CN108919316B - Single-station multi-system hardware delay estimation method based on local spherical symmetry hypothesis - Google Patents

Single-station multi-system hardware delay estimation method based on local spherical symmetry hypothesis Download PDF

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CN108919316B
CN108919316B CN201810985356.3A CN201810985356A CN108919316B CN 108919316 B CN108919316 B CN 108919316B CN 201810985356 A CN201810985356 A CN 201810985356A CN 108919316 B CN108919316 B CN 108919316B
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佘承莉
乐新安
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Institute of Geology and Geophysics of CAS
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Abstract

The invention discloses a single-station multi-system hardware delay estimation method based on a local spherical symmetry hypothesis, belonging to the technical field of space. The technical scheme includes that a single-station GNSS multi-system receiver is used for receiving observation signals including satellite constellations such as Beidou, GPS, GLONASS and the like, and an ionized layer inclined TEC on each observation path is obtained through a phase smoothing pseudo-range method; meanwhile, calculating geometric information on each path, including geographical latitude, geographical longitude and elevation of the penetration point; screening out all satellite combinations which accord with the geometric conditions of local spherical symmetry on each epoch, and constructing an observation equation; solving the combined hardware delay of the receiver and each satellite by using a least square method; and solving the inclined TEC on the paths of the satellite and the receiver and the vertical TEC at the position of the penetration point according to the combined hardware delay. The method has the advantages that based on the local spherical symmetry hypothesis and the multi-system observation technology, the combined hardware delay of the satellite and the receiver can be efficiently and accurately calculated, and the method has important values for further obtaining the real-time high-precision ionized layer TEC and improving the ionized layer space environment monitoring and the short-term prediction.

