CN115357576B - Reliability evaluation method and evaluation device of ephemeris data - Google Patents
Reliability evaluation method and evaluation device of ephemeris data Download PDFInfo
- Publication number
- CN115357576B CN115357576B CN202211229367.1A CN202211229367A CN115357576B CN 115357576 B CN115357576 B CN 115357576B CN 202211229367 A CN202211229367 A CN 202211229367A CN 115357576 B CN115357576 B CN 115357576B
- Authority
- CN
- China
- Prior art keywords
- ephemeris data
- data
- ephemeris
- standard
- determining
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
- G06F16/21—Design, administration or maintenance of databases
- G06F16/215—Improving data quality; Data cleansing, e.g. de-duplication, removing invalid entries or correcting typographical errors
-
- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
- G01S19/25—Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS
- G01S19/258—Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS relating to the satellite constellation, e.g. almanac, ephemeris data, lists of satellites in view
-
- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- 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
- G01S19/396—Determining accuracy or reliability of position or pseudorange measurements
-
- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- 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
- G01S19/42—Determining position
-
- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- 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
- G01S19/52—Determining velocity
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
- G06F16/29—Geographical information databases
Landscapes
- Engineering & Computer Science (AREA)
- Remote Sensing (AREA)
- Radar, Positioning & Navigation (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Computer Networks & Wireless Communication (AREA)
- Databases & Information Systems (AREA)
- Theoretical Computer Science (AREA)
- Data Mining & Analysis (AREA)
- General Engineering & Computer Science (AREA)
- Quality & Reliability (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The application discloses a reliability evaluation method and an evaluation device of ephemeris data, and belongs to the technical field of communication. The method comprises the steps of obtaining first ephemeris data, wherein the first ephemeris data are ephemeris data to be evaluated; determining whether the first ephemeris data is incomplete; under the condition that the first ephemeris data are incomplete, cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data; determining whether the second ephemeris data has a corresponding time point in the standard ephemeris data; under the condition that the second ephemeris data does not have a corresponding time point in the standard ephemeris data, interpolating the second ephemeris data through a Neville algorithm to obtain third ephemeris data; calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis; and determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition. The reliability assessment precision can be improved, and meanwhile, the operation amount is reduced.
Description
Technical Field
The application belongs to the technical field of communication, and particularly relates to a reliability evaluation method and an evaluation device for ephemeris data.
Background
The ephemeris data of the satellites comprise radio signals transmitted by the positioning satellites describing the orbit information of each satellite. The reliability evaluation of ephemeris data mainly uses the standards provided by Global Navigation Satellite System (GNSS) service organizations such as the GPS in the united states, the galileo Satellite positioning System in europe, and the beidou Satellite Navigation System in china, and uses the deviation value between ephemeris data and standard ephemeris data as a measurement standard.
In the related art, when reliability evaluation of ephemeris data is performed, it is usually performed only for precise ephemeris data. The algorithm for the precise ephemeris data generally comprises the steps of firstly extracting net earning coordinates of a corresponding position by using the precise ephemeris, sampling and measuring according to a specification, and then encrypting the precise ephemeris data by using a Lagrange interpolation method, wherein the encryption method generally comprises a Lagrange polynomial interpolation method and a Chebyshev polynomial fitting method. However, lagrange polynomial interpolation is prone to produce longge oscillation and consumes much time when the expansion order is high; the Chebyshev polynomial fitting can avoid data oscillation and jumping at two ends of a fitting interval, but a mathematical model of the Chebyshev polynomial fitting is relatively complex and has large calculation amount.
However, many ephemeris data do not belong to GNSS, and reference data used by many ephemeris data to be checked are not as standard as the ephemeris provided by GNSS, and there are cases of partial point missing and non-equidistant ephemeris. Therefore, the reliability evaluation method applied to the ephemeris data in the related art has poor universality and is not suitable for ephemeris data not belonging to GNSS.
Disclosure of Invention
The embodiment of the application aims to provide a reliability evaluation method and an evaluation device for ephemeris data, which can solve the problems of large calculation amount and low universality of the conventional ephemeris data evaluation method.
In order to solve the technical problem, the present application is implemented as follows:
in a first aspect, the present application provides a method for reliability evaluation of ephemeris data, including:
acquiring first ephemeris data, wherein the first ephemeris data is ephemeris data to be evaluated;
determining whether the first ephemeris data is incomplete;
under the condition that the first ephemeris data is incomplete, cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data;
determining whether the second ephemeris data has a corresponding time point in the standard ephemeris data;
under the condition that the second ephemeris data does not have a corresponding time point in the standard ephemeris data, interpolating the second ephemeris data through a Neville algorithm to obtain third ephemeris data;
calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis;
and determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition.
Further, before the determining whether the first ephemeris data is incomplete, the method further includes:
unifying ephemeris space-time reference of the first ephemeris data;
determining whether the checking time is within the time range of the first ephemeris data and the standard ephemeris data;
and acquiring the time point of the first ephemeris data under the condition that the checking time is within the time range of the first ephemeris data and the standard ephemeris data.
Further, after the interpolating the second ephemeris data by the Neville algorithm to obtain third ephemeris data, the method further includes:
and acquiring the position and the speed of the satellite at the time point according to the third ephemeris data.
Further, the calculating the residual error of the third ephemeris data on the radial axis, the tangential axis, and the normal axis specifically includes:
converting the third ephemeris data and the standard ephemeris data into data in an RTN coordinate system;
and calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis according to the third ephemeris data and the data of the standard ephemeris data in the RTN coordinate system.
Further, when the residual error meets the preset condition, the determining that the third ephemeris data is reliable data specifically includes:
determining a residual error corresponding to each time point in the third ephemeris data;
determining the average value and the standard deviation of the residual errors corresponding to each time point;
and under the condition that the average value is smaller than a first preset threshold value and the standard deviation is smaller than a second preset threshold value, determining that the third ephemeris data are reliable data.
In a second aspect, the present application provides an apparatus for reliability evaluation of ephemeris data, including:
the system comprises a data acquisition module, a data processing module and a data processing module, wherein the data acquisition module is used for acquiring first ephemeris data which is ephemeris data to be evaluated;
a defect determining module, configured to determine whether the first ephemeris data has a defect;
the data cleaning module is used for cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data under the condition that the first ephemeris data is incomplete;
the time point calibration module is used for determining whether the second ephemeris data has a corresponding time point in the standard ephemeris data;
an interpolation module, configured to interpolate, by using a Neville algorithm, the second ephemeris data to obtain third ephemeris data when the second ephemeris data does not have a corresponding time point in the standard ephemeris data;
a residual error calculation module, configured to calculate residual errors of the third ephemeris data in a radial axis, a tangential axis, and a normal axis;
and the reliability determining module is used for determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition.
Further, the apparatus further comprises:
the reference unifying module is used for unifying ephemeris space-time reference of the first ephemeris data;
the time checking module is used for determining whether the checking time is within the time range of the first ephemeris data and the standard ephemeris data;
and the time point acquisition module is used for acquiring the time point of the first ephemeris data under the condition that the checking time is within the time range of the first ephemeris data and the standard ephemeris data.
Further, the apparatus further comprises:
and the speed acquisition module is used for acquiring the satellite position and speed at the time point according to the third ephemeris data.
Further, the residual calculation module includes:
a coordinate system conversion submodule, configured to convert the third ephemeris data and the standard ephemeris data into data in an RTN coordinate system;
and the residual error calculation submodule is used for calculating the residual errors of the third ephemeris data on the radial axis, the tangential axis and the normal axis according to the third ephemeris data and the data of the standard ephemeris data in the RTN coordinate system.
Further, the reliability determination module includes:
the data determining submodule is used for determining a residual error corresponding to each time point in the third ephemeris data;
the statistic submodule is used for determining the average value and the standard deviation of the residual errors corresponding to each time point;
and the reliability determining submodule is used for determining the third ephemeris data as reliable data under the condition that the average value is smaller than a first preset threshold and the standard deviation is smaller than a second preset threshold.
According to the reliability evaluation method of ephemeris data, first ephemeris data is obtained, and the first ephemeris data is ephemeris data to be evaluated; determining whether the first ephemeris data is incomplete; under the condition that the first ephemeris data is incomplete, cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data; determining whether the second ephemeris data has a corresponding time point in standard ephemeris data; under the condition that the second ephemeris data does not have a corresponding time point in the standard ephemeris data, interpolating the second ephemeris data through a Neville algorithm to obtain third ephemeris data; calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis; and determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition. In the embodiment of the application, the ephemeris data can be optimized by cleaning and interpolating the incomplete ephemeris data, and whether the optimized ephemeris data is reliable or not is determined according to the residual error between the optimized ephemeris data and the standard ephemeris data. The scheme provided by the application can improve reliability evaluation precision of ephemeris data and reduce computation workload, is suitable for ephemeris data which does not belong to GNSS data, and is high in universality.
Drawings
FIG. 1 is a flowchart of a method for reliability evaluation of ephemeris data according to an embodiment of the present application;
FIG. 2 is a schematic diagram of an apparatus for reliability evaluation of ephemeris data according to an embodiment of the present application;
fig. 3 is a diagram of steps of a lagrangian interpolation method provided in the embodiment of the present application.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings in combination with embodiments.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some, but not all embodiments of the present application. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort belong to the protection scope of the present application.
First, the background of the field to which the present application relates is explained. Ephemeris refers to a precise table of positions or trajectories of celestial body motion as a function of time during a GPS measurement. The satellite ephemeris can accurately calculate, predict, describe and track the running states of the satellite, the flight object, such as time, position, speed and the like; the precise parameters of flying objects such as celestial bodies, satellites, spacecrafts, missiles, space garbage and the like can be expressed; the flying body can be arranged in a three-dimensional space; depicting past, present and future celestial bodies in time stereo.
The ephemeris data plays an important role in ground navigation and positioning, and therefore reliability evaluation of the ephemeris data is very important.
Example one
Referring to fig. 1, a schematic flow chart of a reliability evaluation method for ephemeris data according to an embodiment of the present application is shown.
The application provides a reliability evaluation method of ephemeris data, which comprises the following steps:
s101: acquiring first ephemeris data, wherein the first ephemeris data are ephemeris data to be evaluated;
in this step, the first ephemeris data may be obtained from an ephemeris data file. Specifically, an ephemeris file is imported into computer software, and a format, a coordinate frame and a time interval to be checked corresponding to the ephemeris file are input.
It will be appreciated that the ephemeris may be divided into "broadcast ephemeris" and post-processed "ephemeris" for a particular application. The broadcast ephemeris is the ephemeris which is calculated and extrapolated from the observation data collected by the tracking station by the main control station for the next two weeks, and then is injected into the GPS satellite to form a navigation message for the user to use. Such ephemeris is therefore of a predictive nature and can be used in real time. The precise ephemeris is also called post-processing ephemeris, which is satellite orbit information calculated by post-processing from observation data of a plurality of satellite tracking stations and used for precise positioning of satellites and the like, and is used for improving and enhancing the ground positioning precision.
In this step, the first ephemeris data is a broadcast ephemeris, and the ephemeris data is calculated and extrapolated by the master station using the observation data collected by the tracking station. The broadcast ephemeris is the telegraph text information which forecasts the number of satellites in a certain time and is carried on the radio signal transmitted by the positioning satellite. The accuracy of the broadcast ephemeris is extremely variable and is influenced by many factors that are incidental to the user, such as the age of the ephemeris, whether the orbit is well-regulated, whether it is in the shadow of the earth and the moon.
The satellite ephemeris is determined by tracking and monitoring the satellite by a ground monitoring station. Since the satellite is subjected to complex influences of various types of perturbation forces during operation, it is difficult to sufficiently and reliably measure the forces or grasp the law of the forces by the ground monitoring station, and therefore a large error is generated in ephemeris prediction. In an observation period, the ephemeris error belongs to a system error, and is a starting data error. The broadcast ephemeris error is one of important error sources of current GPS positioning, which not only seriously affects the accuracy of single-point positioning, but also is an important error source of precise relative positioning, and therefore, the reliability of the first ephemeris data needs to be evaluated.
S102: determining whether the first ephemeris data is incomplete.
The first ephemeris data is incomplete because the ephemeris data may be lost or missing during the detection, transmission and storage processes. For example, the time point in the first ephemeris data is not complete, the satellite position information and velocity information in the first ephemeris data are missing, and the like.
In an alternative embodiment, after the first ephemeris data is obtained and before it is determined whether the first ephemeris data is incomplete, the ephemeris space-time reference of the first ephemeris data may be unified. The space-time reference is a three-dimensional stereo model which comprises geometrical information of geographic space and space-time distribution information, and represents the space position of a satellite in the real world and a time-varying reference thereof in the form of data.
At present, four international satellite navigation systems, namely the United states GPS, the Russian global satellite navigation system (GLONASS), the European Galileo satellite navigation system (Galileo) and the Chinese Beidou system, have space-time benchmarks. It will be appreciated that a uniform reference may need to be selected before the data is processed and evaluated, so that the processing of the data is performed under a uniform reference system.
Optionally, the space-time reference of the Beidou system is used as the space-time reference of the first ephemeris data, and the first ephemeris data is converted to obtain ephemeris information under the Beidou system.
After unifying the space-time reference, determining whether the checking time is within the time range of the first ephemeris data and the standard ephemeris data; and acquiring the time point of the first ephemeris data under the condition that the checking time is within the time range of the first ephemeris data and the standard ephemeris data.
Understandably, if the checking time is not within the range of the first ephemeris data, that is, the checking time does not accord with the ephemeris information to be checked, it indicates that the input information is incorrect, and the process needs to return to S101 again to re-import the data to be checked; or, if the checking time is not within the range of the standard ephemeris data, which also indicates that the input information is incorrect, the process needs to return to S101 again to re-import the data to be checked, so as to obtain correct data to be checked.
After the checking time is determined to be within the time range of the first ephemeris data and the standard ephemeris data, the time point of acquiring the first ephemeris data is recorded as t 1 、t 2 、t 3 8230and 8230. And dividing the first ephemeris data into data units according to the time point.
S103, under the condition that the first ephemeris data is incomplete, cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data;
data cleansing is the process of re-examining and verifying data with the aim of deleting duplicate information, correcting existing errors, and providing data consistency. The data cleaning comprises checking data consistency, processing invalid values and missing values and the like.
In an embodiment of the application, the first ephemeris data is cleaned by a multiple interpolation method to obtain the second ephemeris data.
