and is Gaussian white noise, the following can be obtained:
Figure BDA0003000997770000121
wherein, PΔIs an error matrix
Figure BDA0003000997770000122
E () is expressed as a mean value,
Figure BDA0003000997770000123
to observe the variance of the noise Δ S.
Thus, the astronomical attitude determination error variance is:
Figure BDA0003000997770000124
wherein A ═ VTV)*Is a 3 × 3 square matrix, is a matrix VTThe companion matrix of V is the matrix of V,
Figure BDA0003000997770000125
to the astronomical attitude determination error mean square error coefficient, det () represents a determinant.
And S13, linearly fitting the astronomical attitude determination mean square error and the astronomical attitude determination error mean square error coefficient ξ.
And performing linear fitting on the astronomical attitude determination mean square error and the error weight coefficient k to obtain an approximate linear relation between the astronomical attitude determination mean square error and the error weight coefficient k.
δc＝3.32ξ+1.36
Wherein, deltacThe astronomical attitude determination mean square error is adopted, observation noise can be adjusted in real time through the fitted linear relation, and the combined navigation precision is improved.
Further, step S2 is specifically: the linear Kalman filter is used for combination, and the state equation and the observation equation of the inertia and astronomical integrated navigation system are as follows:
Figure BDA0003000997770000131
wherein X (t) is a system state variable,
Figure BDA0003000997770000132
is the derivative of the system state variable; f (t) is a system matrix; g (t) is a system noise coefficient matrix; w (t) is a system noise matrix; z (t) is an observed quantity; h (t) is an observation matrix; v (t) is observation noise;
s21, equation of state
The inertial/astronomical integrated navigation system adopts a Kalman filtering mode to perform information fusion, and the state equation is as follows:
Figure BDA0003000997770000133
wherein the state variable X (t) is:
Figure BDA0003000997770000134
wherein: phi is aE、φN、φUFor roll, pitch and roll angle errors, δ vE、δvN、δvURepresenting the speed errors of the inertial navigation system in the east, north and sky directions under the geographic coordinate system; delta L, delta lambda and delta h represent errors of longitude, latitude and height of the inertial navigation system in a ground-interior coordinate system; epsilonbx、εby、εbzRepresenting a gyro random constant error; epsilonrx、εry、εrzRepresenting a random error of a gyro first-order Markov process;
Figure BDA0003000997770000135
representing a first order markov process random error of the accelerometer; a (t)18×18A state transition matrix for the system; g (t)18×9Is a noise coefficient matrix; w (t)9×1Is the white noise vector of the system.
The state transition matrix is:
Figure BDA0003000997770000136
Figure BDA0003000997770000137
Figure BDA0003000997770000138
wherein: fNTransformation matrix for corresponding state quantities of gyro and accelerometer, FSBeing gyros and accelerationsConversion matrix from state quantity to error quantity of the meter, FMIn order to transform the matrix for the amount of error,
Figure BDA0003000997770000139
for converting the carrier coordinate system to the geographic coordinate system, O is a null matrix, O3×3Is a 3-row and 3-column empty matrix, Trx、Try、TrzComponents of gyro error-related time in three axes, Tax、Tay、TazThe components of the accelerometer correlation time in the three axes.
The noise matrix is:
Figure BDA0003000997770000141
wherein: o is9×3An empty matrix of 9 rows and 3 columns, O3×3Is an empty matrix of 3 rows and 3 columns, I3×3Is an identity matrix of 3 rows and 3 columns,
Figure BDA0003000997770000142
and converting the vector coordinate system into a geographic coordinate system.
The system noise vector is:
W(t)9×1＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz]T
wherein: omegagx、ωgy、ωgzDriving white noise, omega, for a first order Markov process for three axes of a gyroscoperx、ωry、ωrzWhite noise, omega, in three axes of the gyroscopeax、ωay、ωazWhite noise is driven for the first order markov process for the three axes of the accelerometer.
S22, observation equation
Defining the observed quantity as the difference between the attitude angle of the carrier measured by astronomical navigation and the attitude angle of inertial navigation, wherein the observation equation is as follows:
ZC(t)＝HC(t)X(t)+vC(t)
when the platform error angle is small, the observation matrix can be represented by the following formula:
Figure BDA0003000997770000143
wherein gamma, theta and psi are roll angle, pitch angle and course angle respectively.
Thus, the observation equation can be expressed as:
Figure BDA0003000997770000144
in the formula, gammaI、θI、ψI，γCNS、θCNS、ψCNSRespectively outputting roll, pitch and yaw angles of inertial navigation and astronomical navigation,
Figure BDA0003000997770000145
representing the east, north and sky direction platform error angle v of inertial navigation in the geographic coordinate systemC(t) is attitude error angle observation noise, vC(t) will adapt the size, v, as the observed star vector changesC(t) is represented as follows:
Figure BDA0003000997770000151
