CN115856977A - Relative navigation method based on differential GNSS - Google Patents
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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
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 positionCalling a module for calculating the earth gravity by the position and the speed, and calculating the gravity acceleration g: />
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,
at the current moment, the J2000 system calculates the relative position and the relative speed between the two antennas:
v rel1 =v rel +a i ·Δt 2
wherein the content of the first and second substances,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:
wherein the content of the first and second substances,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:
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:
at relative position and relative speedAs 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:
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 HandleAs state quantities, the relative motion equation is written in the form of a state space, with:
the abbreviation is as follows:
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:
in the formula:
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:
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:
wherein, the predicted value is:
filtering gain:
filtering error covariance:
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;
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(for the last three-axis position), calling a module for calculating the gravity by the position speed, and calculating the gravity acceleration g:
wherein R is e 6378137m for earth mean radius; j. the design is a square 2 =1082.63607e-6,μ
at the current moment, the J2000 system calculates the relative position and the relative speed between the two antennas:
v rel1 =v rel +a i ·Δt 2
wherein the content of the first and second substances,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):
wherein the content of the first and second substances,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:
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:
wherein x, y and z are three-axis positions,is a three-axis speed->Is a triaxial acceleration, n is an angular track speed, relative position and relative speed->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:
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 HandleAs state quantities, the relative motion equation is written in the form of a state space, with:
the abbreviation is as follows:
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:
in the formula:
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:
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:
wherein, the predicted value is:
and (3) filtering gain:
filtering error covariance:
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;
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 positionCalling a module for calculating the earth gravity by the position and the speed, and calculating the gravity acceleration g:
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,
at the current moment, J2000 is the relative position and relative speed between the following two antennas:
v rel1 =v rel +a i ·Δt 2
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:
wherein the content of the first and second substances,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: />
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:
wherein x, y and z are three-axis positions,is a three-axis speed->Is a triaxial acceleration, n is an angular track speed, relative position and relative speed->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:
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 HandleAs state quantities, the relative motion equations are written in state space form, with: />
The abbreviation is as follows:
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:
in the formula:
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:
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:
wherein, the predicted value is:
filtering gain:
filtering error covariance:
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;
clipping Δ z as follows:
Δz max =0.12m,5m≤R<140m;
0.25m,140m≤R<5km;
1.5m,5km≤R≤10km。
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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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