The idea of multiple interpolation is derived from bayesian estimation, which considers the value to be interpolated to be random, its value coming from the observed values. In practice, the values to be interpolated are usually estimated, and then different noise is added to form a plurality of groups of selectable interpolation values. And selecting the most appropriate interpolation value according to a certain selection basis.
The multiple interpolation method comprises three steps: (1) generating for each null value a set of possible interpolation values reflecting the uncertainty of the non-responsive model; each value may be used to interpolate missing values in the data set, resulting in several complete data sets. (2) Each interpolated data set is statistically analyzed using statistical methods for the complete data set. (3) The results from each interpolation data set are selected according to a scoring function to produce the final interpolation value.
Assuming a set of data comprising three variables Y1, Y2, Y3 whose joint distribution is a normal distribution, this set of data was processed into three groups, group a kept the original data, group B lacked only Y3, group C lacked Y1 and Y2. In multiple interpolation, set A will be processed without any processing, set B will be developed with a set of estimates for Y3 (regression of Y3 with respect to Y1, Y2), and set C will be developed with a set of paired estimates for Y1 and Y2 (regression of Y1, Y2 with respect to Y3).
When multiple interpolation is used, the A group is not processed, and the B and C groups are formed by randomly extracting complete samples into m groups (m is selectable m groups of interpolation values), and each group of the number of cases only needs to be capable of effectively estimating parameters. And estimating the distribution of the attributes with missing values, then respectively generating m groups of estimated values related to the parameters for the m groups of samples based on the m groups of observed values, and giving corresponding prediction, namely, the adopted estimation method is a maximum likelihood method, and a specific implementation algorithm in a computer is an expectation maximization method. A set of Y3 values is estimated for group B, and a set of (Y1, Y2) values is estimated for group C using the premise that the joint distribution of Y1, Y2, and Y3 is a normal distribution.
The multi-interpolation method mainly aims at the situation of data incomplete, ephemeris data are cleaned through the multi-interpolation method, incomplete ephemeris is made up, and the multi-interpolation method is almost suitable for the used ephemeris, so that the application range of the evaluation method provided by the embodiment of the application is greatly expanded.
S104: determining whether the second ephemeris data has a corresponding time point in the standard ephemeris data;
when ephemeris information is evaluated, data information at the same time point needs to be compared and calculated, so that each time point in the ephemeris information data to be evaluated is required to have corresponding standard ephemeris data. In the above step, the time point of acquiring the first ephemeris data is denoted as t 1 、t 2 、t 3 8230and 8230. Cleaning the first ephemeris data by a multi-interpolation method to obtain second ephemeris data, wherein the time point of the second ephemeris data is unchanged and is still t 1 、t 2 、t 3 ……t n 。
In this step, t is 1 、t 2 、t 3 ……t n Comparing with the time point in the standard ephemeris data to determine t 1 、t 2 、t 3 ……t n Are present in the data of the standard ephemeris.
S105: under the condition that the second ephemeris data does not have a corresponding time point in the standard ephemeris data, interpolating the second ephemeris data through a Neville algorithm to obtain third ephemeris data;
specifically, the absence of the corresponding time point of the second ephemeris data in the standard ephemeris data means that the time point of the second ephemeris data needs to be interpolated. In the embodiment of the present application, sliding lagrangian interpolation based on Neville algorithm is adopted, and the specific algorithm is shown in fig. 3.
The Neville algorithm is an algorithm which adopts Lagrange interpolation polynomial successive linear interpolation, and can carry out interpolation on ephemeris data at different times by adopting different polynomials according to the precision requirement. Compared with the prior art in which polynomial interpolation is directly applied, the Neville algorithm has the characteristics of less calculation amount and capability of controlling calculation precision. The interpolation of the Neville algorithm is specifically resolved as follows:
let X = { X 1 ,x 2, …,x n Is the interpolation sample set, n is the dimension of the interpolation node, and x is the interpolationThe Neville algorithm steps are as follows:
step 2, calculating Lagrange interpolation polynomial as
L i , j = ((x－x i-j )L i , j-1 –(x－x i )L i-1, j-1 )/(x i －x i-j )
If | L i,j -L i-1,j-1 If | < ε is true, go to step 4 to output difference result L i,j (ii) a If not, go to step 2.
And interpolating the second ephemeris data by a Neville algorithm to obtain third ephemeris data, wherein the third ephemeris data meet the condition that the time points of the third ephemeris data all have corresponding time points in the standard ephemeris data.
In an optional embodiment, after the second ephemeris data is interpolated by a Neville algorithm to obtain third ephemeris data, the position and the velocity of the satellite at the time point are obtained according to the third ephemeris data. The satellite positions and data at this point in time are acquired in preparation for the next step of residual calculation to facilitate comparison with the data corresponding to the point in time of the standard ephemeris.
S106: calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis;
specifically, calculating the residual errors of the third ephemeris data on the radial axis, the tangential axis, and the normal axis specifically includes: converting the third ephemeris data and the standard ephemeris data into data in an RTN coordinate system; and calculating the residual errors of the third ephemeris data on the radial axis, the tangential axis and the normal axis according to the data of the third ephemeris data and the standard ephemeris data in the RTN coordinate system.