wherein, deltacIs the noise coefficient and alpha is the adaptive coefficient.
And S31, verifying and analyzing the influence of the noise matrix observed by the filter on the navigation precision.
TABLE 1 sensor simulation parameter settings
Figure BDA0003000997770000152
In order to effectively explain the influence of observation noise on the navigation precision of the whole inertia/astronomical combined navigation system under different sidereal vectors, simulation verification analysis is carried out in the section, flight path and sensor parameters are shown in a figure 2 and a table 1, Kalman filtering observation matrix noise simulation parameters are shown in a table 2, and simulation results are shown in a figure 3, a figure 4, a figure 5 and a table 3.
Table 2 measured noise simulation parameter settings
Number of stars Astronomical attitude measurement noise (second)
3 3、5、15
6 3、5、15
10 3、5、15
TABLE 3 statistical results of the influence of astronomical attitude observation noise on the error RMS
Figure BDA0003000997770000161
It can be known from the statistics of the error curve and the RMS (root mean square error) error, when the number of the fixed star observations is 3, the mean square error coefficient ξ of the astronomical attitude determination error is larger, so that the astronomical attitude determination error is larger, the reliability is poor, the larger observation noise of the kalman filter can improve the precision of the integrated navigation system, and the output precision can be reduced if the observation noise matrix value is too small. When the observation quantity of the fixed stars is 6, the astronomical attitude determination precision is gradually improved along with the increase of the number of the fixed stars, and the combined navigation precision can be improved by properly reducing astronomical observation noise. When the number of stars observed is 10. The astronomical attitude determination precision is remarkably improved, the attitude output of the astronomical navigation system can be trusted, and the astronomical observation noise is reduced, so that the precision of the whole navigation system is further improved.
According to preset carrier track and navigation sensor parameters, under the condition that the number and the configuration of simulated star vectors are different, the influence of observation noise on the navigation precision of the whole inertia/astronomical combined navigation system is simulated, and the simulation result can obtain that when the observation number of the star vectors is 3, the mean square error coefficient xi of the astronomical attitude determination error is larger, so that the astronomical attitude determination error is larger, the reliability is poor, the larger observation noise of the Kalman filter can improve the precision of the combined navigation system, and if the observation noise matrix value is too small, the output precision can be reduced. When the observation quantity of the fixed stars is 6, the astronomical attitude determination precision is gradually improved along with the increase of the number of the fixed stars, and the combined navigation precision can be improved by properly reducing astronomical observation noise. When the number of stars observed is 10. The astronomical attitude determination precision is remarkably improved, the attitude output of the astronomical navigation system can be trusted, and the astronomical observation noise is reduced, so that the precision of the whole navigation system is further improved.
S32, self-adaptive filtering verification analysis under the condition that the star number is time-varying;
when the visible number of stars dynamically changes, simulation verification analysis is respectively carried out on the navigation performance of adaptive filtering and non-adaptive filtering for comparing the navigation performance of the adaptive filtering with the navigation performance of the non-adaptive filtering, and when the number of stars is small, a Kalman filtering observation noise matrix value is increased so as to reduce the reliability of astronomical attitude information; when the number of stars is large, the Kalman filtering observation noise matrix value is reduced to increase the reliability of the astronomical attitude information, and simulation curves are shown in FIGS. 6, 7 and 8 and Table 4.
TABLE 4 navigation error RMS statistics for dynamically changing sidereal numbers
Figure BDA0003000997770000171
When the number of fixed stars is small, a Kalman filtering observation noise matrix value is increased so as to reduce the reliability of astronomical attitude information; and when the number of stars is large, reducing a Kalman filtering observation noise matrix value to increase the reliability of the astronomical attitude information. It can be seen from the error curve diagram and the error RMS (root mean square) statistical result that the Kalman filtering observation noise matrix value is adjusted in real time according to the star number and the error weight k thereof, the stability and the integrated navigation precision of the system can be improved to a great extent, and the reasonability and the correctness of the researched adaptive filtering algorithm are verified.

