CN115856977A - Relative navigation method based on differential GNSS - Google Patents

Relative navigation method based on differential GNSS Download PDF

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CN115856977A
CN115856977A CN202211677830.9A CN202211677830A CN115856977A CN 115856977 A CN115856977 A CN 115856977A CN 202211677830 A CN202211677830 A CN 202211677830A CN 115856977 A CN115856977 A CN 115856977A
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relative
gnss
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张晓彤
潘菲
张抒扬
华耿湃
龚思进
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Shanghai Aerospace Control Technology Institute
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Shanghai Aerospace Control Technology Institute
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Abstract

The invention discloses a relative navigation method based on differential GNSS, which comprises the steps of utilizing an inertial measurement device installed on an aircraft to estimate the relative maneuvering acceleration of two satellites generated by external force in real time, compensating relative position information output by the GNSS according to the time difference between system time and the GNSS to obtain a measured value at the current moment, determining the quaternion of an output inertial system relative to a body system and the conversion relation among the body system, the inertial system and a target satellite orbit system according to absolute attitude, unifying the acceleration and the relative position information under the target satellite orbit system, finally adopting Kalman filtering to resolve the relative positions of the two satellites, designing a data jump fault processing mechanism, limiting the correction quantity of the GNSS of navigation filtering according to the size of the correction value after Kalman filtering convergence, reducing the influence of measurement jump on navigation and closed loop orbit control, eliminating the problem of measurement value lag caused by the output frequency of a single machine of the differential GNSS, and obtaining high-precision positioning data.

Description

Relative navigation method based on differential GNSS
Technical Field
The invention relates to the problem of relative navigation of cooperative targets, in particular to a relative navigation method based on differential GNSS.
Background
The Global Navigation Satellite System (GNSS) has the characteristics of all-time, all-weather and global coverage, and has mature application technology in low orbit. The single-point GPS positioning accuracy is only up to a meter level under the influence of an ionosphere error, a troposphere error and the like, and the differential GPS technology utilizes the correlation of the errors in time and space, reduces or eliminates the influence of the errors on the positioning accuracy and greatly improves the positioning accuracy. Compared with the traditional microwave and optical relative measurement sensors, the differential GNSS sensor has the advantages of small volume, light weight and no restriction conditions that optical tracking is influenced by space illumination, and is gradually and widely applied to low-orbit satellite formation and space rendezvous and docking tasks. With the increasing application of space relative positioning, the measurement system of the differential GNSS is less limited by the relative distance between two stars and space environment factors, and has higher measurement precision, so the method gradually emerges from relative measurement sensors. However, the GNSS outputs full second measurement values, and the measurement information is built in a stand-alone measurement system, and the lag of the information causes the error of the navigation algorithm to increase.
Disclosure of Invention
The invention aims to provide a relative navigation method based on a differential GNSS, which solves the problem of measurement value lag caused by the output frequency of a single unit of the differential GNSS and obtains high-precision positioning data.
In order to achieve the above object, the present invention provides a relative navigation method based on differential GNSS, comprising the following steps:
s1, GNSS data alignment, recursion of whole second measurement information output by a GNSS to the current moment, and guarantee that the whole second measurement information is aligned to the same time point with the input quantity of other systems;
s2, aligning a coordinate system, and converting the position speed under the GNSS measurement system to a target satellite orbit system;
s3, establishing a relative motion equation and an observation equation;
and S4, resolving the relative positions of the two satellites by adopting a Kalman filtering algorithm, and limiting the correction quantity of the navigation filtering according to the correction value after Kalman filtering convergence.
The step S1 includes:
calculating the time difference: Δ t 2 ＝t gnc -t rel ；
Wherein, t gnc Is the system time, t rel A time scale at the same time as the position and speed of the GNSS output;
from the last beat three-axis position
Figure BDA0004017784530000021
Calling a module for calculating the earth gravity by the position and the speed, and calculating the gravity acceleration g: />
Figure BDA0004017784530000022
Wherein R is e 6378137m for the mean radius of the earth; j is a unit of 2 =1082.63607e-6, μ =398600km/s is the gravitational constant,
Figure BDA0004017784530000023
at the current moment, the J2000 system calculates the relative position and the relative speed between the two antennas:
Figure BDA0004017784530000024
Figure BDA0004017784530000025
v rel1 ＝v rel +a i ·Δt 2
wherein the content of the first and second substances,
Figure BDA0004017784530000026
is a body system to inertial system conversion matrix, f b Is the acceleration of the system, r rel And v rel Position and velocity, r, respectively, of the GNSS rel1 And v rel1 Respectively the position and velocity at the current time.
The step S2 includes:
the relative position of the differential GNSS output is transformed to a target orbital system:
Figure BDA0004017784530000027
wherein the content of the first and second substances,
Figure BDA0004017784530000028
the transformation matrix from the inertial system to the target satellite orbit system is obtained by the target orbit number, and the calculation process is as follows:
Figure BDA0004017784530000031
Figure BDA0004017784530000032
/>
Figure BDA0004017784530000033
wherein, omega, i and u are respectively the ascension point, the orbit inclination angle and the latitude argument of the target.
The step S3 includes:
s3.1, modeling and establishing a state equation by using relative motion dynamics:
under a near-circular orbit, the relative kinetic equation of two stars is as follows, which is called C-W equation for short:
Figure BDA0004017784530000034
Figure BDA0004017784530000035
Figure BDA0004017784530000036
at relative position and relative speed
Figure BDA0004017784530000037
As the system state, the relative motion dynamics equation is expressed in a state space form;
converting a relative kinematic equation under a first orbital coordinate system of the target spacecraft into a second orbital coordinate system of the target spacecraft, wherein the relative kinematic equation is in the form of:
Figure BDA0004017784530000038
Figure BDA0004017784530000039
Figure BDA00040177845300000310
in general, n is replaced by ω, f x 、f y 、f z Are respectively replaced by a x 、a y 、a z (ii) a Handle
Figure BDA0004017784530000041
As state quantities, the relative motion equation is written in the form of a state space, with:
Figure BDA0004017784530000042
the abbreviation is as follows:
Figure BDA0004017784530000043
in the formula:
Figure BDA0004017784530000048
A 11 ＝[0 3×3 ],A 12 ＝I 3×3 ,/>
Figure BDA0004017784530000044
B 1 ＝[0 3×3 ],B 2 ＝I 3×3
Figure BDA0004017784530000045
is the average orbital angular velocity of the target spacecraft, mu is the gravitational constant, a is the orbital radius of the target spacecraft, a x 、a y 、a z Three-axis orbit control relative acceleration of two spacecrafts in an orbit coordinate system;
in each guidance control period, assume U (t) = [ a ] x a y a z ] T For a constant value, an analytical solution of the equation of state is solved using laplace transform:
Figure BDA0004017784530000046
in the formula:
Figure BDA0004017784530000047
Figure BDA0004017784530000051
Figure BDA0004017784530000052
Figure BDA0004017784530000053
/>
Figure BDA0004017784530000054
Figure BDA0004017784530000055
t 0 is the current time, t f For the end time, τ = t f -t 0 ；
Discretizing the state equation to obtain:
X k,k-1 ＝Φ k,k-1 X k-1 +Q k,k-1 U k-1 (ii) a Step S3.2, establishing an observation equation:
Figure BDA0004017784530000056
H k ＝[I 3×3 0 3×3 ]。
the step S4 includes:
s4.1, resolving the relative position of the two stars by adopting a Kalman filtering algorithm:
and (3) state estimation:
Figure BDA0004017784530000061
wherein, the predicted value is:
Figure BDA0004017784530000062
filtering gain:
Figure BDA0004017784530000063
filtering error covariance:
Figure BDA0004017784530000064
prediction error covariance:
P k ＝[I-K k H k ]P k,k-1
step S4.2, limiting the amplitude of the correction quantity delta z of the navigation filtering;
wherein the content of the first and second substances,
Figure BDA0004017784530000065
/>
clipping Δ z as follows:
Δz max ＝0.12m，5m≤R＜140m；
0.25m，140m≤R＜5km；
1.5m，5km≤R≤10km。
the invention estimates the relative maneuvering acceleration of two satellites generated by external force in real time by using an inertial measurement device installed on an aircraft, compensates relative position information output by GNSS according to the time difference between system time and the GNSS to obtain a measured value at the current moment, determines the quaternion of the output inertial system relative to the system and the track information of a target satellite to solve the conversion relation among the system, the inertial system and the target satellite track system by using absolute attitude, unifies the acceleration and the relative position information under the target satellite track system, finally solves the relative positions of the two satellites by using Kalman filtering, designs a data jump fault processing mechanism, limits the correction quantity of navigation filtering according to the size of a correction value after the Kalman filtering is converged, reduces the influence of measurement on navigation and closed-loop track control jump, eliminates the problem of measurement value lag caused by differential GNSS single-machine output frequency, and obtains high-precision positioning data.
Drawings
FIG. 1 is a flowchart of a relative navigation method based on a differential GNSS according to the present invention.
FIG. 2 shows the relative navigation position error of 5 km-10 km distance segments before and after clipping.
FIG. 3 is a graph of relative navigation velocity error before and after clipping for a 5km to 10km range.
FIG. 4 shows the relative navigation position error of the 5 m-140 m distance segment before and after the clipping.
FIG. 5 shows the relative navigation speed error before and after clipping for the distance segment of 5m to 140 m.
Detailed Description
The preferred embodiment of the present invention will be described in detail below with reference to fig. 1 to 5.
As shown in fig. 1, the present invention provides a relative navigation method based on differential GNSS, comprising the following steps:
s1, aligning GNSS data;
recursion of the whole second of measurement information output by the GNSS to the current moment, and ensuring that the measurement information is aligned to the same time point with the input quantity of other systems;
calculating the time difference: Δ t 2 ＝t gnc -t rel ；
Wherein, t gnc Is the system time, t rel A time scale at the same time as the position and speed output by the GNSS;
by
Figure BDA0004017784530000071
(for the last three-axis position), calling a module for calculating the gravity by the position speed, and calculating the gravity acceleration g:
Figure BDA0004017784530000072
wherein R is e 6378137m for earth mean radius; j. the design is a square 2 ＝1082.63607e-6，μ
=398600km/s is the gravitational constant,
Figure BDA0004017784530000073
at the current moment, the J2000 system calculates the relative position and the relative speed between the two antennas:
Figure BDA0004017784530000074
Figure BDA0004017784530000081
v rel1 ＝v rel +a i ·Δt 2
wherein the content of the first and second substances,
Figure BDA0004017784530000082
is a body system to inertial system conversion matrix, f b Is the system lower acceleration r rel And v rel Position and velocity, r, respectively, of the GNSS rel1 And v rel1 Respectively the position and the speed at the current moment;
s2, aligning a coordinate system, and converting the position speed under the GNSS measurement system to a target satellite orbit system;
the relative position of the differential GNSS output is translated to a target orbital system (system time):
Figure BDA0004017784530000083
wherein the content of the first and second substances,
Figure BDA0004017784530000084
the conversion matrix from the inertial system to the target star orbit system is obtained by the target orbit number, and the calculation process is as follows:
Figure BDA0004017784530000085
Figure BDA0004017784530000086
Figure BDA0004017784530000087
wherein, omega, i and u are respectively the ascension point, the orbit inclination angle and the latitude argument of the target;
s3, establishing a relative motion equation and an observation equation;
s3.1, modeling and establishing a state equation by using relative motion dynamics:
under a near-circular orbit, the relative kinetic equation of two stars is as follows, which is called C-W equation for short:
Figure BDA0004017784530000091
/>
Figure BDA0004017784530000092
Figure BDA0004017784530000093
wherein x, y and z are three-axis positions,
Figure BDA0004017784530000094
is a three-axis speed->
Figure BDA0004017784530000095
Is a triaxial acceleration, n is an angular track speed, relative position and relative speed->
Figure BDA0004017784530000096
As a system state, the relative motion dynamics equation is expressed in a state space form;
converting a relative kinematic equation under a first orbital coordinate system of the target spacecraft into a second orbital coordinate system of the target spacecraft, wherein the relative kinematic equation is in the form of:
Figure BDA0004017784530000097