The RTN coordinate system is short for the satellite orbit coordinate system. Wherein R represents Radial (Radial), T represents tangential (Transverse), and N represents Normal (Normal). In order to facilitate the analysis of specific perturbation force (such as atmospheric resistance mainly concentrated in the T direction), the force acting on the satellite in the satellite precision orbit determination is often decomposed into RTN coordinates for analysis. In addition, under the RTN system, still be convenient for carry out the analysis to each item error.
In the step, the third ephemeris data and the standard ephemeris data are converted into data in an RTN coordinate system so as to realize the conversion and operation of a unified coordinate system; and after the conversion is completed, calculating the residual errors of the third ephemeris data on the radial axis, the tangential axis and the normal axis and the standard ephemeris data according to the coordinates of the third ephemeris data and the standard ephemeris data in the RTN coordinate system.
Residual refers to the difference between the actual observed value (data to be inspected) and the standard ephemeris data, and is used for analyzing the reliability, periodicity or other interference of the data. The residual should meet the assumptions of the model and have some properties of error. The residual analysis is called to use the information provided by the residual to examine the reasonability of the model hypothesis and the reliability of the data. Clearly, there are as many residual errors as there are pairs of data.
In this step, t is present 1 、t 2 、t 3 ……t n And when n time points are equal, each time point corresponds to the RTN three numerical values, so that 3n residual errors can be obtained and respectively correspond to the residual errors on the radial shaft, the tangential shaft and the normal shaft.
S107: determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition;
after determining the residuals of the third ephemeris data on the radial, tangential and normal axes, further statistical analysis of the residuals is required. Specifically, a residual error corresponding to each time point in the third ephemeris data is determined; determining the average value and the standard deviation of the residual errors corresponding to each time point; and determining the third ephemeris data as reliable data under the condition that the average value is smaller than a first preset threshold and the standard deviation is smaller than a second preset threshold.
Understandably, residual errors need to be calculated for coordinate points of the radial axis, the tangential axis and the normal axis corresponding to each time point in the third ephemeris data; and dividing the obtained 3n residual values into three sets according to the radial axis, the tangential axis and the normal axis, and respectively carrying out average value calculation and standard deviation calculation on the three sets. The average value can represent the average size of the residual errors, and the standard deviation can represent the distribution dispersion condition of the residual errors.
When the average value is smaller than a first preset threshold value, it is indicated that the residual number set is small as a whole, that is, the deviation between the ephemeris data to be detected and the standard ephemeris data in the axial direction is small;
and under the condition that the average value is smaller than a second preset threshold value, the integral distribution of the residual error number set is indicated to be uniform, namely the ephemeris data to be detected in the axial direction are relatively uniformly distributed near the standard ephemeris data.
The first preset threshold and the second preset threshold are determined according to actual requirements. Alternatively, the first threshold may be 2, and the second preset threshold may be 0.25.
Therefore, under the condition that the average value and the standard difference of the residual errors are respectively smaller than the first preset threshold and the second preset threshold, it can be determined that the third ephemeris data and the standard ephemeris data are not in and out much, and the data to be detected is reliable data.
Of course, it can be understood that, if the average value or the standard deviation of the residual errors corresponding to each time point is too large, it indicates that the ephemeris data to be detected is unreliable data and cannot be used for ground satellite navigation and positioning.
In the embodiment of the application, first ephemeris data is acquired, and the first ephemeris data is ephemeris data to be evaluated; determining whether the first ephemeris data is incomplete; under the condition that the first ephemeris data is incomplete, cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data; determining whether the second ephemeris data has a corresponding time point in the standard ephemeris data; under the condition that the second ephemeris data does not have a corresponding time point in the standard ephemeris data, interpolating the second ephemeris data through a Neville algorithm to obtain third ephemeris data; calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis; and determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition. In the embodiment of the application, the ephemeris data can be optimized by cleaning and interpolating the incomplete ephemeris data, and whether the optimized ephemeris data is reliable or not is determined according to the residual error between the optimized ephemeris data and the standard ephemeris data. The scheme provided by the application can improve the reliability evaluation precision of the ephemeris data and reduce the computation amount, is suitable for almost all ephemeris data, and has high universality.
Example two
Referring to fig. 2, a schematic diagram of an ephemeris data reliability evaluation apparatus 20 according to an embodiment of the present application is shown.