Claims (3)

1. An inertial/astronomical adaptive filtering method based on star number and configuration is characterized by comprising the following steps of:
s1, collecting star light vectors through a star sensor, and carrying out astronomical attitude determination error modeling based on the number and configuration of the collected star light vectors;
s2, deducing an inertia/astronomical self-adaptive filtering method based on the star vector number and configuration according to the actual influence of the star light vector on the astronomical attitude determination error;
and S3, verifying the effectiveness of the inertial/astronomical adaptive filtering method by simulating a starlight vector.
2. The method of inertial/astronomical adaptive filtering based on star number and configuration according to claim 1, wherein step S1 comprises the steps of:
s11, astronomical navigation pose determination;
according to the image point position, calculating to obtain the position information of the fixed star unit vector in the star sensor coordinate system, wherein the calculation formula is as follows:
Figure FDA0003000997760000011
in the formula, skIs the unit vector coordinate, u, of the kth fixed star in the star sensor coordinate systemkProjecting the x-direction coordinate, v, of the image point for the star vectorkProjecting y-squares of image points for star vectorsDirectional coordinates, f is focal length;
denote the vector coordinate system as Ob-xbybzbAbbreviated as "b" and the centroid inertial coordinate system is "Oi-xiyiziThe coordinate system s of the star sensor is regarded as coincidence with the coordinate system b of the carrier, and the star sensor obtains the coordinate s of the fixed star relative to the carrier coordinate system1、s2、…snWherein s isk＝[xsk ysk zsk]TK is 1,2, … n; meanwhile, the coordinates v of the fixed stars relative to the geocentric inertial coordinate system are calculated through the navigation ephemeris1、v2、…vnWherein v isk＝[xik yik zik]TThen skAnd vkThe relationship of (a) to (b) is as follows:
Figure FDA0003000997760000012
in the formula, vkIs the coordinate vector, s, of the kth satellite relative to the Earth's center inertial framekAs a coordinate vector, matrix, of the kth satellite relative to the carrier coordinate system
Figure FDA0003000997760000013
Is an attitude transformation matrix from a star sensor coordinate system s system to a geocentric inertial coordinate system i system
Figure FDA0003000997760000014
The attitude transformation matrix from a carrier coordinate system b to a geocentric inertial coordinate system i is used, the s system is superposed with the b system, and the two matrixes are equivalent;
note the book
Figure FDA0003000997760000021
Then, according to the formula:
Figure FDA0003000997760000022
therefore, when the number n of stars observed by the star sensor is more than or equal to 3, the attitude transformation matrix of the carrier system relative to the inertial system is obtained by least square fitting of each star observation vector
Figure FDA0003000997760000023
Namely, it is
Figure FDA0003000997760000024
Wherein the content of the first and second substances,
Q＝(VTV)-1VT
q is a conversion coefficient matrix;
s12, modeling astronomical attitude determination errors;
the actual vector information of the star relative to the star sensor coordinate system should be:
Figure FDA0003000997760000025
wherein, Delta S is astronomical attitude determination observation error,
Figure FDA0003000997760000026
the actual coordinate vector of the fixed star relative to the star sensor coordinate system is shown, and S is an ideal coordinate vector of the fixed star relative to the star sensor coordinate system;
the attitude transformation matrix thus solved is:
Figure FDA0003000997760000027
wherein the content of the first and second substances,
Figure FDA0003000997760000028
taking a carrier coordinate system b as a reference coordinate system, and recording an astronomical attitude determination error vector as
Figure FDA0003000997760000029
Figure FDA00030009977600000210
When the astronomical attitude determination error angles are all small, the attitude transformation matrix
Figure FDA00030009977600000211
Expressed as:
Figure FDA00030009977600000212
wherein b' is expressed as a calculation carrier coordinate system with errors,
Figure FDA00030009977600000213
is the actual attitude transformation matrix of the carrier coordinate system relative to the inertial coordinate system,
Figure FDA00030009977600000214
is the actual attitude transformation matrix variation of the carrier coordinate system relative to the inertial coordinate system,
Figure FDA0003000997760000031
is an attitude transformation matrix from an actual carrier coordinate system to an ideal carrier coordinate system,
Figure FDA0003000997760000032
for an error angle of rotation in the x-axis direction,
Figure FDA0003000997760000033
for an error angle of rotation in the y-axis direction,
Figure FDA0003000997760000034
is an error angle of rotation in the z-axis direction;
further obtaining:
Figure FDA0003000997760000035
wherein the content of the first and second substances,
Figure FDA0003000997760000036
error matrix is recorded
Figure FDA0003000997760000037
Has a covariance matrix of PΔAnd then:
Figure FDA0003000997760000038
let the covariance matrix of matrix M be PMAnd then:
Figure FDA0003000997760000039
astronomical attitude determination error vector
Figure FDA00030009977600000310
Has a covariance matrix of
Figure FDA00030009977600000313
Then:
Figure FDA00030009977600000311
further obtaining:
Figure FDA00030009977600000312
wherein, PMCovariance matrix as matrix M
Figure FDA00030009977600000314
Is a covariance matrix of the attitude determination error vector, and tr () is a trace of a matrix;
when the measurement noise delta S of the star sensor is certain and is Gaussian white noise, the following results are obtained:
Figure FDA0003000997760000041
wherein, PΔIs an error matrix
Figure FDA0003000997760000042
E () is expressed as a mean value,
Figure FDA0003000997760000043
variance of the observed noise Δ S;
thus, the astronomical attitude determination error variance is:
Figure FDA0003000997760000044
wherein A ═ VTV)*Is a 3 × 3 square matrix, is a matrix VTThe companion matrix of V is the matrix of V,
Figure FDA0003000997760000045
for the mean square error coefficient of astronomical attitude determination errors, det () represents determinant;
s13, linearly fitting the astronomical attitude determination mean square error and the attitude determination error mean square error coefficient xi
Linearly fitting the astronomical attitude determination mean square error and the attitude determination error mean square error coefficient xi to obtain the approximate linear relation of the astronomical attitude determination mean square error and the attitude determination error mean square error coefficient xi
δc＝3.32ξ+1.36
Wherein, deltacAnd the astronomical attitude determination mean square error is obtained, observation noise is adjusted in real time through a fitted linear relation, and the combined navigation precision is improved.
3. The method for inertial/astronomical adaptive filtering based on star number and configuration according to claim 1, wherein the step S2 is implemented as follows:
the linear Kalman filter is used for combination, and the state equation and the observation equation of the inertia and astronomical integrated navigation system are as follows:
Figure FDA0003000997760000051
wherein, X (t) is a system state variable;
Figure FDA0003000997760000052
is the derivative of the system state variable; f (t) is a system matrix; g (t) is a system noise coefficient matrix; w (t) is a system noise matrix; z (t) is an observed quantity; h (t) is an observation matrix; v (t) is observation noise;
the inertial/astronomical integrated navigation system adopts a Kalman filtering mode to perform information fusion, and the state equation is as follows:
Figure FDA0003000997760000053
wherein the state variable X (t) is:
Figure FDA0003000997760000054
the state transition matrix is:
Figure FDA0003000997760000055
Figure FDA0003000997760000056
Figure FDA0003000997760000057
the noise matrix is:
Figure FDA0003000997760000058
the system noise vector is:
W(t)9×1＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz]T
wherein: phi is aE、φN、φUFor roll, pitch and roll angle errors, δ vE、δvN、δvURepresenting the speed errors of the inertial navigation system in the east, north and sky directions under the geographic coordinate system; delta L, delta lambda and delta h represent errors of longitude, latitude and height of the inertial navigation system in a ground-interior coordinate system; epsilonbx、εby、εbzRepresenting a gyro random constant error; epsilonrx、εry、εrzRepresenting a random error of a gyro first-order Markov process;
Figure FDA0003000997760000061
representing a first order markov process random error of the accelerometer; a (t)18×18A state transition matrix for the system; g (t)18×9Is a noise coefficient matrix; w (t)9×1Is the white noise vector of the system;
FNtransformation matrix for corresponding state quantities of gyro and accelerometer, FSFor conversion of gyroscope and accelerometer state quantity into error quantityMatrix, FMIs an error amount transformation matrix, O is a null matrix with all elements being 0, O3×3Is an empty matrix of 3 rows and 3 columns, O9×3Is an empty matrix of 9 rows and 3 columns,
Figure FDA0003000997760000062
for transformation of the carrier coordinate system into the geographic coordinate system, I3×3In an identity matrix of three rows and three columns, Trx、Try、TrzComponents of gyro error-related time in three axes, Tax、Tay、TazFor the time of accelerometer correlation, the component in three axes, ωgx、ωgy、ωgzDriving white noise, omega, for a first order Markov process for three axes of a gyroscoperx、ωry、ωrzWhite noise, omega, in three axes of the gyroscopeax、ωay、ωazDriving white noise for a first order markov process for three axes of the accelerometer;
defining the observed quantity as the difference between the attitude angle of the carrier measured by astronomical navigation and the attitude angle of inertial navigation, wherein the observation equation is as follows:
ZC(t)＝HC(t)X(t)+vC(t)
at small platform error angles, the observation matrix is represented by the following formula:
Figure FDA0003000997760000063
in the formula, HC(t) is an observation matrix, and gamma, theta and psi are respectively a roll angle, a pitch angle and a course angle;
thus, the observation equation is expressed as:
Figure FDA0003000997760000064
in the formula, gammaI、θI、ψI，γCNS、θCNS、ψCNSAre respectively provided withRoll, pitch and yaw angles output for inertial navigation and astronomical navigation,
Figure FDA0003000997760000065
representing the east, north and sky direction platform error angle v of inertial navigation in the geographic coordinate systemC(t) is attitude error angle observation noise, vC(t) will adapt the size, v, as the observed star vector changesC(t) is represented as follows:
Figure FDA0003000997760000071
wherein, deltacIs the noise coefficient and alpha is the adaptive coefficient.
CN202110346872.3A 2021-03-31 2021-03-31 Inertial/astronomical self-adaptive filtering method based on number and configuration of fixed stars Active CN113188540B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110346872.3A CN113188540B (en) 2021-03-31 2021-03-31 Inertial/astronomical self-adaptive filtering method based on number and configuration of fixed stars

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110346872.3A CN113188540B (en) 2021-03-31 2021-03-31 Inertial/astronomical self-adaptive filtering method based on number and configuration of fixed stars

Publications (2)

Publication Number Publication Date
CN113188540A true CN113188540A (en) 2021-07-30
CN113188540B CN113188540B (en) 2024-05-03

Family

ID=76974184

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110346872.3A Active CN113188540B (en) 2021-03-31 2021-03-31 Inertial/astronomical self-adaptive filtering method based on number and configuration of fixed stars

Country Status (1)

Country Link
CN (1) CN113188540B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114370870A (en) * 2022-01-05 2022-04-19 中国兵器工业计算机应用技术研究所 Filter updating information screening method suitable for pose measurement Kalman filtering

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6102338A (en) * 1996-08-30 2000-08-15 Mitsubishi Denki Kabushiki Kaisha Attitude determination system for artificial satellite
CN101825467A (en) * 2010-04-20 2010-09-08 南京航空航天大学 Method for realizing integrated navigation through ship's inertial navigation system (SINS) and celestial navigation system (SNS)
CN106932804A (en) * 2017-03-17 2017-07-07 南京航空航天大学 Inertia/the Big Dipper tight integration navigation system and its air navigation aid of astronomy auxiliary

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6102338A (en) * 1996-08-30 2000-08-15 Mitsubishi Denki Kabushiki Kaisha Attitude determination system for artificial satellite
CN101825467A (en) * 2010-04-20 2010-09-08 南京航空航天大学 Method for realizing integrated navigation through ship's inertial navigation system (SINS) and celestial navigation system (SNS)
CN106932804A (en) * 2017-03-17 2017-07-07 南京航空航天大学 Inertia/the Big Dipper tight integration navigation system and its air navigation aid of astronomy auxiliary

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
XIAOLIN NING: "A Fast Calibration Method of the Star Sensor Installation Error Based on Observability Analysis for the Tightly Coupled SINS/ CNS-Integrated Navigation System", IEEE SENSORS JOURNAL, vol. 18, no. 16, pages 6794 - 6802 *
赵慧: "基于恒星几何构型分布的天文定位误差建模及误差特性分析", 兵工学报, vol. 36, no. 5, pages 813 - 822 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114370870A (en) * 2022-01-05 2022-04-19 中国兵器工业计算机应用技术研究所 Filter updating information screening method suitable for pose measurement Kalman filtering
CN114370870B (en) * 2022-01-05 2024-04-12 中国兵器工业计算机应用技术研究所 Filter update information screening method suitable for pose measurement Kalman filtering

Also Published As

Publication number Publication date
CN113188540B (en) 2024-05-03

Similar Documents

Publication Publication Date Title
CN107525503B (en) Adaptive cascade Kalman filtering method based on combination of dual-antenna GPS and MIMU
CN111947652B (en) Inertia/vision/astronomy/laser ranging combined navigation method suitable for lunar lander
CN102252673B (en) Correction method for on-track aberration of star sensor
CN104792340B (en) A kind of star sensor installation error matrix and navigation system star ground combined calibrating and the method for correction
CN104655152B (en) A kind of real-time Transfer Alignments of airborne distributed POS based on federated filter
CN106871928B (en) Strap-down inertial navigation initial alignment method based on lie group filtering
Murrell Precision attitude determination for multimission spacecraft
CN106482734A (en) A kind of filtering method for IMU Fusion
CN102636081B (en) Transfer alignment method and device based on visual movement modeling
CN107728182A (en) Flexible more base line measurement method and apparatus based on camera auxiliary
CN103852085B (en) A kind of fiber strapdown inertial navigation system system for field scaling method based on least square fitting
CN101246012B (en) Combinated navigation method based on robust dissipation filtering
CN103323026A (en) Attitude standard deviation estimation and correction method of star sensor and payload
CN108562305B (en) Five-position quick coarse calibration method for installation error of inertial/astronomical deep integrated navigation system
CN108387227A (en) The multinode information fusion method and system of airborne distribution POS
CN103674021A (en) Integrated navigation system and method based on SINS (Strapdown Inertial Navigation System) and star sensor
CN111044074A (en) Star sensor calibration device and star observation calibration method based on field star observation
CN106017452B (en) Double tops disturbance rejection north finding method
CN107607127B (en) External field-based star sensor internal parameter calibration and precision rapid verification system
CN107764261A (en) A kind of distributed POS Transfer Alignments analogue data generation method and system
CN107101649B (en) A kind of in-orbit error separating method of spacecraft Guidance instrumentation
CN112240941B (en) Relative calibration method and system for gravity satellite-borne accelerometer
CN112461262A (en) Device and method for correcting errors of three-axis magnetometer
CN111238469A (en) Unmanned aerial vehicle formation relative navigation method based on inertia/data chain
CN107576977A (en) The UAV Navigation System and method adaptively merged based on multi-source information

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant