CN112578418B - Heaven and earth joint orbit calculation method for navigation constellation measurement and control management - Google Patents

Heaven and earth joint orbit calculation method for navigation constellation measurement and control management Download PDF

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CN112578418B
CN112578418B CN202011329906.XA CN202011329906A CN112578418B CN 112578418 B CN112578418 B CN 112578418B CN 202011329906 A CN202011329906 A CN 202011329906A CN 112578418 B CN112578418 B CN 112578418B
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CN112578418A (en
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朱俊
李�杰
呼延宗泊
王冲
房亚男
张峰
王家松
周来检
杨奇
马豪
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China Xian Satellite Control Center
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Abstract

The invention discloses a space-ground combined orbit calculation method for navigation constellation measurement and control management, which designs a space-ground based whole network orbit calculation process for avoiding rank deficiency of a normal equation, utilizes a long-term prediction ephemeris as a virtual observation for constraint, combines traditional foundation S-band measurement data and a Ka inter-satellite link weighting fusion algorithm, comprehensively processes traditional foundation S-band tracking data and inter-satellite link bidirectional distance measurement, obtains a precise ephemeris product, and is used for supporting navigation satellite measurement and control management and inter-satellite link management.

Description

Heaven and earth joint orbit calculation method for navigation constellation measurement and control management
Technical Field
The invention belongs to the technical field of aerospace measurement and control, and particularly relates to a space-ground combined orbit calculation method for navigation constellation measurement and control management.
Background
The traditional satellite measurement and control system mainly relies on a ground-based S/X waveband measurement and control station to track an in-orbit satellite, collect various measurement data (ranging, speed measuring and angle measuring) and send the measurement data to a measurement and control center to calculate the satellite orbit, thereby supporting the satellite measurement and control management and in-orbit application. Under the support of a foundation system, the satellites lack mutual connection, and the current measurement and control center collects station measurement data by establishing a single-satellite task environment to complete independent orbit calculation of each satellite, including orbit determination and forecast.
The navigation constellation utilizes a Satellite-borne Ka-band phased array antenna to establish an Inter-Satellite Link (ISL), adopts a Time Division Multiple Access (TDMA) mode and a plurality of satellites to carry out Inter-Satellite relative ranging, and can be used for supporting Satellite orbit calculation. Compared with the traditional foundation system, the method has the advantages that: (1) inter-satellite measurement is not restricted by visible arc segments of a ground station, and a longer continuous tracking arc segment is provided; (2) the method is not influenced by atmospheric propagation delay, and the measurement precision is higher; (3) the method depends on the support of a small number of ground measurement and control stations, saves ground measurement and control resources, and improves the autonomous survival capability of the satellite.
Compared with the traditional ground-based measurement data, the inter-satellite distance measurement comprises the relative position information of two satellites, the traditional single-satellite orbit calculation mode cannot be adopted, and the whole-network orbit determination method needs to be adopted. In addition, under the condition of no ground station support, absolute space position reference is lacked when the whole network orbit determination is carried out by only utilizing inter-satellite distance measurement, and the normal equation deficit rank of the orbit parameter estimation is obtained. Therefore, a multi-source information comprehensive constraint method is provided, which comprises the steps of (1) a priori orbit based on long-term prediction ephemeris; (2) tracking and measuring a small number of conventional foundation measurement and control stations; (3) bidirectional measurement is carried out on a foundation Ka tracking station; and the information is subjected to weighted fusion, so that the observation condition is improved, and the orbit determination precision is improved.
Disclosure of Invention
The invention aims to provide a space-ground combined orbit calculation method for navigation constellation measurement and control management, and provides an orbit determination method based on long-term prediction ephemeris, traditional foundation measurement and control station data and inter-satellite link Ka two-way distance measurement multi-source information fusion, so that observation conditions are improved, orbit determination precision is improved, and various satellite orbit information required by measurement and control management is generated.
The technical scheme adopted by the invention is that a navigation constellation measurement and control management-oriented heaven-earth joint orbit calculation method is implemented according to the following steps:
step 1, collecting and collecting original external measurement data packets and telemetering data packets, and decoding to obtain multi-satellite external measurement data and Ka inter-satellite link data;
according to the starting time of orbit determination t 0 ,t f ]Extracting long-term ephemeris (t) in a central database i ,X i ) Wherein t is i ∈[t 0 ,t f ]，
Figure BDA0002795463730000022
Represents t i A forecast ephemeris of time;
step 2, preprocessing multi-extraterrestrial measurement data and preprocessing Ka inter-satellite link data to obtain orbit determination observation data in a compatible format;
step 3, taking the forecast ephemeris at different moments as virtual observation, and calculating an equation 1 according to orbit determination observation data in a compatible format of each epoch; obtaining a normal equation 2 according to the multi-satellite external measurement data; processing Ka intersatellite link data to obtain a normal equation 3 and a normal equation 4;
and 4, weighting and fusing the normal equation 1 and the normal equation 2 with the normal equation 3 and the normal equation 4, and generating the whole network precise ephemeris after orbit determination and solution.
The invention is also characterized in that:
in step 1, according to the fixed orbit arc segment [ t ] 0 ,t f ]Extracting the last generated long-term ephemeris, and taking t 0 Ephemeris of time of day
Figure BDA0002795463730000021
As initial orbit determination values; and sampling the long-term prediction ephemeris with the sampling time interval of 5 minutes and the sampling data of each time of t i The ephemeris at that time is also used as a virtual observation.
The specific process of preprocessing the multi-extraterrestrial data in the step 2 is as follows: and carrying out troposphere correction and ionosphere correction on multi-extraterrestrial measurement data, wherein the multi-extraterrestrial measurement data comprise distance measurement, speed measurement and angle measurement, the distance measurement is the distance between a satellite and a ground measurement station, the speed measurement is the radial speed of the satellite relative to the ground measurement station, and the angle measurement is the azimuth and the pitch angle of the satellite in a station center horizontal coordinate system.
The concrete process of the Ka inter-satellite link data preprocessing in the step 2 is as follows: and establishing link matching for the Ka inter-satellite link data, namely finding two data of a receiving end A-transmitting end B and a receiving end B-transmitting end A to obtain the bi-directional Ka inter-satellite link data in the same ranging frame, wherein the time interval of the ranging frame is 3s.
The specific process of the step 3 is as follows:
step 3.1, according to t i ∈[t 0 ,t f ]Virtual observation of time of day
Figure BDA0002795463730000037
Establishing a virtual observation equation:
Figure BDA0002795463730000038
in the formula (1), y X,i For virtual observation X i Theoretical value of (v) X,i Represents the observed noise with a mean of 0; a. The X,i Represents an observation matrix A X,i ＝[1 1 1 0 0 0 0] T ，
Figure BDA0002795463730000031
Representing the state of the track to be determined and a kinetic parameter q;
Figure BDA0002795463730000039
is a unit weight variance; w is a X,i Representing an observation weight matrix; and then superposing the virtual observation equations of the epochs to obtain:
Figure BDA0002795463730000032
the corresponding normal equation 1 is obtained:
Figure BDA0002795463730000033
step 3.2, analogously, for t i ∈[t 0 ,t f ]Conventional foundation S-band ranging observation rho at moment i Establishing a distance measurement observation equation:
Figure BDA0002795463730000034
wherein, the state p to be estimated is consistent with the formula (1); observation matrix A s,i Expressed as:
Figure BDA0002795463730000035
wherein
Figure BDA0002795463730000036
ρ x 、ρ y 、ρ z Representing three components in a coordinate system of the survey station, wherein M represents a conversion matrix from a ground-fixed coordinate system to the coordinate system of the survey station; HG represents a conversion matrix from an inertial coordinate system to a ground-fixed coordinate system;
and (3) superposing the ranging observation equation of each epoch to obtain a normal equation 2:
Figure BDA0002795463730000041
step 3.3, for t i ∈[t 0 ,t f ]Establishing an inter-Ka-satellite link observation equation according to the inter-Ka-satellite link data at the moment to obtain a normal equation 3:
Figure BDA0002795463730000042
observation matrix A Ka And S-band distance measurement observation matrix A s,i Are consistent in form; weight matrix w Ka Corresponding to Ka band observation data, consisting of
Figure BDA0002795463730000043
Determining;
step 3.4, for t i ∈[t 0 ,t f ]And (3) establishing observation equation of constellation whole network estimation by Ka inter-satellite link data (2) at the moment:
Figure BDA0002795463730000044
wherein，
Figure BDA0002795463730000045
Represents the state of the constellation to be estimated,
Figure BDA0002795463730000046
representing the state to be estimated of the kth (k =1, \8230;, n) satellite; for inter-satellite link observations between satellites j, k
Figure BDA0002795463730000047
The observation matrix is:
Figure BDA0002795463730000048
where ρ = | x j -x k L represents the geometric distance between two stars; w is a ISL A weight matrix representing Ka inter-satellite link data (2) is formed by
Figure BDA0002795463730000049
Determining;
and (3) superposing the observation equation of the whole network estimation of each epoch constellation to obtain a method equation 4:
Figure BDA00027954637300000410
the specific process of the step 4 is as follows: and (3) superposing the normal equation 1 and the normal equation 2, the normal equation 3 and the normal equation 4 to obtain:
Figure BDA00027954637300000411
aligning the vectors p to be estimated before combination, and supplementing the parts of the corresponding observation matrixes needing to be expanded by 0;
solving the linear equation set to obtain the estimated value of the fusion orbit determination as follows:
Figure BDA0002795463730000051
to estimate the result
Figure BDA0002795463730000052
And performing long-term orbit prediction as an initial value to obtain the whole network precise ephemeris.