A data obtaining module 201, configured to obtain first ephemeris data, where the first ephemeris data is ephemeris data to be evaluated;
a defect determining module 202, configured to determine whether the first ephemeris data has a defect;
a data cleaning module 203, configured to clean the first ephemeris data by a multiple interpolation method to obtain second ephemeris data when the first ephemeris data has a defect;
a time point calibration module 204, configured to determine whether the second ephemeris data has a corresponding time point in the standard ephemeris data;
an interpolation module 205, configured to interpolate, by using a Neville algorithm, the second ephemeris data to obtain third ephemeris data when the second ephemeris data does not have a corresponding time point in the standard ephemeris data;
a residual calculation module 206, configured to calculate residuals of the third ephemeris data on a radial axis, a tangential axis, and a normal axis;
optionally, the residual calculation module 206 includes:
a coordinate system conversion submodule 2061 for converting the third ephemeris data and the standard ephemeris data into data in an RTN coordinate system;
a residual calculation submodule 2062, configured to calculate the residual of the third ephemeris data on the radial axis, the tangential axis, and the normal axis according to the data of the third ephemeris data and the data of the standard ephemeris data in the RTN coordinate system.
And a reliability determining module 207, configured to determine that the third ephemeris data is reliable data when the residual error meets a preset condition.
Optionally, the reliability determining module 207 includes:
a data determining submodule 2071, configured to determine a residual error corresponding to each time point in the third ephemeris data;
a statistic submodule 2072, configured to determine an average value and a standard deviation of the residual errors corresponding to each time point;
and a reliability determining submodule 2073, configured to determine that the third ephemeris data is reliable data when the average value is smaller than a first preset threshold and the standard deviation is smaller than a second preset threshold.
Further, the apparatus for evaluating reliability of ephemeris data may further include:
the reference unifying module is used for unifying ephemeris space-time reference of the first ephemeris data;
the time checking module is used for determining whether the checking time is within the time range of the first ephemeris data and the standard ephemeris data;
and the time point acquisition module is used for acquiring the time point of the first ephemeris data under the condition that the checking time is within the time range of the first ephemeris data and the standard ephemeris data.
Further, the apparatus for evaluating reliability of ephemeris data may further include:
and the bit rate acquisition module is used for acquiring the satellite position and the satellite speed at the time point according to the third ephemeris data.
The reliability evaluation device 20 for ephemeris data provided in this embodiment of the application can implement each process implemented in the above reliability evaluation method for ephemeris data, and is not described here again to avoid repetition.
In the embodiment of the present application, by providing the data acquisition module 201, the incomplete determination module 202, the data cleaning module 203, the time point calibration module 204, the interpolation module 205, the residual calculation module 206, and the reliability determination module 207, the incomplete ephemeris data is cleaned and interpolated to optimize the ephemeris data, and then whether the optimized ephemeris data is reliable is determined according to the residual between the optimized ephemeris data and the standard ephemeris data. The scheme provided by the application can improve the reliability evaluation precision of the ephemeris data and reduce the computation amount, is suitable for almost all ephemeris data, and has high universality.
The virtual device in the embodiment of the present application may be a device, and may also be a component, an integrated circuit, or a chip in a terminal.
The present invention may be methods, apparatus, systems and/or computer program products. The computer program product may include a computer-readable storage medium having computer-readable program instructions embodied therewith for carrying out aspects of the invention.
The computer-readable storage medium may be a tangible device that can hold and store the instructions for use by the instruction execution device. The computer readable storage medium may be, for example, an electronic memory device, a magnetic memory device, an optical memory device, an electromagnetic memory device, a semiconductor memory device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a Static Random Access Memory (SRAM), a portable compact disc read-only memory (CD-ROM), a Digital Versatile Disc (DVD), a memory stick, a floppy disk, a mechanical coding device, such as a punch card or an in-groove protruding structure with instructions stored thereon, and any suitable combination of the foregoing. Computer-readable storage media as used herein is not to be construed as transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission medium (e.g., optical pulses through a fiber optic cable), or electrical signals transmitted through electrical wires.
The computer-readable program instructions described herein may be downloaded from a computer-readable storage medium to a respective computing/processing device, or to an external computer or external storage device via a network, such as the internet, a local area network, a wide area network, and/or a wireless network. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. The network adapter card or network interface in each computing/processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in a computer-readable storage medium in the respective computing/processing device.
The computer program instructions for carrying out operations of the present invention may be assembler instructions, instruction Set Architecture (ISA) instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C + + or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider). In some embodiments, aspects of the present invention are implemented by personalizing an electronic circuit, such as a programmable logic circuit, a Field Programmable Gate Array (FPGA), or a Programmable Logic Array (PLA), with state information of computer-readable program instructions, which can execute the computer-readable program instructions.
Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer-readable program instructions.
These computer-readable program instructions may be provided to a processing unit of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processing unit of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer-readable program instructions may also be stored in a computer-readable storage medium that can direct a computer, programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer-readable medium storing the instructions comprises an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.
The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer, other programmable apparatus or other devices implement the functions/acts specified in the flowchart and/or block diagram block or blocks.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
It is noted that, unless expressly stated otherwise, all features disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features. Where used, it is further preferred, even further and more preferred that the brief introduction of the further embodiment is made on the basis of the preceding embodiment, the contents of which further, preferably, even further or more preferred the rear band is combined with the preceding embodiment as a complete constituent of the further embodiment. Several further, preferred, still further or more preferred arrangements of the back tape of the same embodiment may be combined in any combination to form a further embodiment.
It will be appreciated by persons skilled in the art that the embodiments of the invention described above and shown in the drawings are given by way of example only and are not limiting of the invention. The objects of the present invention have been fully and effectively accomplished. The functional and structural principles of the present invention have been shown and described in the embodiments, and any variations or modifications may be made to the embodiments of the present invention without departing from the principles described.
Finally, it should be noted that: the above embodiments are only used for illustrating the technical solutions of the present disclosure, and not for limiting the same; while the present disclosure has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art will understand that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present disclosure.
The above description is only an example of the present invention and is not intended to limit the present invention. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (6)
1. A reliability evaluation method of ephemeris data is characterized by comprising the following steps:
acquiring first ephemeris data, wherein the first ephemeris data is ephemeris data to be evaluated;
unifying ephemeris space-time references of the first ephemeris data; determining whether the checking time is within the time range of the first ephemeris data and the standard ephemeris data; under the condition that the checking time is within the time range of the first ephemeris data and the standard ephemeris data, acquiring the time point of the first ephemeris data; determining whether the first ephemeris data is incomplete;
under the condition that the first ephemeris data is incomplete, cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data;
determining whether the second ephemeris data has a corresponding time point in the standard ephemeris data;
under the condition that the second ephemeris data does not have a corresponding time point in the standard ephemeris data, interpolating the second ephemeris data through a Neville algorithm to obtain third ephemeris data;
calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis;
and determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition.
2. The method for reliability assessment of ephemeris data according to claim 1, wherein the calculating the residual error of the third ephemeris data in radial, tangential and normal axes specifically comprises:
converting the third ephemeris data and the standard ephemeris data into data in an RTN coordinate system;
and calculating the residual errors of the third ephemeris data on the radial axis, the tangential axis and the normal axis according to the data of the third ephemeris data and the standard ephemeris data in the RTN coordinate system.
3. The method for reliability evaluation of ephemeris data according to claim 1, wherein the determining that the third ephemeris data is reliable data when the residual error meets a preset condition is specifically:
determining a residual error corresponding to each time point in the third ephemeris data;
determining the average value and the standard deviation of the residual errors corresponding to each time point;
and determining the third ephemeris data as reliable data under the condition that the average value is smaller than a first preset threshold and the standard deviation is smaller than a second preset threshold.
4. An apparatus for reliability evaluation of ephemeris data, comprising:
the system comprises a data acquisition module, a data processing module and a data processing module, wherein the data acquisition module is used for acquiring first ephemeris data which is ephemeris data to be evaluated;
the reference unifying module is used for unifying ephemeris space-time reference of the first ephemeris data;
the time checking module is used for determining whether the checking time is within the time range of the first ephemeris data and the standard ephemeris data;
a time point obtaining module, configured to obtain a time point of the first ephemeris data when the checking time is within a time range of the first ephemeris data and the standard ephemeris data;
a defect determining module, configured to determine whether the first ephemeris data has a defect;
the data cleaning module is used for cleaning the first ephemeris data through a multiple interpolation method to obtain second ephemeris data under the condition that the first ephemeris data is incomplete;
the time point calibration module is used for determining whether the second ephemeris data has a corresponding time point in the standard ephemeris data;
the interpolation module is used for interpolating the second ephemeris data through a Neville algorithm under the condition that the second ephemeris data does not have a corresponding time point in the standard ephemeris data to obtain third ephemeris data;
a residual error calculation module, configured to calculate residual errors of the third ephemeris data in a radial axis, a tangential axis, and a normal axis;
and the reliability determining module is used for determining the third ephemeris data as reliable data under the condition that the residual error meets a preset condition.
5. The ephemeris data reliability assessment device according to claim 4, wherein the residual error calculation module comprises:
a coordinate system conversion submodule, configured to convert the third ephemeris data and the standard ephemeris data into data in an RTN coordinate system;
and the residual error calculation sub-module is used for calculating residual errors of the third ephemeris data on a radial axis, a tangential axis and a normal axis according to the third ephemeris data and the standard ephemeris data in the RTN coordinate system.
