CN117949980A - Data period number design method suitable for low-orbit satellite broadcast ephemeris - Google Patents
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Abstract
The invention belongs to the field of satellite positioning time service, and discloses a data period number design method suitable for low-orbit satellite broadcasting ephemeris, which comprises the following steps: aiming at the data period number of each parameter in the ephemeris parameters and the star clock parameters, the bit number of the data period number is allocated to the bit number of the reference time domain and the data age domain, so that a plurality of candidate allocation schemes are obtained; selecting a target allocation scheme from the plurality of candidate allocation schemes according to the expected data age variation range of the parameter and the expected longest non-repetition time length of the data period number; and designing the data period number according to the target allocation scheme. The invention expands the value range of the data period number as much as possible under the condition of using the bit number, ensures that the data period number can not appear repeatedly aiming at the same satellite in a period of time, can reflect the data age, and meets the requirement of the low-orbit satellite high-frequency broadcasting satellite Zhong Xingli.
Description
Technical Field
The invention belongs to the field of satellite positioning time service, and particularly relates to a data period number design method suitable for low-orbit satellite broadcast ephemeris.
Background
Owing to the characteristics of low height, high speed, low manufacturing cost and the like of the low-orbit satellite, the navigation positioning time service based on the low-orbit enhanced GNSS (global satellite positioning system) has a series of advantages of strong signal strength, short convergence time, white noise due to multipath effect and the like, and more attention is paid in recent years. In order to realize high-precision low-orbit enhanced precision single-point positioning and time service of the ground by utilizing the low-orbit navigation signal, the precision orbit and the star clock of the low-orbit satellite are provided for a user in real time.
In the delivery of GNSS real-time products, low frequency broadcast star ephemeris is often used to provide orbit and star clock products with lower precision, and then transmitted to the user side by using internet or SBAS (Satellite-Based Augmentation System ) to synthesize high frequency correction based on broadcast star Zhong Xingli at the user side, thereby obtaining high precision star Zhong Xingli products, wherein the broadcasting period of low frequency broadcast star Zhong Xingli is usually 1 hour to several hours. For the low-orbit satellite, because the low-orbit satellite is closer to the ground, the orbit is influenced by complex atmospheric resistance, the satellite clock is influenced by various complex systematic phenomena, and the long-period forecast of the broadcasting satellite Zhong Xingli generates larger errors, so that the low-frequency broadcasting satellite ephemeris is not applicable any more, the method of directly broadcasting the satellite ephemeris with higher frequency through satellite signals can be adopted to meet the requirements of users, and the ring of broadcasting additional high-frequency correction is omitted.
In GNSS broadcast ephemeris, the ephemeris data period number (Issue Of DATA EPHEMERIS, IODE) is used to distinguish between different sets Of updated ephemeris parameters, the star Zhong Shuju period number (Issue Of Data Clock, IODC) is used to distinguish between different sets Of updated star clock parameters, and it is necessary to ensure that the IODE and IODC do not appear repeatedly for the same satellite for a considerable period Of time, thus ensuring its uniqueness during that period Of time. In the united states GPS (global positioning system), the IODE is described by 8 bits, and has a value ranging from 0 to 255; IODC is described by 10 bits and has a value in the range of 0 to 1023. In the european Galileo system, the same data as the IODE and IODC of the GPS system are IODnav, which is described by 10 bits, ranging from 0 to 1023. In the navigation circuit Of the Beidou B1C, B a signal in China, 8-bit IODE and 10-bit IODC are used for distinguishing different groups Of updated ephemeris and star clock parameters, and meanwhile, the IODE and IODC are also used for reflecting the Data Age (Age Of Data, AOD) Of the group Of parameters, namely the difference from the reference time Of the ephemeris or star clock parameters to the last measurement time so as to calculate the extrapolation time Of the group Of ephemeris or star clock parameters, and the extrapolation time is used as the basis for judging the accuracy Of the parameters, for example, the IODE is 0-59, and the Data Age is less than 12 hours.
For low-orbit satellites, the situation changes: because of the rapid change of orbit and star clock and the complexity of modeling, in order to obtain a broadcast star Zhong Xingli with higher precision, high-frequency update of the star clock needs to be ensured, and especially for the star clock parameters, the update speed is faster than that of the ephemeris parameters. Taking the ephemeris parameters as an example, assuming that the update time is 10 minutes, 8-bit data can ensure that the ephemeris is not repeated within 42 hours, but the data age can not be distinguished continuously, and because of frequent update, the IODE with the value of 0-59 and 60-119 is likely to represent ephemeris with different ephemeris reference times and identical ages.
Thus, the existing design of IODE and IODC cannot accommodate the requirements of low-orbit satellite high-frequency broadcasters Zhong Xingli.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a data period number design method suitable for low-orbit satellite broadcasting ephemeris.
The technical problems to be solved by the invention are realized by the following technical scheme:
a data session number design method suitable for low-orbit satellite broadcast ephemeris, comprising:
Aiming at the data period number of each parameter in the ephemeris parameters and the star clock parameters, the bit number of the data period number is allocated to the bit number of the reference time domain and the data age domain, so that a plurality of candidate allocation schemes are obtained;
Selecting a target allocation scheme from the plurality of candidate allocation schemes according to the expected data age variation range of the parameter and the expected longest non-repetition time length of the data period number;
And designing the data period number according to the target allocation scheme.
Optionally, the selecting a target allocation scheme from the plurality of candidate allocation schemes according to the expected data age variation range for the parameter and the expected longest non-repetition time length for the data period number includes:
respectively calculating the data age change range and the longest non-repeated time length of the data period number under each candidate allocation scheme;
And selecting a candidate allocation scheme with the data age variation range and the longest non-repetition time length meeting expectations from the multiple candidate allocation schemes as a target allocation scheme according to the data age variation range expected by the parameters and the longest non-repetition time length expected by the data period.
Optionally, when designing the ephemeris data period number IODE, the calculation method of the longest non-repetition duration under each candidate allocation scheme includes:
for each candidate allocation scheme, calculating the longest non-repetition duration of the IODE according to a first bit number of a corresponding reference time domain set in the candidate allocation scheme by using a first formula;
the first formula is:
；
Wherein, Representing ephemeris parameter update period,/>Is in minutes; /(I)Representing the first number of bits; Representing a downward rounding; /(I) Representing the longest non-repeating duration of the IODE,/>In hours.
Optionally, when designing the ephemeris data period number IODE, the calculation manner of the data age variation range under each candidate allocation scheme includes:
For each candidate allocation scheme, calculating a maximum change value of the data age change range by using a second formula according to the second bit number of the corresponding data age field set in the candidate allocation scheme, and obtaining the data age change range under the candidate allocation scheme according to the maximum change value;
The second formula is:
；
Wherein, Representing ephemeris parameter update period,/>Is in minutes; /(I)Representing the second number of bits; /(I)Maximum change value representing data age range of ephemeris parameters,/>, for a data age range of changeIn minutes.
Optionally, when designing star Zhong Shuju, no. IODC, the calculation method of the longest non-repeated duration under each candidate allocation scheme includes:
For each candidate allocation scheme, calculating IODC the longest non-repetition duration by using a third formula according to a third bit number of the corresponding reference time domain set in the candidate allocation scheme;
the third formula is:
；
Wherein, Representing the update period of the star clock parameter,/>In seconds; /(I)Representing the number of said third bits,Representing a downward rounding; /(I)Representing the longest non-repeating duration of IODC,/>In minutes.
Optionally, when designing star Zhong Shuju, no. IODC, the calculation method of the data age variation range under each candidate allocation scheme includes:
for each candidate allocation scheme, calculating a maximum change value of the data age change range by using a fourth formula according to the fourth bit number of the corresponding data age field set in the candidate allocation scheme, and obtaining the data age change range under the candidate allocation scheme according to the maximum change value;
the fourth formula is:
；
Wherein, Representing the update period of the star clock parameter,/>In seconds; /(I)Representing the fourth number of bits; maximum change value representing data age change range of star clock parameter,/> In seconds.
Alternatively, the process may be carried out in a single-stage,No more than 1 hour.