Figure BDA0004017784530000098
Figure BDA0004017784530000099
wherein f is x 、f y 、f z Is a three-axis acceleration; in general, n is replaced by ω, f x 、f y 、f z Are respectively replaced by a x 、a y 、a z (ii) a Handle
Figure BDA00040177845300000910
As state quantities, the relative motion equation is written in the form of a state space, with:
Figure BDA00040177845300000911
the abbreviation is as follows:
Figure BDA00040177845300000912
in the formula:
Figure BDA00040177845300000913
A 11 ＝[0 3×3 ],A 12 ＝I 3×3 ,
Figure BDA0004017784530000101
B 1 ＝[0 3×3 ],B 2 ＝I 3×3
Figure BDA0004017784530000102
is the average orbital angular velocity of the target spacecraft, mu is the gravitational constant, a is the orbital radius of the target spacecraft, a x 、a y 、a z Three-axis orbit control relative acceleration of two spacecrafts in an orbit coordinate system;
the state equation form under the near-circular orbit is simple, the analytic solution can be obtained by adopting Laplace transform under the condition that the thrust is assumed to be a constant value, the analytic solution is simple in form and convenient to use;
in each guidance control period, assume U (t) = [ a ] x a y a z ] T For a constant value, an analytical solution of the equation of state is obtained:
Figure BDA0004017784530000103
in the formula:
Figure BDA0004017784530000104
Figure BDA0004017784530000105
Figure BDA0004017784530000106
Figure BDA0004017784530000111
Figure BDA0004017784530000112
Figure BDA0004017784530000113
/>
t 0 is the current time, t f For the end time, τ = t f -t 0 ；
Discretizing the state equation to obtain:
X k,k-1 ＝Φ k,k-1 X k-1 +Q k,k-1 U k-1 ；
s3.2, establishing an observation equation:
Figure BDA0004017784530000114
H k ＝[I 3×3 0 3×3 ]；
s4, resolving the relative positions of the two stars by adopting a Kalman filtering algorithm, and limiting the correction amount of the navigation filtering according to the correction value after Kalman filtering convergence to reduce the influence of measurement jump on navigation and closed-loop orbit control;
s4.1, resolving the relative position of the two stars by adopting a Kalman filtering algorithm:
and (3) state estimation:
Figure BDA0004017784530000115
wherein, the predicted value is:
Figure BDA0004017784530000121
and (3) filtering gain:
Figure BDA0004017784530000122
filtering error covariance:
Figure BDA0004017784530000123
prediction error covariance:
P k ＝[I-K k H k ]P k,k-1
step S4.2, limiting the amplitude of the correction quantity delta z of the navigation filtering;
wherein the content of the first and second substances,
Figure BDA0004017784530000124
the phase differential positioning error due to GNSS carriers is as follows:
relative position accuracy: better than 0.1m (single shaft) (R is more than or equal to 5m and less than 140 m); better than 0.2m (single axis) (R is more than or equal to 140m and less than 5 km); is better than 1m (single shaft) (R is more than or equal to 5km and less than or equal to 10 km);
relative speed accuracy: better than 0.05m/s (uniaxial) (R is more than or equal to 5km and less than or equal to 10 km); better than 0.03m/s (uniaxial) (R is more than or equal to 5m and less than or equal to 5 km);
according to the above accuracy index, clipping Δ z is as follows:
Δz max ＝0.12m(5m≤R＜140m)；
0.25m(140m≤R＜5km)；
1.5m(5km≤R≤10km)。
fig. 2 shows the relative navigation position error of the 5 km-10 km distance segment before and after amplitude limiting, fig. 3 shows the relative navigation speed error of the 5 km-10 km distance segment before and after amplitude limiting, and as can be seen from fig. 2 and fig. 3, after the jump of the amplitude 3m is subjected to amplitude limiting, the navigation position error is less than 0.5m, and the speed error is less than 0.1m/s (the error before amplitude limiting is 3m, 0.5m/s), so as to meet the requirement of rail control.
Fig. 4 shows the relative navigation position error of the distance segment of 5m to 140m before and after amplitude limiting, fig. 5 shows the relative navigation speed error of the distance segment of 5m to 140m before and after amplitude limiting, and as can be seen from fig. 4 and fig. 5, after the jump with the amplitude of 0.5m is processed by amplitude limiting, the navigation position error is less than 0.1m, and the speed error is less than 0.02m/s, which meets the system requirements.
The method estimates the relative maneuvering acceleration of two satellites generated by external force in real time by using an inertial measurement device installed on an aircraft, compensates relative position information output by the GNSS according to the time difference between system time and the GNSS to obtain a measured value at the current moment, determines the quaternion of the output inertial system relative to the system and the orbit information of a target satellite by using an absolute attitude to solve the conversion relation among the system, the inertial system and the orbit system, unifies the acceleration and the relative position information under the orbit system of the target satellite, finally solves the relative positions of the two satellites by using Kalman filtering, designs a data jump fault processing mechanism, limits the correction quantity of navigation filtering according to the size of a correction value after the Kalman filtering is converged, reduces the influence of measurement jump on navigation and closed-loop orbit control, eliminates the problem of measurement value lag caused by the output frequency of a differential GNSS single machine, and obtains high-precision positioning data.
It should be noted that, in the embodiments of the present invention, the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, which are only for convenience of describing the embodiments, and do not indicate or imply that the referred device or element must have a specific orientation, be configured and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (5)

1. A relative navigation method based on differential GNSS is characterized by comprising the following steps:
step S1, GNSS data alignment, which is to recur the whole second measurement information output by the GNSS to the current moment and ensure that the whole second measurement information is aligned to the same time point with the input quantity of other systems;
s2, aligning a coordinate system, and converting the position speed under the GNSS measurement system to the position speed under the target satellite orbit system;
s3, establishing a relative motion equation and an observation equation;
and S4, resolving the relative positions of the two satellites by adopting a Kalman filtering algorithm, and limiting the correction quantity of the navigation filtering according to the correction value after Kalman filtering convergence.
2. The differential GNSS based relative navigation method according to claim 1, wherein the step S1 comprises:
calculating the time difference: Δ t 2 ＝t gnc -t rel ；
Wherein, t gnc Is the system time, t rel A time scale at the same time as the position and speed output by the GNSS;
from the last beat three-axis position
Figure FDA0004017784520000011
Calling a module for calculating the earth gravity by the position and the speed, and calculating the gravity acceleration g:
Figure FDA0004017784520000012
wherein R is e 6378137m for earth mean radius; j. the design is a square 2 =1082.63607e-6, μ =3.98600418e14 is the gravitational constant,
Figure FDA0004017784520000013
at the current moment, J2000 is the relative position and relative speed between the following two antennas:
Figure FDA0004017784520000014
Figure FDA0004017784520000015
v rel1 ＝v rel +a i ·Δt 2
wherein the content of the first and second substances,
Figure FDA0004017784520000021
is a body system to inertial system conversion matrix, f b Is the system lower acceleration r rel And v rel Position and velocity, r, respectively, of the GNSS rel1 And v rel1 Respectively the position and velocity at the current moment.
3. The differential GNSS based relative navigation method according to claim 2, wherein the step S2 comprises:
the relative position of the differential GNSS output is transformed to a target orbital system:
Figure FDA0004017784520000022
wherein the content of the first and second substances,
Figure FDA0004017784520000023
the transformation matrix from the inertial system to the target satellite orbit system is obtained by the target orbit number, and the calculation process is as follows: />
Figure FDA0004017784520000024
Figure FDA0004017784520000025
Figure FDA0004017784520000026
Wherein, omega, i and u are respectively the ascension point, the orbit inclination angle and the latitude argument of the target.
