CN108871326B - A kind of single-shaft-rotation modulation inertia-astronomy deep integrated navigation method - Google Patents
A kind of single-shaft-rotation modulation inertia-astronomy deep integrated navigation method Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
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- 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
Abstract
The invention discloses a kind of single-shaft-rotation modulation inertia-astronomy deep integrated navigation method, this method uses the attitude error of celestial body vector correction aircraft, and altitude of the heavenly body corrects the location error of aircraft；It solves the problems, such as that the constant value biasing due to accelerometer causes horizontal reference precision lower using single-shaft-rotation modulation technology, and then improves inertia/celestial combined navigation precision.The present invention can significantly improve the navigation accuracy of system, make up inertia/astronomy deep integrated navigation technique study deficiency.
Description
Technical field
The invention belongs to navigation field, a kind of single-shaft-rotation modulation inertia-astronomy deep integrated navigation method.
Background technique
In recent years, inertia/celestial combined navigation system is not strong with its independence, high by electromagnetic interference, good concealment, precision
The features such as, it is widely applied in aerospace and national defense and military fields.Traditional shallow Combinated navigation method of inertia/astronomy
In, celestial navigation needs while observing three or three or more fixed stars to determine the position and attitude of aircraft, it leads with inertia
The posture that boat resolves compares as measurement, by the navigational parameter for filtering the system that acquires.Inertia/astronomy deep integrated navigation side
In method, celestial navigation is directly merged celestial body vector or altitude of the heavenly body with inertial navigation data, it does not need to compute repeatedly
Error and when only a fixed star is observed, also can preferably work, but need to utilize inertial navigation when calculating altitude of the heavenly body
The horizontal reference of offer, however due to the constant value deviation of inertia device, so that the precision of horizontal reference is lower, influence inertia/day
The positioning accuracy of literary deep integrated navigation system.
Summary of the invention
The technical problem to be solved by the present invention is for make up it is existing to inertia-astronomy deep integrated navigation technique study not
Foot, improves the precision of integrated navigation, proposes a kind of inertia based on single-shaft-rotation modulation-astronomy deep integrated navigation method.
The technical solution adopted by the present invention are as follows: a kind of inertia based on single-shaft-rotation modulation-astronomy deep integrated navigation method,
Using the attitude error of celestial body vector correction aircraft, the location error of altitude of the heavenly body amendment aircraft is used.Due to acceleration
The constant value biasing of meter causes horizontal reference precision lower, affects the positioning accuracy of celestial navigation system, thereby reduces combination
The precision of navigation.In single-shaft-rotation modulation formula strapdown inertial navigation system, by using single-shaft-rotation modulation technology, water is improved
The precision of flat benchmark, and then improve the navigation accuracy of combined system.Specifically includes the following steps:
1. single-shaft-rotation modulation conceptual design
Rotation modulation technology is a kind of Error Compensation Technology for inertial navigation system, and process can indicate are as follows: just
Beginning, moment aircraft remained static, i.e. the position of aircraft immobilizes, and in aircraft interior, indexing mechanism controls IMU
Start to be rotated with certain angular speed around vertical direction, revolving speed it is known that then IMU coordinate system and aircraft body coordinate system it
Between transition matrix are as follows:
In formula, w is the angular velocity of rotation of rotary shaft, and t is rotation time.
Strapdown resolving carries out all in navigational coordinate system, it is therefore desirable to relevant measurement be transformed into navigation system, be
So that the effect of rotation modulation is easily understood, aircraft body coordinate system is set and navigational coordinate system is overlapped, that is,For list
Bit matrix,It can then be indicated in the constant value deviation of t moment inertial measurement component in navigational coordinate system are as follows:
In formula, εn=[εE εN εU]TWithIt respectively represents in navigational coordinate system and IMU coordinate system
The constant value drift of gyro.WithRespectively represent navigational coordinate system neutralization
The constant value biasing of accelerometer in IMU coordinate system.