Alternatively, the process may be carried out in a single-stage,No more than 30 seconds.
Alternatively, both ephemeris data period number IODE and star Zhong Shuju period number IODC are designed to 10 bits.
The invention provides a data period number design method suitable for low orbit satellite broadcast ephemeris, which is used for carrying out bit number distribution of a reference time domain and a data age domain on each data period number in IODE and IODC to obtain a plurality of candidate distribution schemes, and then selecting a target distribution scheme from the candidate distribution schemes according to the expected longest non-repeated time length and the expected data age variation range, thereby designing the data period number according to the target distribution scheme. Therefore, on one hand, the value range of the data period number is expanded as much as possible under the condition of limiting the number of bits to be used, the data period number is ensured not to appear repeatedly for the same satellite in a period of time, meanwhile, the data age can be reflected, and the requirement of the low-orbit satellite high-frequency broadcasting satellite Zhong Xingli is met.
Drawings
FIG. 1 is a flow chart of a method for designing a data epoch number for a Low-orbit satellite broadcast ephemeris provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of an IODE designed in an embodiment of the present invention;
FIG. 3 is a schematic diagram of another IODE designed in an embodiment of the present invention;
FIG. 4 is a schematic diagram of one IODC designed in an embodiment of this invention;
fig. 5 is a schematic diagram of another IODC designed in an embodiment of this invention.
Detailed Description
Due to the rapid changes in low orbit satellite orbit and clock and modeling complexity, orbit and clock parameter update frequencies are different and no longer appear as the same set as the GNSS broadcast satellites Zhong Xingli. In order to obtain a high-precision broadcast star Zhong Xingli, high-frequency updating is required to be ensured, and in order to meet the requirement, the method is convenient for users to use under the condition of taking high-frequency message broadcasting into consideration. Referring to fig. 1, the method comprises the steps of:
s10, aiming at the data period number of each parameter of the ephemeris parameters and the star clock parameters, the bit number of the data period number is allocated to the bit number of the reference time domain and the data age domain, and a plurality of candidate allocation schemes are obtained.
Illustratively, when designing an ephemeris data period number (IODE), an ephemeris parameter update period is assumedIn minutes as measurement unit,/>For the number of bits of IODE,/>Is the first number of bits allocated to the reference time domain of the IODE,/>The second number of bits allocated to the data age field of the IODE is:
(1)。
thus, the corresponding reference time domain in the IODE The individual bits may represent/>Is the range of values of (1) corresponding to the data age domain in the IODE >The individual bits may represent/>Is a range of values.
According to formula (1) for IODEThe bits are divided in a plurality of different ways to obtain a plurality of candidate allocation schemes.
Illustratively, when designing IODC, a star clock parameter update period is assumedIn seconds,/>Number of bits IODC,/>Is the third number of bits allocated to the reference time domain of IODC,/>The fourth number of bits allocated to the data age field of IODC is:
(2)。
Thus, IODC corresponds to the reference time domain The individual bits may represent/>In the range of values of IODC corresponding to the data age field/>The individual bits may represent/>Is a range of values.
According to the pair IODC of formula (2)The bits are divided in a plurality of different ways to obtain a plurality of candidate allocation schemes.
S20, selecting a target allocation scheme from the plurality of candidate allocation schemes according to the expected data age change range of the parameters and the expected longest non-repeated duration of the data period number.
Specifically, according to the expected data age variation range of the parameters and the expected longest non-repeated time length of the data period number, selecting a target allocation scheme from the multiple candidate allocation schemes, wherein the target allocation scheme comprises the following steps:
(1) Respectively calculating the data age change range and the longest non-repeated time length of the data period number under each candidate allocation scheme;
(2) And selecting a candidate allocation scheme with the data age variation range and the longest non-repetition time length meeting expectations from the multiple candidate allocation schemes obtained in the step S10 as a target allocation scheme according to the data age variation range expected by the parameters and the longest non-repetition time length expected by the data age variation range and the data period.