To estimate the result
Figure BDA0002795463730000053
The specific process of obtaining the whole network precise ephemeris by performing long-term orbit prediction as an initial value is as follows: the estimation result is
Figure BDA0002795463730000054
And (3) as an initial value of the long-term orbit, combining a dynamics model to perform parallel integral calculation of multi-satellite dynamics of the constellation satellite to obtain the whole network precise ephemeris.
The invention has the beneficial effects that:
the invention relates to a space-ground combined orbit calculation method for navigation constellation measurement and control management, which designs a space-ground whole network orbit calculation process for avoiding rank deficiency of a normal equation, utilizes a long-term prediction ephemeris as a virtual observation for constraint, combines traditional foundation S-band measurement data and a Ka inter-satellite link weighting fusion algorithm, comprehensively processes traditional foundation S-band tracking data and inter-satellite link bidirectional distance measurement, and obtains a precise ephemeris product for supporting navigation satellite measurement and control management and inter-satellite link management.
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FIG. 1 is a schematic diagram of a conventional single-star measurement and control management system;
FIG. 2 is a schematic view of measurement and control management oriented to navigation constellation;
FIG. 3 is a schematic diagram of a space-ground-based whole network fusion orbit determination process of prior orbit constraints;
FIG. 4 is a schematic diagram of multi-satellite S-outsourced data/Ka-inter-satellite range compatibility format data;
FIG. 5 is a data residual error diagram of inter-satellite link of the Beidou satellite combined orbit determination;
FIG. 6 is a diagram of the combined orbit determination precision of the inter-satellite/satellite-ground links of the Beidou satellites.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
The invention provides a full-network precise ephemeris and long-term prediction ephemeris product for navigation constellation measurement and control management. The traditional orbit calculation is oriented to satellite measurement and control management, and mainly comprises a single-satellite orbit determination and prediction process, as shown in figure 1; the invention is oriented to navigation constellation measurement and control management, mainly utilizes inter-satellite relative measurement information, and only needs a small amount of ground measurement and control station support as shown in figure 2; as shown in FIG. 3, the invention designs a space-ground combined orbit calculation scheme, which comprises comprehensive data processing flows of various data preprocessing, observation data processing and normal equation production, normal equation superposition and parameter solving, dynamic extrapolation and ephemeris forecast, and can simultaneously meet the requirements of constellation measurement and control management and inter-satellite link management.
In addition, the multi-satellite oriented S-outsider/Ka-inter-satellite distance measurement, speed measurement and angle measurement are data files with compatible formats, and the data type, the satellite SCID and the station ID are used as key index words, as shown in FIG. 4.
The invention relates to a space and ground combined orbit calculation method for navigation constellation measurement and control management, which is implemented according to the following steps:
step 1, collecting and collecting original external measurement data packets and remote measurement data packets, and decoding to obtain multi-extraterrestrial measurement data and Ka inter-satellite link data;
according to the starting time of orbit determination t 0 ,t f ]Extracting long-term ephemeris (t) at a central database i ,X i ) Wherein t is i ∈[t 0 ,t f ]，
Figure BDA0002795463730000061
Denotes t i A forecast ephemeris of time;
according to fixed orbit arc section [ t ] 0 ,t f ]Extracting the last generated long-term ephemeris, and taking t 0 Ephemeris of time of day
Figure BDA0002795463730000062
As initial orbit determination values; and for long-term ephemeris forecastSampling with 5 min sampling time interval and t sampling data i The ephemeris at that time is also used as a virtual observation.
Step 2, preprocessing multi-extraterrestrial measurement data and preprocessing Ka inter-satellite link data to obtain orbit determination observation data with a compatible format;
the specific process of the Ka inter-satellite link data preprocessing comprises the following steps: and establishing link matching for the Ka inter-satellite link data, namely finding two data of a receiving end A-transmitting end B and a receiving end B-transmitting end A to obtain the bi-directional Ka inter-satellite link data in the same ranging frame, wherein the time interval of the ranging frame is 3s.
The specific process of preprocessing the multi-extraterrestrial data comprises the following steps: and carrying out troposphere correction and ionosphere correction on multi-extraterrestrial measurement data, wherein the multi-extraterrestrial measurement data comprise distance measurement, speed measurement and angle measurement, the distance measurement is the distance between a satellite and a ground measurement station, the speed measurement is the radial speed of the satellite relative to the ground measurement station, and the angle measurement is the azimuth and the pitch angle of the satellite in a station center horizontal coordinate system.
Step 3, taking the forecast ephemeris at different moments as virtual observation, and calculating an equation 1 according to orbit determination observation data in a compatible format of each epoch; obtaining a normal equation 2 according to the multi-satellite external measurement data; processing Ka intersatellite link data to obtain a normal equation 3 and a normal equation 4; the specific process of the step 3 is as follows:
step 3.1, according to t i ∈[t 0 ,t f ]Virtual observation of time of day
Figure BDA0002795463730000071
Establishing a virtual observation equation:
Figure BDA0002795463730000072
in the formula (1), y X,i For virtual observation X i Theoretical value of v X,i Represents the observed noise with a mean of 0; a. The X,i Represents an observation matrix A X,i ＝[1 1 1 0 0 0 0] T ，
Figure BDA0002795463730000073
Representing the state of the orbit to be determined and a kinetic parameter q;
Figure BDA0002795463730000074
is a unit weight variance; w is a X,i Representing an observation weight matrix; and then superposing the virtual observation equations of the epochs to obtain:
Figure BDA0002795463730000075
the corresponding normal equation 1 is obtained:
Figure BDA0002795463730000076
step 3.2, analogously, for t i ∈[t 0 ,t f ]Conventional ground-based S-band range observation rho at time i Establishing a distance measurement observation equation:
Figure BDA0002795463730000077
wherein, the state p to be estimated is consistent with the formula (1); observation matrix A s,i Expressed as:
Figure BDA0002795463730000078
wherein
Figure BDA0002795463730000079
ρ x 、ρ y 、ρ z Representing three components in a coordinate system of the measuring station, wherein M represents a conversion matrix from a ground-fixed coordinate system to the coordinate system of the measuring station; HG represents a conversion matrix from an inertial coordinate system to a ground-fixed coordinate system;
and superposing the ranging observation equations of the epochs to obtain a normal equation 2:
Figure BDA0002795463730000081
step 3.3,For t i ∈[t 0 ,t f ]Establishing an inter-Ka-satellite link observation equation according to the inter-Ka-satellite link data at the moment to obtain a normal equation 3:
Figure BDA0002795463730000082
observation matrix A Ka And S-band distance measurement observation matrix A s,i Are consistent in form; weight matrix w Ka Corresponding to Ka band observation data, consisting of
Figure BDA0002795463730000083
Determining;
step 3.4, for t i ∈[t 0 ,t f ]And (3) establishing observation equation of constellation whole network estimation by Ka inter-satellite link data (2) at the moment:
Figure BDA0002795463730000084
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002795463730000085
represents the state of the constellation to be estimated,
Figure BDA0002795463730000086
representing the state to be estimated of the kth (k =1, \8230;, n) satellite; for inter-satellite link observations between satellites j, k
Figure BDA0002795463730000087
The observation matrix is:
Figure BDA0002795463730000088
where ρ = | x j -x k L represents the geometric distance between two stars; w is a ISL A weight matrix representing the Ka inter-satellite link data (2) of
Figure BDA0002795463730000089
Determining;
and (3) superposing the observation equation of the whole network estimation of each epoch constellation to obtain a method equation 4:
Figure BDA00027954637300000810
and 4, weighting and fusing the normal equation 1 and the normal equation 2 with the normal equation 3 and the normal equation 4, and generating the whole network precise ephemeris after orbit determination and solution. The specific process of the step 4 is as follows: and (3) superposing the normal equation 1 and the normal equation 2, the normal equation 3 and the normal equation 4 to obtain:
Figure BDA0002795463730000091
aligning the vectors p to be estimated before combination, and supplementing the parts of the corresponding observation matrixes needing to be expanded by 0;
solving the linear equation set to obtain the estimated value of the fusion orbit determination as follows:
Figure BDA0002795463730000092
to estimate the result
Figure BDA0002795463730000093
And performing long-term orbit prediction as an initial value to obtain the whole network precise ephemeris.
To estimate the result
Figure BDA0002795463730000094
The specific process of obtaining the whole network precise ephemeris by performing long-term orbit prediction as an initial value is as follows: will estimate the result
Figure BDA0002795463730000095
And (3) as an initial value of the long-term orbit, combining the dynamic model to perform parallel integral calculation of the multi-satellite dynamics of the constellation satellite to obtain the whole network precise ephemeris.
Examples
The method provided by the invention is applied to the engineering in the measurement and control process of the Beidou satellite, the orbit determination precision is obviously higher than that of the traditional S frequency band measurement and control orbit determination mode, and the high-precision characteristic of the inter-satellite link is effectively utilized. By adopting the combined orbit determination method provided by the invention, the data residual rms of the inter-satellite link is about 0.3m, as shown in FIG. 5, the radial precision of the Beidou satellite orbit is better than 0.2 m, and the three-dimensional position precision is better than 3m, as shown in FIG. 6, an effective means is provided for realizing the refined measurement and control of the Beidou satellite.
Through the mode, the invention relates to a space-ground combined orbit calculation method for navigation constellation measurement and control management, which designs a space-ground whole network orbit calculation process for avoiding rank deficiency of a normal equation, utilizes a long-term prediction ephemeris as a virtual observation for constraint, combines traditional foundation S-band measurement data and a Ka inter-satellite link weighting fusion algorithm, comprehensively processes traditional foundation S-band tracking data and inter-satellite link bidirectional distance measurement, and obtains a precise ephemeris product for supporting navigation satellite measurement and control management and inter-satellite link management.

Claims (6)

1. A space and ground combined orbit calculation method for navigation constellation measurement and control management is characterized by being implemented according to the following steps:
step 1, collecting and collecting original external measurement data packets and telemetering data packets, and decoding to obtain multi-satellite external measurement data and Ka inter-satellite link data;
according to the starting time of orbit determination t 0 ,t f ]Extracting long-term ephemeris (t) at a central database i ,X i ) Wherein t is i ∈[t 0 ,t f ]，
Figure FDA0003945816810000011
Denotes t i A forecast ephemeris of time;
step 2, preprocessing multi-extraterrestrial measurement data and preprocessing Ka inter-satellite link data to obtain orbit determination observation data with a compatible format;
step 3, taking the forecast ephemeris at different moments as virtual observation, and calculating an equation 1 according to orbit determination observation data in a compatible format of each epoch; obtaining a normal equation 2 according to the multi-satellite external measurement data; processing Ka intersatellite link data to obtain a normal equation 3 and a normal equation 4, wherein the specific process is as follows:
step 3.1, according to t i ∈[t 0 ,t f ]And (3) virtual observation of the moment, establishing a virtual observation equation:
Figure FDA0003945816810000012
in the formula (1), y X,i For theoretical values of virtual observations, v X,i Represents the observed noise with a mean of 0; a. The X,i A representation of an observation matrix is shown,
Figure FDA0003945816810000013
the method comprises the steps of representing the state to be estimated and the dynamic parameter q of n satellites, wherein k =1, \8230;
Figure FDA0003945816810000014
is a unit weight variance; w is a X,i Representing an observation weight matrix; and then superposing the virtual observation equations of the epochs to obtain:
Figure FDA0003945816810000015
the corresponding normal equation 1 is obtained:
Figure FDA0003945816810000016
step 3.2, analogously, for t i ∈[t 0 ,t f ]Conventional foundation S-band ranging observation rho at moment i Establishing a distance measurement observation equation:
Figure FDA0003945816810000021
wherein, the k, k =1, \8230, the states p to be estimated of n satellites k Is the same as the formula (1); observation matrix A s,i Expressed as:
Figure FDA0003945816810000022
wherein
Figure FDA0003945816810000023
ρ x 、ρ y 、ρ z Representing three components in a coordinate system of the measuring station, wherein M represents a conversion matrix from a ground-fixed coordinate system to the coordinate system of the measuring station; HG represents a conversion matrix from an inertial coordinate system to a ground-fixed coordinate system;
and superposing the ranging observation equations of the epochs to obtain a normal equation 2:
Figure FDA0003945816810000024
step 3.3, for t i ∈[t 0 ,t f ]Establishing an inter-Ka-satellite link observation equation according to the inter-Ka-satellite link data at the moment to obtain a normal equation 3:
Figure FDA0003945816810000025
observation matrix A Ka And S-band distance measurement observation matrix A s,i Are consistent in form; weight matrix w Ka Corresponding to Ka band observation data, consisting of
Figure FDA0003945816810000026
Determining;
step 3.4, for t i ∈[t 0 ,t f ]Establishing an observation equation of the constellation whole network estimation by Ka inter-satellite link data at the moment:
Figure FDA0003945816810000027
wherein the content of the first and second substances,
Figure FDA0003945816810000028
represents the state of the constellation to be estimated,
Figure FDA0003945816810000029
representing the state to be estimated of n satellites, wherein k =1, \8230; for inter-satellite link observations between satellites j, k
Figure FDA00039458168100000210
The observation matrix is:
Figure FDA00039458168100000211
where ρ = | x j -x k L represents the geometric distance between two stars; w is a ISL A weight matrix representing Ka inter-satellite link data, consisting of
Figure FDA00039458168100000212
Determining;
and (3) superposing the observation equation of the whole network estimation of each epoch constellation to obtain a method equation 4:
Figure FDA00039458168100000213
and 4, weighting and fusing the normal equation 1 and the normal equation 2 with the normal equation 3 and the normal equation 4, and generating the whole network precise ephemeris after orbit determination and solution.
2. The method for computing the heaven-earth combined orbit for navigation constellation measurement and control management according to claim 1, wherein in the step 1, the orbit determination arc segment [ t ] is used 0 ,t f ]Extracting the last generated long-term ephemeris and taking t 0 Ephemeris of time of day
Figure FDA0003945816810000031
As initial orbit determination values; and sampling the long-term prediction ephemeris with the sampling time interval of 5 minutes and the sampling data of each time of t i The ephemeris at that time is also used as a virtual observation.
3. The method for computing the space-ground combined orbit for the measurement and control management of the navigation constellation according to claim 1, wherein the specific process of preprocessing the multi-satellite external measurement data in the step 2 is as follows: and carrying out troposphere correction and ionosphere correction on multi-extraterrestrial measurement data, wherein the multi-extraterrestrial measurement data comprise distance measurement, speed measurement and angle measurement, the distance measurement is the distance between a satellite and a ground measurement station, the speed measurement is the radial speed of the satellite relative to the ground measurement station, and the angle measurement is the azimuth and the pitch angle of the satellite in a station center horizontal coordinate system.
4. The method for computing the space-ground combined orbit for the measurement and control management of the navigation constellation according to claim 1, wherein the specific process of the Ka inter-satellite link data preprocessing in the step 2 is as follows: and establishing link matching for the Ka inter-satellite link data, namely finding two pieces of data of a receiving end A-transmitting end B and a receiving end B-transmitting end A to obtain the double-unidirectional Ka inter-satellite link data in the same ranging frame, wherein the time interval of the ranging frame is 3s.
5. The method for computing the heaven-earth combined orbit for the measurement and control management of the navigation constellation according to claim 1, wherein the specific process in the step 4 is as follows: and (3) superposing the normal equation 1 and the normal equation 2, the normal equation 3 and the normal equation 4 to obtain:
Figure FDA0003945816810000032
n in equation 1
Figure FDA0003945816810000033
In equation 2
Figure FDA0003945816810000034
In equation 3
Figure FDA0003945816810000035
In equation 4
Figure FDA0003945816810000036
Are combined to obtain b from equation 1
Figure FDA0003945816810000037
In equation 2
Figure FDA0003945816810000038
In equation 3
Figure FDA0003945816810000039
In equation 4
Figure FDA00039458168100000310
Combining to obtain;
the track state p to be determined before combination needs to be aligned, and the part of the corresponding observation matrix needing to be expanded is supplemented by 0;
solving the linear equation set to obtain the estimated value of the fusion orbit determination as follows:
Figure FDA0003945816810000041
to estimate the result
Figure FDA0003945816810000042
And performing long-term orbit prediction as an initial value to obtain the whole network precise ephemeris.
6. The method of claim 5, wherein the estimation result is used as a space-ground joint orbit calculation method for measurement and control management of navigation constellation
Figure FDA0003945816810000043
The specific process of obtaining the whole network precise ephemeris by long-term orbit prediction as an initial value is as follows: the estimation result is
Figure FDA0003945816810000044
And (3) as an initial value of the long-term orbit, combining a dynamics model to perform parallel integral calculation of multi-satellite dynamics of the constellation satellite to obtain the whole network precise ephemeris.
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