By formula (2) and (3) as it can be seen that in the horizontal direction, the constant value deviation of inertial measurement component, which is modulated into, has sine
Or the change curve of cosine form, therefore in a complete rotation period, their mean value is zero, will not be caused to system
Additional deviation will not influence the precision of integrated navigation system.However along the gyro and accelerometer in rotary axis direction
Constant value deviation does not change, it can cause the position error of Strapdown Inertial Navigation System to increase with the accumulation of time, in conclusion
Single-shaft-rotation technology is only capable of the inertia device constant value deviation of modulation vertical rotary axis direction, and the constant value with rotary shaft parallel direction
Deviation is propagated still according to original mode.In order to modulate IMU constant value deviation in three directions, sensitivity can be used
Axis and the non-coincidence indexable scheme of rotary shaft.As shown in Fig. 2, o-x in figurebybzbRepresent body coordinate system, o-xpypzpRepresent IMU
Coordinate system, θbpRepresent the established angle between IMU and aircraft.During single-shaft-rotation modulation, rotation modulation technology is to gyro
It is had the same effect with the deviation of accelerometer.
We analyze by taking the modulation result of gyro as an example, navigation system and this system weight in initial time aircraft
It closes, gyro is around zbAxis carries out continuous positive and negative rotation rotation with constant angular speed, and spin matrix can indicate are as follows:
The drift of gyro can indicate are as follows:
In formula, εn=[εE εN εU]TWithIt respectively represents in navigational coordinate system and IMU coordinate system
The constant value drift of middle gyro；Represent the transition matrix between aircraft body coordinate system and navigational coordinate system；Generation
One positive and negative rotation period of table, from formula (6) it is found that when gyro is when x and z directions zero bias are equal, and θbpWhen being 45 °, gyro is three
Constant value drift in axis direction can theoretically be modulated into zero.
2. single-shaft-rotation modulation ins error establishing equation
The strapdown resolving process of single-shaft-rotation modulation formula Strapdown Inertial Navigation System is identical with inertial navigation, single-shaft-rotation modulation formula
The error equation of Strapdown Inertial Navigation System is also consistent with traditional Strapdown Inertial Navigation System.
(1) attitude error equations
In the case where small misalignment, attitude error equations can be indicated are as follows:
In formula, φ=[φE,φN,φU]T；Represent rotational-angular velocity of the earth in navigation system；εpRespectively represent IMU coordinate
Gyroscope constant value drift in system；For the transition matrix between ideal navigational coordinate system and computer platform coordinate system；For
Transition matrix between IMU coordinate system and aircraft body coordinate system；I indicates unit matrix,It represents by aircraft body system
To the transition matrix of computer navigation coordinate system；
(2) velocity error equation
According to the navigation principle and specific force equation of single-shaft-rotation modulation formula inertial navigation, the calculation formula of speed can be obtained
Are as follows:
In formula, vn=[vE,vN,vU]TFor the speed of aircraft, gn=[0,0 ,-g]TTerrestrial gravitation vector acceleration is represented,
Wherein the size of g is 9.788m/s2。
Velocity error is defined as:According to formula (8), velocity error equation can be indicated are as follows:
In formula, δ vn=[δ vE,δvN,δvU]。
(3) location error equation
Position (i.e. longitude and latitude) differential equation of aircraft can be obtained by formula (10):
Differential is carried out by formula (10), then location error equation are as follows:
(4) inertial device error equation
The error equation of gyroscope constant value drift and accelerometer bias can be write as:
In conclusion the total error equation of system can be write as:
In formula,For the transition matrix between ideal navigational coordinate system and computer platform coordinate system, δ r=[δ L, δ
λ]TFor location error.
3. the foundation of the single-shaft-rotation modulation inertia based on celestial body vector sum altitude of the heavenly body/astronomy deep combination model
For the attitude error for only having modified aircraft in the inertia based on celestial body vector/astronomy deep combination, and due to adding
The problem of location error caused by the constant value deviation of speed and velocity error are dissipated with the increase of time, proposes based on day
The inertia of body vector sum altitude of the heavenly body/astronomy deep integrated navigation method, it does not correct aircraft merely with celestial body Vector Message
Attitude error, and utilize observed altitude of the heavenly body to correct the location information of aircraft.
During calculating altitude of the heavenly body, need to use the horizontal reference of Strapdown Inertial Navigation System, due to IMU constant value deviation
It influences, so that the precision of horizontal reference is lower.So IMU takes uniaxial positive and negative rotation, that is, use rotation modulation inertial navigation technique to mention
The precision for the horizontal reference that high inertial navigation provides.To the higher navigation accuracy of acquisition, navigation information is not only estimated,
Also to estimate the constant value deviation of gyro and accelerometer in IMU.Its state equation uses the error equation of inertial navigation system,
Measurement uses starlight vector and altitude of the heavenly body, and filtering method uses UKF.
State equation is established to system first.According to combined filter principle, the error side of strapdown inertial navigation system is chosen
The state equation of Cheng Zuowei system is usedExpression state
Amount, φE,φN,φUEast orientation, north orientation, day are respectively indicated to the misaligned angle of the platform；δvE,δvNIndicate the velocity error of east orientation, north orientation；δ
L, δ λ respectively indicate the latitude error of aircraft, longitude error；Respectively represent three axial directions of gyro in IMU coordinate system
Constant value drift；Respectively represent the biasing of three axial directions of accelerometer in IMU coordinate system.According to inertial navigation original
Reason, state equation are as follows:
In formula, φ=[φE,φN,φU]T；It is the angular velocity of rotation of relative inertness system for navigation in navigation system；Generation
Rotational-angular velocity of the earth in table navigation system；Rotational angular velocity of the aircraft navigation system with respect to earth system in representative navigation system；δr
=[δ L, δ λ]TFor location error；For the output of accelerometer in navigational coordinate system.According to formula (15), Ke Yijian
It is written as:
In formula, W is the noise matrix of system.F is the state-transition matrix of state equation, can be indicated are as follows:
In formula,It is transition matrixFront two row.FNIt can indicate are as follows:
In formula:
In formula, RxRepresent the principal radius of curvature in local meridian plane, RyIt represents perpendicular to the principal curvatures in plane on meridian plane half
Diameter；ωieThe rotation angular speed of axis is rotated about for the earth.
Measurement selects celestial body vector sum altitude of the heavenly body.The starlight vector s in measurement equationsIt can indicate are as follows:
In formula,Indicate that star sensor installs matrix；siIndicate the starlight vector information of i-th of fixed star；For from the earth's core
Inertial coodinate system is to the transition matrix between terrestrial coordinate system.
Altitude of the heavenly body H can be indicated are as follows:
SinH=sin (L+ δ L) sin △+cos (L+ δ L) cos △ cos (tGHA+λ+δλ) (20)
In formula, △ is the declination of this fixed star；L indicates latitude；δ L indicates latitude error；tGHAIndicate celestial body Greenwich hour angle；
The longitude of λ expression aircraft position；The longitude error of δ λ expression aircraft position.
Choose measurement Z=[ss；SinH] according to formula (19) and formula (20), measurement equation can indicate are as follows:
Z=h (X)+V (21)
In formula, V is measurement system noise.
Beneficial effects of the present invention:
1. single-shaft-rotation modulation inertial navigation technique, using sensitive axes and the non-coincidence continuous positive and negative rotation indexing scheme of rotary shaft,
The biasing of IMU constant value has modulation in three directions, solves since the constant value biasing of accelerometer leads to horizontal reference precision
It is low, the problem of influencing celestial navigation system positioning accuracy, and then reduce integrated navigation precision.
2. single-shaft-rotation modulation inertial navigation/astronomy deep integrated navigation method, using celestial body vector sum altitude of the heavenly body as measurement
Information can not only correct the attitude error of aircraft, and can correct the location information of aircraft, improve the navigation of total system
Precision.
3. the algorithm of the invention, design science optimization is safe and reliable to operation.
Detailed description of the invention
Fig. 1 is that a kind of single-shaft-rotation modulation formula of single-shaft-rotation modulation inertia/astronomy deep integrated navigation method of the present invention is prompt
Join inertial navigation system and resolves schematic diagram；
Fig. 2 is a kind of single-shaft-rotation modulation structure of single-shaft-rotation modulation inertia/astronomy deep integrated navigation method of the present invention
Figure；
Fig. 3 is a kind of single-shaft-rotation modulation formula inertia/astronomy of single-shaft-rotation modulation inertia/astronomy deep integrated navigation method
Integrated navigation schematic diagram.
Specific embodiment
With reference to the accompanying drawing and specific embodiment further illustrates the present invention.
With reference to figures 1 through shown in Fig. 3, a kind of single-shaft-rotation modulation inertial navigation/astronomy deep integrated navigation method, including following skill
Art step:
1. single-shaft-rotation modulation conceptual design
Rotation modulation technology is a kind of Error Compensation Technology for inertial navigation system, and process can indicate are as follows: just
Beginning, moment aircraft remained static, i.e. the position of aircraft immobilizes, and in aircraft interior, indexing mechanism controls IMU
Start to be rotated with certain angular speed around vertical direction, revolving speed it is known that then IMU coordinate system and aircraft body coordinate system it
Between transition matrix are as follows:
In formula, w is the angular velocity of rotation of rotary shaft, and t is rotation time.
Strapdown resolving carries out all in navigational coordinate system, it is therefore desirable to relevant measurement be transformed into navigation system, be
So that the effect of rotation modulation is easily understood, aircraft body coordinate system is set and navigational coordinate system is overlapped, that is,For list
Bit matrix,It can then be indicated in the constant value deviation of t moment inertial measurement component in navigational coordinate system are as follows:
In formula, εn=[εE εN εU]TWithIt respectively represents in navigational coordinate system and IMU coordinate system
The constant value drift of gyro.WithRespectively represent navigational coordinate system neutralization
The constant value biasing of accelerometer in IMU coordinate system.
By formula (23) and (24) as it can be seen that in the horizontal direction, the constant value deviation of inertial measurement component, which is modulated into, to be had just
The change curve of string or cosine form, therefore in a complete rotation period, their mean value is zero, will not be made to system
At additional deviation, the precision of integrated navigation system will not influence.However along the gyro and accelerometer in rotary axis direction
Constant value deviation do not change, it can cause the position error of Strapdown Inertial Navigation System to increase with the accumulation of time, to sum up institute
State, single-shaft-rotation technology be only capable of modulation vertical rotary axis direction inertia device constant value deviation, and with rotary shaft parallel direction
Constant value deviation is propagated still according to original mode.In order to modulate IMU constant value deviation in three directions, can be used
Sensitive axes and the non-coincidence indexable scheme of rotary shaft.As shown in Fig. 2, o-x in figurebybzbRepresent body coordinate system, o-xpypzpGeneration
Table I MU coordinate system, θbpRepresent the established angle between IMU and aircraft.During single-shaft-rotation modulation, rotation modulation technology pair
The deviation of gyro and accelerometer has the same effect.
We analyze by taking the modulation result of gyro as an example, navigation system and this system weight in initial time aircraft
It closes, gyro is around zbAxis carries out continuous positive and negative rotation rotation with constant angular speed, and spin matrix can indicate are as follows:
The drift of gyro can indicate are as follows:
In formula, εn=[εE εN εU]TWithIt respectively represents in navigational coordinate system and IMU coordinate system
The constant value drift of middle gyro；Represent the transition matrix between aircraft body coordinate system and navigational coordinate system；Generation
One positive and negative rotation period of table, from formula (27) it is found that when gyro is when x and z directions zero bias are equal, and θbpWhen being 45 °, gyro is three
Constant value drift in axis direction can theoretically be modulated into zero.
2. single-shaft-rotation modulation ins error establishing equation
The strapdown resolving process of single-shaft-rotation modulation formula Strapdown Inertial Navigation System is identical with inertial navigation, single-shaft-rotation modulation formula
The error equation of Strapdown Inertial Navigation System is also consistent with traditional Strapdown Inertial Navigation System.
(1) attitude error equations
In the case where small misalignment, attitude error equations can be indicated are as follows:
In formula, φ=[φE,φN,φU]T；Represent rotational-angular velocity of the earth in navigation system；εpRespectively represent IMU coordinate
Gyroscope constant value drift in system；For the transition matrix between ideal navigational coordinate system and computer platform coordinate system；For
Transition matrix between IMU coordinate system and aircraft body coordinate system；I indicates unit matrix,It represents by aircraft body system
To the transition matrix of computer navigation coordinate system.
(2) velocity error equation
According to the navigation principle and specific force equation of single-shaft-rotation modulation formula inertial navigation, the calculation formula of speed can be obtained
Are as follows:
In formula, vn=[vE,vN,vU]TFor the speed of aircraft, gn=[0,0 ,-g]TTerrestrial gravitation vector acceleration is represented,
Wherein the size of g is 9.788m/s2。
Velocity error is defined as:According to formula (29), velocity error equation can be indicated are as follows:
In formula, δ vn=[δ vE,δvN,δvU]。
(3) location error equation
Position (i.e. longitude and latitude) differential equation of aircraft can be obtained by formula following formula:
Differential is carried out by formula (31), then location error equation are as follows:
(4) inertial device error equation
The error equation of gyroscope constant value drift and accelerometer bias can be write as:
In conclusion the total error equation of system can be write as:
In formula,For the transition matrix between ideal navigational coordinate system and computer platform coordinate system, δ r=[δ L, δ
λ]TFor location error.