Illustratively, assume an ephemeris parameter update periodTaking minutes as a measurement unit, when designing the IODE, the calculation mode of the longest non-repeated time length under each candidate allocation scheme comprises the following steps: for each candidate allocation scheme, calculating the longest non-repeated time length by using a first formula according to the first bit number of the corresponding reference time domain set in the candidate allocation scheme.
The first formula is:
(3)；
In the formula (3), the amino acid sequence of the compound, Representing ephemeris parameter update period,/>Is in minutes; /(I)Representing a first number of bits; Representing a downward rounding; /(I) Representing the longest non-repeating duration of the IODE,/>In hours.
Exemplary, same assumption ephemeris parameter update periodTaking minutes as a measurement unit, when designing the IODE, the calculation mode of the data age change range under each candidate allocation scheme comprises the following steps: for each candidate allocation scheme, calculating a maximum change value of the data age change range by using a second formula according to the second bit number of the corresponding data age field set in the candidate allocation scheme, and obtaining the data age change range corresponding to the candidate allocation scheme according to the maximum change value;
the second formula is:
(4)；
In the formula (4), the amino acid sequence of the compound, Representing ephemeris parameter update period,/>Is in minutes; /(I)Representing a second number of bits; maximum change value representing data age range of ephemeris parameters,/>, for a data age range of change In minutes.
According toObtaining a data age change range corresponding to the candidate allocation scheme: /(I)~(/>+/>) Minutes,/>Is the starting value of the range of variation of the data age.
Illustratively, assume a star clock parameter update periodTaking seconds as a unit of measure, when IODC is designed, the calculation method of the longest non-repeated duration under each candidate allocation scheme includes: for each candidate allocation scheme, calculating the longest non-repeated time length by using a third formula according to the third bit number of the corresponding reference time domain set in the candidate allocation scheme;
The third formula is:
(5)；
In the formula (5), the amino acid sequence of the compound, Representing the update period of the star clock parameter,/>In seconds; /(I)Representing the third number of bits,/>Representing a downward rounding; /(I)Representing the longest non-repeating duration of IODC,/>In minutes.
Exemplary, same assumption star clock parameter update periodTaking seconds as a unit of measurement, when IODC is designed, the calculation method of the data age variation range under each candidate allocation scheme includes: for each candidate allocation scheme, calculating a maximum change value of the data age change range by using a fourth formula according to the fourth bit number of the corresponding data age field set in the candidate allocation scheme, and obtaining the data age change range corresponding to the candidate allocation scheme according to the maximum change value;
The fourth formula is:
(6)；
In the formula (6), the amino acid sequence of the compound, Representing the update period of the star clock parameter,/>In seconds; /(I)Representing a fourth number of bits; maximum change value representing data age change range of star clock parameter,/> In seconds.
According toObtaining a data age change range corresponding to the candidate allocation scheme: /(I)~(/>+/>) Second, wherein the second is; Is the starting value of the range of variation of the data age.
In addition, when selecting a candidate allocation scheme, from among a plurality of candidate allocation schemes, for which both the data age variation range and the longest non-repetition period satisfy the expectations, according to the expected data age variation range and the expected longest non-repetition period, if there is no candidate allocation scheme satisfying the expectations among all the candidate allocation schemes, it may be considered to increase the number of bits of the data period number, for example, to increase 2 bits.
S30: and designing a data option number according to the target allocation scheme.
Illustratively, for IODE, assume the first number of bits allocated in its target allocation scheme5, Second number of bits/>3, The IODE may be designed in the form as shown in fig. 2 or fig. 3.
Illustratively, for IODC, assume that the third number of bits is allocated in its target allocation scheme6, Fourth bit number/>4, IODC may be designed in the form as shown in fig. 4 or fig. 5.
The embodiment of the invention provides a data period number design method suitable for low-orbit satellite broadcast ephemeris, which is used for distributing the bit number of a reference time domain and a data age domain aiming at the data period number of each parameter in ephemeris parameters and star clock parameters to obtain a plurality of candidate distribution schemes; then, a target allocation scheme is selected from the candidate allocation schemes according to the expected data age variation range and the longest non-repeated duration of the expected data period number, so that the data period number is designed according to the target allocation scheme. Therefore, on one hand, the value range of the data period number is expanded as much as possible under the condition of limiting the number of bits, the data period number is ensured not to appear repeatedly for the same satellite in a period of time, meanwhile, the data age of the ephemeris parameters and the star clock parameters can be reflected, and the requirement of the low-orbit satellite high-frequency broadcasting star Zhong Xingli is met.
In one embodiment, an ephemeris parameter update periodPreferably, the time is not more than 1 hour, so that the broadcast ephemeris with higher precision can be realized, the high-frequency update of the broadcast ephemeris is ensured, and the broadcast ephemeris is more suitable for the use scene of a low-orbit satellite.
Table 1 shows that an 8-bit IODE is found in differentThe following several candidate allocation schemes, as can be seen from Table 1, ephemeris parameter update period/>Longer means that the IODE has a longer longest non-repeating duration/>Meanwhile, the data age variation range of the ephemeris parameters is larger, but the method also means that the ephemeris fitting time length is increased, the updating frequency of the orbit determination result is reduced, and the accuracy is reduced.
TABLE 1
In addition, whenAt a certain time, increase the bit number/>, of the IODEIs lengthened/>And the most direct way to extend the data age range of ephemeris parameters. For example, table 2 shows that a 10-bit IODE is found at different/>As can be seen from a comparison of tables 1 and 2, the following several candidate allocations, a 10-bit IODE is more suitable for updating the high frequency low orbit satellite ephemeris parameters if conditions allow.
TABLE 2
In one embodiment, the star clock parameter update periodPreferably, the time is not more than 30 seconds, so that a high-precision broadcasting satellite clock can be realized, high-frequency updating of the broadcasting satellite clock is guaranteed, and the broadcasting satellite clock is more suitable for the use scene of a low-orbit satellite.
The low-orbit satellite clock needs to be updated more frequently to maintain high accuracy than the low-orbit satellite ephemeris, table 3 shows that 8 bits IODC are differentThe following several candidate allocation schemes, as can be seen from Table 3, the star clock parameter update period/>Longer means IODC has a longer longest non-repeating duration/>The data age variation range of the star clock parameter is larger, but the data age variation range also means that the time length of the star Zhong Nige is increased, the updating frequency of the orbit determination result is reduced, and the accuracy is reduced.
TABLE 3 Table 3
It can also be seen from table 3 that the 8-bit IODC can only ensure that the high-frequency star clock does not appear repeatedly for a few tens of minutes or even less, and is not very suitable for broadcasting of low-rail high-frequency star clocks, so that it is considered to solve this problem by increasing the number of bits of IODC.
Table 4 shows that IODC of 10 bits are found in the differentAs can be seen from table 4, the following several candidate allocations, if conditions allow, 10 bits IODC are more suitable for updating the high frequency low orbit satellite clock parameters.
TABLE 4 Table 4
In a preferred implementation, both IODE and IODC may be designed to be 10 bits. For example, inNot more than 1 hour,/>With no more than 30 seconds, both IODE and IODC are designed to be 10 bits.
In summary, the data period number design method suitable for the low-orbit satellite broadcast ephemeris provided by the embodiment of the invention can simultaneously express the information of two dimensions of the reference time and the data age of the ephemeris without expanding the bit number of the data period number as much as possible, thereby not only considering the longest unrepeated time of the IODE and IODC, but also reflecting the change range of the parameter age of the ephemeris.
It should be noted that the terms "first," "second," and the like are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. The implementations described in the following exemplary examples do not represent all implementations consistent with the invention. Rather, they are merely examples of apparatus and methods consistent with aspects of the invention.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Further, one skilled in the art can engage and combine the different embodiments or examples described in this specification.
Although the application is described herein in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in view of the drawings and the disclosure. In the description of the present application, the word "comprising" does not exclude other elements or steps, the "a" or "an" does not exclude a plurality, and the "a" or "an" means two or more, unless specifically defined otherwise. Moreover, some measures are described in mutually different embodiments, but this does not mean that these measures cannot be combined to produce a good effect.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (9)
1. A data session number design method suitable for low-orbit satellite broadcast ephemeris, comprising:
Aiming at the data period number of each parameter in the ephemeris parameters and the star clock parameters, the bit number of the data period number is allocated to the bit number of the reference time domain and the data age domain, so that a plurality of candidate allocation schemes are obtained;
Selecting a target allocation scheme from the plurality of candidate allocation schemes according to the expected data age variation range of the parameter and the expected longest non-repetition time length of the data period number;
And designing the data period number according to the target allocation scheme.
2. The method for designing a data epoch for use in a low earth orbit satellite broadcast ephemeris of claim 1, wherein selecting a target allocation scheme from the plurality of candidate allocation schemes based on a desired range of variation of data age for the parameter and a desired maximum non-repeating time period for the data epoch, comprises:
respectively calculating the data age change range and the longest non-repeated time length of the data period number under each candidate allocation scheme;
And selecting a candidate allocation scheme with the data age variation range and the longest non-repetition time length meeting expectations from the multiple candidate allocation schemes as a target allocation scheme according to the data age variation range expected by the parameters and the longest non-repetition time length expected by the data period.
3. The method for designing a data epoch for low earth orbit satellite broadcast ephemeris according to claim 2, wherein when designing the ephemeris data epoch IODE, the calculation of the longest non-repeating time length for each candidate allocation scheme includes:
for each candidate allocation scheme, calculating the longest non-repetition duration of the IODE according to a first bit number of a corresponding reference time domain set in the candidate allocation scheme by using a first formula;
the first formula is:
；
Wherein, Representing ephemeris parameter update period,/>Is in minutes; /(I)Representing the first number of bits; /(I)Representing a downward rounding; /(I)Representing the longest non-repeating duration of the IODE,/>In hours.
4. The method for designing a data epoch for low earth orbit satellite broadcast ephemeris according to claim 2, wherein when designing the ephemeris data epoch IODE, the calculation method of the data age variation range under each candidate allocation scheme includes:
For each candidate allocation scheme, calculating a maximum change value of the data age change range by using a second formula according to the second bit number of the corresponding data age field set in the candidate allocation scheme, and obtaining the data age change range under the candidate allocation scheme according to the maximum change value;
The second formula is:
；
Wherein, Representing ephemeris parameter update period,/>Is in minutes; /(I)Representing the second number of bits; maximum change value representing data age range of ephemeris parameters,/>, for a data age range of change In minutes.
5. The method for designing a data session number for low-orbit satellite-broadcast ephemeris according to claim 2, wherein when designing the satellite Zhong Shuju session number IODC, the calculation method for the longest non-repeating time length under each candidate allocation scheme comprises:
For each candidate allocation scheme, calculating IODC the longest non-repetition duration by using a third formula according to a third bit number of the corresponding reference time domain set in the candidate allocation scheme;
the third formula is:
；
Wherein, Representing the update period of the star clock parameter,/>In seconds; /(I)Representing the third number of bits,/>Representing a downward rounding; /(I)Representing the longest non-repeating duration of IODC,/>In minutes.
6. The method for designing a data period number for low-orbit satellite-broadcast ephemeris according to claim 2, wherein when designing the star Zhong Shuju period number IODC, the calculation method for the data age variation range under each candidate allocation scheme includes:
for each candidate allocation scheme, calculating a maximum change value of the data age change range by using a fourth formula according to the fourth bit number of the corresponding data age field set in the candidate allocation scheme, and obtaining the data age change range under the candidate allocation scheme according to the maximum change value;
the fourth formula is:
；
Wherein, Representing the update period of the star clock parameter,/>In seconds; /(I)Representing the fourth number of bits; /(I)Maximum change value representing data age change range of star clock parameter,/>In seconds.
7. The method for designing a data session number for a low-orbit satellite broadcast ephemeris according to claim 3 or 4,No more than 1 hour.
8. The method for designing a data session number for a low-orbit satellite broadcast ephemeris according to claim 5 or 6,No more than 30 seconds.
9. The method for designing data futures for low-orbit satellite broadcast ephemeris according to claim 1, wherein the ephemeris data futures IODE and the star Zhong Shuju futures IODC are each designed to 10 bits.
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