6. The ephemeris data reliability assessment device according to claim 4, wherein the reliability determination module comprises:
the data determining sub-module is used for determining a residual error corresponding to each time point in the third ephemeris data;
the statistic submodule is used for determining the average value and the standard deviation of the residual errors corresponding to each time point;
and the reliability determining submodule is used for determining the third ephemeris data as reliable data under the condition that the average value is smaller than a first preset threshold and the standard deviation is smaller than a second preset threshold.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211229367.1A CN115357576B (en) | 2022-10-08 | 2022-10-08 | Reliability evaluation method and evaluation device of ephemeris data |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211229367.1A CN115357576B (en) | 2022-10-08 | 2022-10-08 | Reliability evaluation method and evaluation device of ephemeris data |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115357576A CN115357576A (en) | 2022-11-18 |
| CN115357576B true CN115357576B (en) | 2023-02-07 |
Family
ID=84008016
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211229367.1A Active CN115357576B (en) | 2022-10-08 | 2022-10-08 | Reliability evaluation method and evaluation device of ephemeris data |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115357576B (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101261317A (en) * | 2008-04-25 | 2008-09-10 | 浙江大学 | High dynamic state multi- mode satellite navigation signal source analogue method and its device |
| CN101968542A (en) * | 2010-09-29 | 2011-02-09 | 中国科学院国家天文台 | Method for tracking lunar probe by using earth station |
| US8538682B1 (en) * | 2009-04-24 | 2013-09-17 | Qualcomm Incorporated | Systems and methods for satellite navigation using locally generated ephemeris data |
| CN106569232A (en) * | 2016-10-31 | 2017-04-19 | 航天恒星科技有限公司 | Space signal accuracy evaluation method and system |
| CN114035216A (en) * | 2021-11-10 | 2022-02-11 | 北京百度网讯科技有限公司 | Positioning method, device, equipment and storage medium |
| CN114355418A (en) * | 2021-12-07 | 2022-04-15 | 中国科学院国家授时中心 | Beidou foundation enhancement system-based posterior data quality assessment method and system |
-
2022
- 2022-10-08 CN CN202211229367.1A patent/CN115357576B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101261317A (en) * | 2008-04-25 | 2008-09-10 | 浙江大学 | High dynamic state multi- mode satellite navigation signal source analogue method and its device |
| US8538682B1 (en) * | 2009-04-24 | 2013-09-17 | Qualcomm Incorporated | Systems and methods for satellite navigation using locally generated ephemeris data |
| CN101968542A (en) * | 2010-09-29 | 2011-02-09 | 中国科学院国家天文台 | Method for tracking lunar probe by using earth station |
| CN106569232A (en) * | 2016-10-31 | 2017-04-19 | 航天恒星科技有限公司 | Space signal accuracy evaluation method and system |
| CN114035216A (en) * | 2021-11-10 | 2022-02-11 | 北京百度网讯科技有限公司 | Positioning method, device, equipment and storage medium |
| CN114355418A (en) * | 2021-12-07 | 2022-04-15 | 中国科学院国家授时中心 | Beidou foundation enhancement system-based posterior data quality assessment method and system |
Non-Patent Citations (1)
| Title |
|---|
| GPS数据处理中卫星精密星历插值方法分析;卓宁;《战术导弹技术》;20100715(第04期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115357576A (en) | 2022-11-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| KR101036846B1 (en) | Computing long term orbit and clock models with variable time-horizons | |
| CN108107455A (en) | A kind of satellite clock correction Real-time Forecasting Method based on phase hit | |
| KR20160084316A (en) | Method of multiplen satellite measurement failure detection and isolation for gnss | |
| WO2012071320A1 (en) | Coded filter | |
| Abad et al. | Fourth‐and Fifth‐Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System | |
| US8223068B2 (en) | Method and system for logging position data | |
| CN109752739B (en) | Observation data processing method and device, terminal equipment and storage medium | |
| Langel et al. | Overbounding the effect of uncertain Gauss‐Markov noise in Kalman filtering | |
| JP5685776B2 (en) | A method for correcting prediction errors of time-varying signal values that are subject to interference due to various uncontrollable system effects | |
| CN114791614A (en) | Clock error forecasting method and device | |
| CN113325446A (en) | Multi-mode common-frequency GNSS carrier phase time transfer method and system | |
| CN114002712B (en) | GNSS real-time satellite clock error determination system and method based on data adaptive selection | |
| CN117148398B (en) | Two-network-integrated station distribution geometric configuration assessment method, system and equipment | |
| CN115357576B (en) | Reliability evaluation method and evaluation device of ephemeris data | |
| Qu et al. | Recursive source localisation by time difference of arrival sensor networks with sensor position uncertainty | |
| Shukla et al. | Approach for near‐real‐time prediction of ionospheric delay using Klobuchar‐like coefficients for Indian region | |
| JP2008249402A (en) | Device and method for estimating inter-frequency bias | |
| CN109239750B (en) | Method and device for monitoring track parameters and electronic terminal | |
| CN116840874A (en) | Differential data quality monitoring method and device, electronic equipment and storage medium | |
| CN115755131A (en) | Satellite positioning method, device and medium | |
| CN114355410B (en) | Satellite navigation real-time precise single-point positioning system and method based on parallel computing | |
| CN116224746A (en) | High-stability time reference establishment method for satellite-ground atomic clock fusion | |
| Yin et al. | Performance analysis of L2 and L5 CNAV broadcast ephemeris for orbit calculation | |
| Zhu et al. | Continuous modelling of global navigation satellite system multipath errors for sidereal filtering | |
| CN114035203A (en) | Pseudo-range signal transmission method, pseudo-range signal transmission device, storage medium, and electronic device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |