CN111487660B - High-precision real-time micro-nano satellite cluster navigation method - Google Patents
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
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- G01S19/423—Determining position by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system by combining or switching between position solutions derived from different satellite radio beacon positioning systems
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Abstract
The invention provides a micro-nano satellite cluster distributed navigation scheme based on a Global Navigation Satellite System (GNSS) single-frequency receiver, which is used for constructing micro-nano satellite cluster absolute and relative orbit dynamics models suitable for high-precision navigation, establishing a fusion mechanism of single-frequency combined observation data and carrier phase difference data, and further designing a high-precision micro-nano satellite cluster navigation method. The invention adopts the idea of distributed navigation, namely each satellite in the cluster can send own GNSS measurement information to other satellites, and each satellite can utilize the received other satellites and the own GNSS measurement information to navigate all the satellites of the cluster. The specific implementation method of the invention is to carry out correction based on Kalman filtering on the estimators of satellite positions, speeds and other state quantities calculated by a dynamic model by utilizing GNSS observables and relative position vectors obtained based on carrier difference, thereby obtaining high-precision absolute and relative position information of a satellite cluster and realizing the purpose of carrying out high-precision navigation on the satellite cluster. The invention has the advantages of high navigation precision and good real-time performance.
Description
Technical Field
The invention provides a micro-nano Satellite cluster Navigation method with higher precision and real-time performance, and relates to a method for performing high-precision Navigation on a Satellite cluster by using a GNSS (global Navigation Satellite system) broadcast ephemeris, single-frequency pseudo-range and carrier phase information and inter-Satellite relative position vectors obtained based on carrier differential calculation and by utilizing extended Kalman filtering. Belonging to the technical field of navigation.
Background
The GNSS-based satellite precision orbit determination technology can be traced back to the 1975 feasibility study of the rockschid missile company in the united states on applying the GPS to the spacecraft navigation. Research suggests that below 800km orbit height, navigation using satellite-borne GPS receivers is technically completely feasible, and navigation at higher orbits also has tremendous research and development space. In 1982, the LandSat-4 satellite earth resource in the United states uses a satellite-borne GPS receiver to realize the navigation precision with the position error less than 50m under the condition of no SA interference, and the feasibility of the application of the GPS technology in the field of spacecraft navigation is proved.
With the development of decades, the low orbit satellite orbit determination technology based on GNSS tends to mature. Currently, the orbit determination method is divided into two methods, one is a reduced kinetics method, and the other is a kinematic method.
The reduced dynamics method was originally proposed by scholars such as T.P.Yunck, S.CWu et al and 1986, and was applied to the actual satellite orbit determination task. The method fuses the orbit dynamics equation of the satellite with the GPS observation equation, and optimally solves between the dynamics information and the geometric information, thereby weakening the error influence of the dynamics model, and realizing the continuous orbit determination under the condition of poor geometric distribution or data interruption of the GPS satellite. The method gives full play to the advantages of both satellite orbit dynamics and GPS measurement, and the provided orbit solution is the satellite mass center. The orbit determination of a GOCE satellite by using dual-frequency GPS to receive data has been verified as early as 2000 by P.N.A.M Visser and J.van den Ijssel, and the orbit accuracy obtained by a reduced dynamics method can reach the centimeter level.
In 2002, Chiaradia researches a method for carrying out real-time reduced dynamic orbit determination on a Topex/Poseidon satellite by using single-frequency GPS data, achieves the orbit determination precision of tens of meters, and verifies the feasibility of carrying out real-time orbit determination on a low-orbit satellite by using a cheap single-frequency GPS receiver.
Nowadays, a post-processing reduced dynamics orbit determination method is very mature, the orbit determination precision is high, the reduced dynamics orbit determination method based on single frequency and real time is also widely researched, but the reduced dynamics method has the most essential problems of complex calculation, large calculation amount, influence by the precision of a dynamics model and the like, so that the reduced dynamics method cannot be well applicable to the situations of small satellites with limited task budget and satellite resources, micro-nano satellite orbit determination tasks, satellite orbit change and the like. Thus, a more versatile, relatively less studied GNSS kinematic orbit determination method should receive more extensive attention.
A kinematic orbit determination method based on GNSS is a method for positioning and resolving only depending on GNSS pseudo-range information and carrier phase information received by a receiver. The orbit solution provided by the method is the position of the phase center of the antenna of the satellite-borne GNSS receiver.
In 2003, Montenbruck verifies the precision of the pure kinematics orbit determination method, and the method adopting single-frequency measurement data and GRAPHIC combined ionosphere elimination finally obtains 1-1.5m orbit determination three-dimensional error, thereby demonstrating the high-precision orbit determination feasibility of pure kinematics. However, compared to the reduced kinetics method, the kinematics orbit determination method is less studied, especially in the single-frequency real-time domain.
In summary, the invention provides a high-precision real-time micro-nano satellite cluster navigation method, which utilizes GNSS broadcast ephemeris, single-frequency pseudo-range and carrier phase information received by a receiver to correct state quantity predicted values obtained by absolute and relative dynamic models through an Extended Kalman Filter (EKF) to obtain a high-precision navigation result. And by utilizing a distributed design concept, a final high-precision navigation result of the satellite cluster is obtained by fusing the navigation result of each satellite in the satellite cluster.
Disclosure of Invention
Objects of the invention
The invention provides a distributed high-precision real-time navigation method based on a GNSS broadcast ephemeris, a single-frequency pseudo range and carrier phase information, and aims to solve the problem of high-precision orbit determination of a micro-nano satellite cluster. The method has the advantages of high precision and good real-time performance, and is suitable for real-time absolute navigation and positioning scenes of small satellites or micro-nano satellite clusters by utilizing a GNSS receiver.
(II) technical scheme
For convenience of description, taking a satellite cluster formed by three satellites A, B, C as an example, the high-precision real-time micro/nano satellite cluster navigation method provided by the invention has the following implementation steps:
the method comprises the following steps: computing state predictions for satellites in a cluster
The satellite A obtains the state prediction value of the position and the speed of the satellite A by using an absolute dynamic model, and obtains the state prediction values of the satellite B and the satellite C in the cluster by using a relative dynamic model.
The resultant force of the acting forces received by the satellite in space can be decomposed into component forces in the x, y and z directions along a coordinate system, and is marked as F x ,F y ,F z Thus, the absolute kinetic equation for a satellite can be written as:
expressed in vector form as:
wherein m represents the satellite whole satellite mass, and the ith perturbation force considered in the i-table type dynamic model.
The establishment of a relative kinetic model is discussed below. Taking satellite A, B as an example, the position vector of the two under the inertial system is r A ＝(x A ,y A ,z A ) T ,r B ＝(x B ,y B ,z B ) T Thus, the relative positions of the two can be expressed as:
r AB ＝r A -r B (3)
each perturbation force can be expressed as a function f of a position vector r i (r) performing first order Taylor expansion on each perturbation force at A, and neglecting high order small quantity to obtain B perturbation force as:
considering the small distance scale between the formation flying satellites a and B, only a first order taylor expansion can meet the accuracy requirement. Further, a relative kinetic model between the A star and the B star can be obtained as follows:
the space scale of the satellite cluster related by the invention is 100m to 100 km. Under such a spatial scale, the perturbation forces such as sunlight pressure, sun-moon attraction, atmospheric resistance and the like, which each satellite of the satellite cluster receives, can be considered to be equal in magnitude and direction, and can be counteracted in relative motion, so that only the term of earth attraction remains in the relative dynamic model, and further the relative dynamic model can be simplified as follows:
expressed in vector form as:
wherein
Is the gravity gradient at the location of satellite a.
Further, for a more general case, assuming that a satellite cluster is composed of a star and other N satellites, a simplified absolute and relative integrated kinetic model can be obtained as follows:
the absolute state predicted value of the satellite A and the predicted values of the relative position vectors from the satellites B and C to the satellite A can be obtained through the absolute and relative dynamics models, and then the predicted values of the absolute positions of the satellites B and C are obtained.
Step two: all satellites receive GNSS measurement information and send self-carrier phase information to other satellites
The single-frequency GRAPHIC combined observation model is used for fusing the single-frequency pseudo range and carrier phase information of the GNSS to the satellite A, so that the GNSS observation amount after ionospheric delay is removed is obtained, and the single-frequency GRAPHIC combined measurement can be expressed as follows:
where, P represents a single frequency pseudorange measurement,
for carrier phase information containing ambiguities, ρ represents the true distance between the GNSS satellite and the satellite, δ t is the satellite clock error, N G Is Graphic ambiguity,. epsilon G Combining measurement noise for GRAPHIC to obtain absolute position measurement information for satellite AAnd (4) information.
In addition, satellite a transmits GNSS carrier phase information obtained by itself to satellites B and C, while receiving GNSS carrier phase information transmitted by satellites B and C to satellite a.
Step three: obtaining relative position vectors using received GNSS carrier phase information
And predicting the states of the three satellites by using absolute and relative dynamic models. And then, obtaining a predicted value of a relative position vector between the satellites by using the predicted value:
r AB0 ＝r A0 -r B0 (10)
wherein r is AB0 Represents the relative position vector between satellites A and B, r A0 ，r B0 The absolute positions of satellites a and B, respectively, predicted using a kinetic model.
And the constructed precise carrier phase double-difference equation can be used for eliminating or weakening the orbit error of the satellite, the clock error of a receiver and the influence of the refraction errors of an ionosphere and a troposphere so as to improve the positioning precision. According to the principle of integer ambiguity generation, the real value of the integer ambiguity should be a definite integer. After an initial set of real integer ambiguity solutions is obtained, a search region is created around the initial set of real integer ambiguity solutions, candidate integer solutions are selected in the search region by a method, and a final integer ambiguity solution is selected from the candidate solutions according to a certain criterion.
The double difference carrier phase equation is:
namely, it is
Wherein: x k For relative position correction terms, N is double-difference integer ambiguity
The item uses the LAMBDA method to determine the carrier phase ambiguity N. Since the LAMDA method is a well-established algorithm, the LAMDA algorithm will not be explained in detail here. Thereby obtaining a relative position correction vector δ r AB And then obtaining an accurate relative position vector:
r AB ＝r AB0 +δr AB (15)
step four: calculating high-precision navigation result by utilizing absolute and relative integrated navigation algorithm
According to the method, an Extended Kalman Filter (EKF) is utilized, a state equation is constructed by absolute and relative dynamics models, a measurement equation is constructed by GNSS observed quantity, a predicted value of the state quantity is corrected, and a high-precision navigation result is obtained.
The state quantity X includes the position, velocity, carrier ambiguity, and clock offset of each satellite of the satellite constellation, and is expressed as:
X＝(x A ,y A ,z A ,v xA ,v yA ,v zA ,N GA ,cδt A ,x B ,y B ,z B ,v xB ,v yB ,v zB ,N GB ,cδt B ,x C ,y C ,z C ,v xC ,v yC ,v zC ,N GC ,cδt C ) T
(16)
firstly, a state equation of a satellite state quantity X is constructed according to the selected dynamic model, and the position speed of the satellite calculated in the step one is used as a state quantity predicted value.
And constructing a measurement equation according to the GNSS measurement principle and the carrier differential measurement relative position vector principle.
Observed quantities are respectively single-frequency GRAPHIC combined measurement:
and relative position vector:
the jacobian matrix H is thus obtained, where the rows corresponding to GNSS measurements can be expressed as:
where the row corresponding to the relative position vector may be represented as:
further, the Kalman filter recursion equation set is as follows:
wherein the content of the first and second substances,
is t k-1 To t k The state transition matrix of the time of day,
after linearization of the system, at t k-1 The residual error predicted value of the moment,
is a system pair t k An estimate of the residual of the time of day.
Is t after EKF treatment k And (4) optimal estimation of the system state quantity at the moment, namely a navigation result.
Step five: repeating the steps from one to four
And for any epoch time, repeating the first step to the fourth step to further obtain the navigation results of all satellites in the satellite cluster at the time
Step six: high-precision navigation information obtained by fusing navigation results of satellite clusters
The first step to the fifth step are also applied to the satellite B and the satellite C, so that three groups of state quantity estimated values based on the navigation method can be obtained at any epoch moment, and the three groups of state quantity estimated values are fused to obtain the high-precision navigation information of the satellite cluster.
Through the steps, a high-precision real-time navigation result based on the GNSS broadcast ephemeris, the single-frequency pseudo-range information and the carrier phase information can be obtained. Therefore, the requirement of the micro-nano satellite cluster for realizing high-precision real-time navigation by utilizing a GNSS receiver can be met.
(III) advantages
The high-precision real-time micro/nano satellite cluster navigation method provided by the invention has the advantages that:
the method provided by the invention adopts a distributed concept, namely, each satellite in the satellite cluster can obtain a high-precision navigation result of the satellite cluster through the method. The design concept can avoid the situation that navigation cannot be realized due to the fault of a certain satellite, and meanwhile, the precision of the satellite cluster navigation result can be further improved by fusing the navigation result of each satellite in the cluster.
And compared with a navigation algorithm only adopting the GNSS pseudo-range information, the method has higher navigation precision. And the GNSS receiving antenna for receiving the single-frequency pseudo-range information is more suitable for carrying the micro-nano satellite from the perspective of volume mass and power consumption.
Drawings
FIG. 1 is a flow chart of the steps of the present invention
FIG. 2 is a flow chart of expanding a Kalman filter
Detailed Description
The following will explain the specific implementation of the present invention in detail by taking a satellite cluster formed by three satellites A, B, C as an example, with reference to fig. 1 and the technical solution.
The method comprises the following steps: computing state predictions for satellites in a cluster
The satellite A obtains the state prediction value of the position and the speed of the satellite A by using an absolute dynamic model, and obtains the state prediction values of the satellite B and the satellite C in the cluster by using a relative dynamic model.
The resultant force of the acting forces received by the satellite in space can be decomposed into component forces in the x, y and z directions along a coordinate system, and is marked as F x ,F y ,F z Thus, the absolute kinetic equation for a satellite is expressed in vector form as:
wherein m represents the satellite whole satellite mass, and the ith perturbation force considered in the i-table type dynamic model.
The space scale of the satellite cluster related by the invention is 100m to 100 km. Under such a spatial scale, the perturbation force such as sunlight pressure, gravity of the sun and moon, atmospheric resistance and the like received by each satellite of the satellite cluster can be considered to be equal in magnitude and direction, and can be counteracted in relative motion, so that only the gravity of the earth remains in the relative dynamic model, and further the vector form of the relative dynamic model can be simplified as follows:
wherein
Is the gravity gradient at the location of satellite a.
Further, for a more general case, assuming that a satellite cluster is composed of a star and other N satellites, a simplified absolute and relative integrated kinetic model can be obtained as follows:
the absolute state predicted value of the satellite A and the predicted values of the relative position vectors from the satellites B and C to the satellite A can be obtained through the absolute and relative dynamics models, and then the predicted values of the absolute positions of the satellites B and C are obtained.
This step corresponds to the first block in figure one.
Step two: all satellites receive GNSS measurement information and send self-carrier phase information to other satellites
The GNSS is used for single-frequency GRAPHIC combined measurement of the satellite A, and the satellite A obtains the absolute measurement information of the satellite A.
Furthermore, satellite a transmits GNSS carrier phase information obtained by itself to satellites B and C, while receiving GNSS carrier phase information transmitted by satellites B and C to satellite a.
This step corresponds to the second block in the first drawing.
Step three: obtaining a relative position vector using received GNSS carrier phase information
Predicting the states of three satellites by using absolute and relative dynamics models, and obtaining a predicted value of a relative position vector between the satellites by using the predicted value:
r AB0 ＝r A0 -r B0 (26)
wherein r is AB0 Representing the relative position vector between satellites A and B, r A0 ，r B0 The absolute positions of satellites a and B, respectively, predicted using a kinetic model.
And the constructed precise carrier phase double-difference equation can be used for eliminating or weakening the orbit error of the satellite, the clock error of a receiver and the influence of the refraction errors of an ionosphere and a troposphere so as to improve the positioning precision. According to the principle of integer ambiguity generation, the real value of the integer ambiguity should be a definite integer. After an initial set of real integer ambiguity solutions is obtained, a search region is created around the initial set of real integer ambiguity solutions, candidate integer solutions are selected in the search region by a method, and a final integer ambiguity solution is selected from the candidate solutions according to a certain criterion.
The project determines the carrier phase ambiguity N by using an LAMBDA method. Since the LAMDA method is a well-established algorithm, the LAMDA algorithm will not be explained in detail here. Thereby obtaining a relative position correction vector δ r AB To obtain an accurate relative position vector
r AB ＝r AB0 +δr AB (27)
This step corresponds to the third block in the first drawing.
Step four: calculating high-precision navigation result by utilizing absolute and relative integrated navigation algorithm
According to the method, an Extended Kalman Filter (EKF) is utilized, a state equation is constructed by using absolute and relative dynamic models, a measurement equation is constructed by using GNSS single-frequency GRAPHIC combined observation and carrier difference-based relative position vector observation as observed quantities, and the state quantities are optimally estimated to obtain a high-precision navigation result.
The step corresponds to the fourth block in the first attached drawing, and a Kalman filter calculation flow chart is expanded and is shown in the second attached drawing.
Step five: repeating the steps from one to four
And for any epoch time, repeating the first step to the fourth step, and further obtaining the navigation results of all satellites in the satellite cluster at the time
Step six: high-precision navigation information obtained by fusing navigation results of satellite clusters
And step one to step five are also applied to the satellite B and the satellite C, so that three groups of state quantity estimated values based on the navigation method can be obtained at any epoch moment, and the three groups of state quantity estimated values are fused to obtain the high-precision navigation information of the satellite cluster.
Through the steps, a high-precision real-time navigation result based on the GNSS broadcast ephemeris, the single-frequency pseudo-range information and the carrier phase information can be obtained. Therefore, the requirement of the micro-nano satellite cluster for realizing high-precision real-time navigation by utilizing a GNSS receiver can be met.
Claims (1)
1. A high-precision real-time micro-nano satellite cluster navigation method takes a satellite cluster formed by three satellites A, B, C as an example, and is characterized in that: the method comprises the following steps:
the method comprises the following steps: computing state predictions for satellites in a cluster
The satellite A calculates a state predicted value of the position and the speed of the satellite A by using an absolute dynamic model, and calculates the state predicted values of the satellite B and the satellite C in the cluster by using a relative dynamic model;
step two: all satellites receive GNSS measurement information and send self-carrier phase information to other satellites
Taking a satellite A as an example, a single-frequency GRAPHIC combined observation model is utilized to fuse the single-frequency pseudo range and carrier phase information of the GNSS to the satellite A, so that the GNSS observed quantity after ionospheric delay is removed is obtained, and the satellite A obtains the absolute measurement information of the satellite A; in addition, the satellite A sends GNSS carrier phase information obtained by the satellite A to the satellites B and C, and simultaneously receives the GNSS carrier phase information sent by the satellites B and C to the satellite A;
step three: all satellites obtain relative position vectors by using received GNSS carrier phase information
The satellite A obtains relative position vectors of the satellite B and the satellite C relative to the satellite A based on carrier difference by utilizing the satellite A and the received carrier phase information of the satellite B and the satellite C;
step four: calculating high-precision navigation result by using absolute and relative integrated navigation algorithm
Constructing a state equation by using an Extended Kalman Filter (EKF) and an absolute and relative dynamic model, constructing a measurement equation by using GNSS observed quantity, and correcting a predicted value of the state quantity to obtain a high-precision navigation result;
step five: repeating the steps one to four
Repeating the first step to the fourth step for any epoch moment, and further obtaining navigation results of all satellites in the satellite cluster at the moment;
step six: high-precision navigation information obtained by fusing navigation results of satellite clusters
The first step to the fifth step are also applied to the satellite B and the satellite C, so that three groups of state quantity estimated values based on the navigation method can be obtained at any epoch moment, and the three groups of state quantity estimated values are fused to obtain the high-precision navigation information of the satellite cluster.
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