4. The differential GNSS based relative navigation method according to claim 3, wherein the step S3 comprises:
s3.1, modeling and establishing a state equation by using the relative motion dynamics:
under a near-circular orbit, the relative kinetic equation of two stars is as follows, which is called C-W equation for short:
Figure FDA0004017784520000031
Figure FDA0004017784520000032
Figure FDA0004017784520000033
wherein x, y and z are three-axis positions,
Figure FDA0004017784520000034
is a three-axis speed->
Figure FDA0004017784520000035
Is a triaxial acceleration, n is an angular track speed, relative position and relative speed->
Figure FDA0004017784520000036
As a system state, the relative motion dynamics equation is expressed in a state space form;
converting a relative kinematic equation under a first orbital coordinate system of the target spacecraft into a second orbital coordinate system of the target spacecraft, wherein the relative kinematic equation is in the form as follows:
Figure FDA0004017784520000037
Figure FDA0004017784520000038
Figure FDA0004017784520000039
wherein, f x 、f y 、f z Is a three-axis acceleration; in general, n is replaced by ω, f x 、f y 、f z Are respectively replaced by a x 、a y 、a z (ii) a Handle
Figure FDA00040177845200000310
As state quantities, the relative motion equations are written in state space form, with: />
Figure FDA00040177845200000311
The abbreviation is as follows:
Figure FDA00040177845200000312
in the formula:
Figure FDA00040177845200000315
A 11 ＝[0 3×3 ],A 12 ＝I 3×3 ,
Figure FDA00040177845200000313
B 1 ＝[0 3×3 ],B 2 ＝I 3×3
Figure FDA00040177845200000314
is the average orbital angular velocity of the target spacecraft, mu is the gravitational constant, a is the orbital radius of the target spacecraft, a x 、a y 、a z Three-axis orbit control relative acceleration of two spacecrafts in an orbit coordinate system;
in each guidance control period, assume U (t) = [ a ] x a y a z ] T For a constant value, an analytical solution of the state equation is solved by using laplace transform:
Figure FDA0004017784520000041
in the formula:
Figure FDA0004017784520000042
Figure FDA0004017784520000043
/>
Figure FDA0004017784520000044
Figure FDA0004017784520000045
Figure FDA0004017784520000046
Figure FDA0004017784520000051
t 0 is the current time, t f For the end time, τ = t f -t 0 ；
Discretizing the state equation to obtain:
X k,k-1 ＝Φ k,k-1 X k-1 +Q k,k-1 U k-1 ；
s3.2, establishing an observation equation:
Figure FDA0004017784520000052
H k ＝[I 3×3 0 3×3 ]。
5. the differential GNSS based relative navigation method according to claim 4, wherein the step S4 comprises:
s4.1, resolving the relative position of the two stars by adopting a Kalman filtering algorithm:
and (3) state estimation:
Figure FDA0004017784520000053
wherein, the predicted value is:
Figure FDA0004017784520000054
/>
filtering gain:
Figure FDA0004017784520000055
filtering error covariance:
Figure FDA0004017784520000056
prediction error covariance:
P k ＝[I-K k H k ]P k,k-1
s4.2, limiting the correction quantity delta z of the navigation filtering;
wherein the content of the first and second substances,
Figure FDA0004017784520000057
clipping Δ z as follows:
Δz max ＝0.12m，5m≤R＜140m；
0.25m，140m≤R＜5km；
1.5m，5km≤R≤10km。
CN202211677830.9A 2022-12-26 2022-12-26 Relative navigation method based on differential GNSS Pending CN115856977A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116734864A (en) * 2023-08-14 2023-09-12 中国西安卫星测控中心 Autonomous relative navigation method for spacecraft under constant observed deviation condition

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116734864A (en) * 2023-08-14 2023-09-12 中国西安卫星测控中心 Autonomous relative navigation method for spacecraft under constant observed deviation condition
CN116734864B (en) * 2023-08-14 2023-11-28 中国西安卫星测控中心 Autonomous relative navigation method for spacecraft under constant observed deviation condition

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