3. the foundation of the single-shaft-rotation modulation inertia based on celestial body vector sum altitude of the heavenly body/astronomy deep combination model
For the attitude error for only having modified aircraft in the inertia based on celestial body vector/astronomy deep combination, and due to adding
The problem of location error caused by the constant value deviation of speed and velocity error are dissipated with the increase of time, proposes based on day
The inertia of body vector sum altitude of the heavenly body/astronomy deep integrated navigation method, it does not correct aircraft merely with celestial body Vector Message
Attitude error, and utilize observed altitude of the heavenly body to correct the location information of aircraft.
During calculating altitude of the heavenly body, need to use the horizontal reference of Strapdown Inertial Navigation System, due to IMU constant value deviation
It influences, so that the precision of horizontal reference is lower.So IMU takes uniaxial positive and negative rotation, that is, use rotation modulation inertial navigation technique to mention
The precision for the horizontal reference that high inertial navigation provides.To the higher navigation accuracy of acquisition, navigation information is not only estimated,
Also to estimate the constant value deviation of gyro and accelerometer in IMU.Its state equation uses the error equation of inertial navigation system,
Measurement uses starlight vector and altitude of the heavenly body, and filtering method uses UKF.
State equation is established to system first.According to combined filter principle, the error side of strapdown inertial navigation system is chosen
The state equation of Cheng Zuowei system is usedExpression state
Amount, φE,φN,φUEast orientation, north orientation, day are respectively indicated to the misaligned angle of the platform；δvE,δvNIndicate the velocity error of east orientation, north orientation；δ
L, δ λ respectively indicate the latitude error of aircraft, longitude error；Respectively represent three axial directions of gyro in IMU coordinate system
Constant value drift；Respectively represent the biasing of three axial directions of accelerometer in IMU coordinate system.According to inertial navigation original
Reason, state equation are as follows:
In formula, φ=[φE,φN,φU]T；It is the angular velocity of rotation of relative inertness system for navigation in navigation system；Generation
Rotational-angular velocity of the earth in table navigation system；Rotational angular velocity of the aircraft navigation system with respect to earth system in representative navigation system；δr
=[δ L, δ λ]TFor location error；For the output of accelerometer in navigational coordinate system.It, can be with according to formula (36)
It writes a Chinese character in simplified form are as follows:
In formula, W is the noise matrix of system.F is the state-transition matrix of state equation, can be indicated are as follows:
In formula,It is transition matrixFront two row.FNIt can indicate are as follows:
In formula:
In formula, RxRepresent the principal radius of curvature in local meridian plane, RyIt represents perpendicular to the principal curvatures in plane on meridian plane half
Diameter；ωieThe rotation angular speed of axis is rotated about for the earth.
Measurement selects celestial body vector sum altitude of the heavenly body.The starlight vector s in measurement equationsIt can indicate are as follows:
In formula,Indicate that star sensor installs matrix；siIndicate the starlight vector information of i-th of fixed star；For from the earth's core
Inertial coodinate system is to the transition matrix between terrestrial coordinate system.
Altitude of the heavenly body H can be indicated are as follows:
SinH=sin (L+ δ L) sin △+cos (L+ δ L) cos △ cos (tGHA+λ+δλ) (41)
In formula, △ is the declination of this fixed star；L indicates latitude；δ L indicates latitude error；tGHAIndicate celestial body Greenwich hour angle；
The longitude of λ expression aircraft position；The longitude error of δ λ expression aircraft position.
Choose measurement Z=[ss；SinH] according to formula (40) and formula (41), measurement equation can indicate are as follows:
Z=h (X)+V (42)
In formula, V is measurement system noise.
Claims (1)
1. a kind of single-shaft-rotation modulation inertia-astronomy deep integrated navigation method, which comprises the steps of:
Step 1: being directed to single-shaft-rotation modulation inertial navigation technique, the rotation approach of IMU is formulated, the constant value of IMU is made to be biased in three sides
It is modulated upwards；The rotation approach of the IMU:
IMU rotation uses the indexable scheme of sensitive axes and the non-coincidence continuous positive and negative rotation of rotary shaft, o-xbybzbRepresent ontology coordinate
System, o-xpypzpRepresent IMU coordinate system, θbpThe established angle between IMU and aircraft is represented, in the navigation of initial time aircraft
System and this system are overlapped, and gyroscope is around zbAxis carries out continuous positive and negative rotation rotation with constant angular speed, and spin matrix can be with table
It is shown as:
In formula, w is the angular velocity of rotation of rotary shaft, and t is rotation time；
The drift of gyro can indicate are as follows:
In formula, εn=[εE εN εU]TWithRespectively represent in navigational coordinate system and IMU coordinate system in top
The constant value drift of spiral shell；Represent the transition matrix between aircraft body coordinate system and navigational coordinate system；Represent one
A positive and negative rotation period, from formula (3) it is found that when gyro is when x and z directions zero bias are equal, and θbpWhen being 45 °, gyro is in three axis sides
Upward constant value drift can theoretically be modulated into zero；
Step 2: establishing single-shaft-rotation modulation ins error equation；
Step 3: establishing single-shaft-rotation modulation inertial navigation-astronomy deep combination state using celestial body vector sum altitude of the heavenly body as measurement
Equation and measurement equation,
State equation is established to system first, according to combined filter principle, the error equation for choosing strapdown inertial navigation system is made
For the state equation of system, useIndicate quantity of state,
φE,φN,φUEast orientation, north orientation, day are respectively indicated to the misaligned angle of the platform；δvE,δvNIndicate the velocity error of east orientation, north orientation；δL,δ
λ respectively indicates the latitude error of aircraft, longitude error；Respectively represent three axial directions of gyro in IMU coordinate system
Constant value drift；Respectively represent the biasing of three axial directions of accelerometer in IMU coordinate system；According to inertial navigation principle,
Its state equation are as follows:
In formula, φ=[φE,φN,φU]T；It is the angular velocity of rotation of relative inertness system for navigation in navigation system；Representative is led
Rotational-angular velocity of the earth in boat system；Rotational angular velocity of the aircraft navigation system with respect to earth system in representative navigation system；δ r=[δ
L,δλ]TFor location error；It can be write a Chinese character in simplified form for the output of accelerometer in navigational coordinate system according to formula (4)
Are as follows:
W is the noise matrix of system in formula, and F is the state-transition matrix of state equation, can be indicated are as follows:
In formula,It is transition matrixFront two row, FNIt can indicate are as follows:
In formula:
In formula, RxRepresent the principal radius of curvature in local meridian plane, RyIt represents perpendicular to the principal radius of curvature in plane on meridian plane；
ωieThe rotation angular speed of axis is rotated about for the earth；
Measurement selects celestial body vector sum altitude of the heavenly body, the starlight vector s in measurement equationsIt can indicate are as follows:
In formula,Indicate that star sensor installs matrix；siIndicate the starlight vector information of i-th of fixed star；For from Earth central inertial
Coordinate system is to the transition matrix between terrestrial coordinate system；
Altitude of the heavenly body H can be indicated are as follows:
SinH=sin (L+ δ L) sin Δ+cos (L+ δ L) cos Δ cos (tGHA+λ+δλ) (9)
In formula, Δ is the declination of this fixed star；L indicates latitude；δ L indicates latitude error；tGHAIndicate celestial body Greenwich hour angle；λ table
Show the longitude of aircraft position；The longitude error of δ λ expression aircraft position；
Choose measurement Z=[ss；SinH] according to formula (8) and formula (9), measurement equation can indicate are as follows:
Z=h (X)+V (10)
In formula, V is measurement system noise.
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| CN110986934B (en) * | 2019-12-12 | 2022-10-18 | 北京自动化控制设备研究所 | Navigation method and system of integrated double-shaft rotation inertial navigation astronomical integrated navigation system |
| CN111121766B (en) * | 2019-12-17 | 2023-07-07 | 南京理工大学 | Astronomical and inertial integrated navigation method based on starlight vector |
| CN111351480B (en) * | 2020-03-17 | 2021-10-15 | 北京航空航天大学 | Aircraft attitude adjusting path optimization method based on rotation |
| CN111947653A (en) * | 2020-08-13 | 2020-11-17 | 北京航空航天大学 | Dual-mode inertial/visual/astronomical navigation method for lunar surface inspection tour detector |
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