Description

Single-station multi-system hardware delay estimation method based on local spherical symmetry hypothesis
Technical Field
The invention belongs to the field of GNSS hardware delay calculation method design, and particularly relates to a single-station multi-system hardware delay estimation method based on local spherical symmetry hypothesis.
Background
Total Electron Content (TEC) is not only an important parameter describing the morphology and structure of the ionosphere, but also an ionosphere correction parameter often applied to fine positioning and navigation services. Nowadays, TEC is mainly measured by GNSS receiver, and the largest error source is hardware delay from GNSS receiver and satellite, therefore, how to accurately calculate these hardware delay is the basis for conducting ionospheric studies using GNSS.
The existing literature shows that the hardware delays of both the satellite and the receiver are relatively stable and are generally considered to be constant within one day. Commonly used estimation methods include: (1) factory calibration: calibrating the hardware delay of the GNSS receiver before delivery by using the calibrated GNSS receiver; (2) and (3) calibrating the dependent TEC model: mapping a vertical TEC published in a TEC model to an oblique TEC on a GNSS observation path, interpolating according to time and place, solving a combined hardware delay of a receiver and a GNSS satellite according to the difference between the two, particularly, directly deducting a hardware delay part of the satellite from the observed oblique TEC depending on hardware delay data of each satellite provided by other mechanisms, and then making a difference between the observed TEC and the model TEC to obtain the hardware delay of the receiver; (3) calibration depending on GNSS station network observations: a dense GNSS ground observation platform network is utilized, a plane where the satellite penetration point heights around the platform network are located is divided into two-dimensional grids, the vertical TECs in the grids are assumed to be equal in a limited space-time range, and the vertical TECs in each grid and hardware delay of a GNSS receiver and a satellite are solved through an observation equation. The three methods have certain limitations, the first method is influenced by the aging of the GNSS satellite and the receiver and the environment, and the hardware delay of the first method is no longer the value of factory calibration; the second method depends on the precision of the ionized layer TEC model, and the calculated combined hardware delay is not accurate in the place where the ionized layer model description is not accurate enough; the third method is suitable for accurate solution of the local TEC, but depends on an observation network formed by a plurality of stations, and has large calculation amount and insufficient flexibility and simplicity.
Aiming at the limitations of the three methods, a single-station multi-system hardware delay estimation method based on local spherical symmetry assumption is provided, the method reasonably assumes that the method is locally symmetrical on a spherical surface taking a single station as a center according to the characteristics of a ground-based GNSS TEC, fully utilizes observation data of constellations such as BDS, GPS, GLONASS and the like, establishes an equation for all observation data meeting the assumption condition, and solves the combined hardware delay of the station and each satellite by using a least square method. The method only needs observation data of one station, does not need to depend on observation data of a TEC model or other stations, has small calculation amount, has the characteristics of independence, rapidness and flexibility, can obtain the vertical TEC above the station by utilizing combined hardware delay, and provides stable and reliable data support for ionosphere morphology research and ionosphere correction.
Disclosure of Invention
Aiming at the limitation of the conventional method in solving the GNSS hardware delay, the invention provides a single-station multi-system hardware delay estimation method based on the local spherical symmetry assumption.
A single-station multi-system hardware delay estimation method based on a local spherical symmetry hypothesis is characterized by comprising the following steps:
step 1: receiving observation signals including satellite constellations such as Beidou, GPS, GLONASS and the like by using a single-station GNSS multi-system receiver, and obtaining the ionized layer inclined TEC on each observation path by a phase smoothing pseudo range method;
step 2: calculating geometric information on each path, including geographic latitude, geographic longitude and elevation of the penetration point;
and step 3: screening out all satellite combinations which accord with the geometric conditions of local spherical symmetry on each epoch, and constructing an observation equation;
and 4, step 4: solving the combined hardware delay of the receiver and each satellite by using a least square method; and obtaining the inclined TEC on the paths of the satellite and the receiver according to the combined hardware delay, and converting the inclined TEC into the vertical TEC of the penetration point position according to a mapping function.
In step 1, the calculation formula of the ionized layer inclined TEC is as follows:
Figure BDA0001779581080000031
where the superscript i denotes the GNSS satellite number, the subscript t denotes the time of day, the subscripts 1 and 2 denote the two carriers of the GNSS, the subscript obs denotes the observations,
Figure BDA0001779581080000032
ionospheric bias TEC observation values (unit TECU, 1TECU is 1.0 × 10) on GNSS receiver observation paths from the ith satellite to the ground at the time t16Electron/m2) C is the speed of light, f1And f2Respectively representing the two carrier frequencies of the GNSS satellites,
Figure BDA0001779581080000033
and
Figure BDA0001779581080000034
number 1 and number 2 carriers representing the ith satellite, respectivelyThe phase observation of the wave frequency at time t,
Figure BDA0001779581080000041
and
Figure BDA0001779581080000042
the corresponding pseudo-range observations are respectively represented, and N is the number of observation samples of the ith satellite in a continuous observation arc.
Here, the diagonal TEC contains hardware delay, and the relationship between it and the "true" TEC can be expressed as:
Figure BDA0001779581080000043
wherein the subscript real represents the "true" value,
Figure BDA0001779581080000044
it represents the ionospheric tilt TEC true value on the GNSS receiver observation path from the ith satellite to the ground at time t,
Figure BDA0001779581080000045
is the receiver hardware delay (B)R) And satellite hardware delay (B)i) To sum, i.e.
Figure BDA0001779581080000046
Their units are also TECUs.
In step 2, the calculation formulas of the geographical latitude, the geographical longitude and the elevation of the position of the penetration point above the station are as follows:
Figure BDA0001779581080000047
Figure BDA0001779581080000048
Figure BDA0001779581080000049
wherein the content of the first and second substances,
Figure BDA00017795810800000410
and
Figure BDA00017795810800000411
respectively the geographical latitude and the geographical longitude of the ith satellite at the point of penetration height at time t,
Figure BDA00017795810800000412
is the elevation angle relative to the GNSS satellites at the point of penetration,
Figure BDA00017795810800000413
then the elevation angle on the ground relative to the GNSS satellite, ζ is the azimuth angle of the GNSS satellite relative to the station, REIs the average radius of the earth, z is the height at which the ionosphere penetration points are located,
Figure BDA00017795810800000414
is the angle of the earth's sphere,
Figure BDA00017795810800000415
θ0and λ0Respectively, the geographical latitude and longitude of the ground station.
According to the elevation angle at the penetration point, the vertical TEC can be conveniently converted, and the formula is as follows:
Figure BDA0001779581080000051
wherein the content of the first and second substances,
Figure BDA0001779581080000052
represents the mapping function of the ith satellite at time t, which is a function of the elevation angle of the point of penetration,
Figure BDA0001779581080000053
in step 3, the local spherical symmetry condition is determined by the elevation angle and the azimuth angle between two satellites, and when the difference between the elevation angle and the azimuth angle is not greater than 10 ° and not greater than 15 °, the vertical TECs between the two satellites are considered to be equal, and the vertical TEC is the "true" TEC after the hardware delay is removed. For any two satellites i and j meeting the local spherical symmetry condition, the observation equation between them is as follows:
Figure BDA0001779581080000054
wherein, i and j respectively represent satellite numbers,
Figure BDA0001779581080000055
and
Figure BDA0001779581080000056
respectively representing the mapping functions of the ith and jth satellites at time t.
It is clear that for a fixed combination of satellites i and j, their observation equations within one day are all related to
Figure BDA0001779581080000057
And
Figure BDA0001779581080000058
the equations for these two unknowns, there is a large amount of redundant data. To reduce computational redundancy, averaging is performed over all time instants, resulting in a simplified equation as follows:
Figure BDA0001779581080000059
where T represents the number of observation samples for this satellite combination,
Figure BDA00017795810800000510
and
Figure BDA00017795810800000511
respectively representing the average values of the mapping functions in the ith and jth satellite combinations.
In step 4, based on step 3, the combination of satellites numbered i and j is denoted as the combination numbered k, and the simplified equations of the satellite combinations can be combined into the following sparse matrix form:
Figure BDA0001779581080000061
wherein M represents the number of combined hardware delays to be solved, K represents the number of satellite combinations, bmDenotes the combined hardware delay, y, of the m-th satellite and the receiverkRepresents the combined observations of satellites numbered i and j in combination k:
Figure BDA0001779581080000062
Figure BDA0001779581080000063
from the element fkiThe K M matrix F is a sparse matrix with only two non-zero elements in each row, the row index K indicating the serial number of the satellite combination, the column index i indicating the satellite numbered i, FkiRepresenting the mean of the mapping function for satellite i in combination k.
In this observation matrix FB ═ Y, only the vector B is an unknown quantity, and can be solved by the least square method.
The method has the advantages that based on multisystem observation conditions and local spherical symmetry hypothesis, the method effectively utilizes resources of GNSS constellations such as Beidou, GPS, GLONASS and the like, can quickly and accurately calculate the combined hardware delay of the station and the GNSS satellite by only depending on one station, has the capability of resolving the ionosphere vertical TEC in real time, and has important application value in future ionosphere space environment monitoring.
Drawings
Fig. 1 is a time-dependent change curve of an ionosphere oblique TEC observation value of a beidou satellite No. 1 calculated by the method provided by the invention.
Fig. 2 is a distribution diagram of ionosphere penetration point geographical latitude and longitude calculated by the method provided by the invention.
FIG. 3 is a diagram of the time-dependent elevation and azimuth of two satellites calculated by the method of the present invention.
FIG. 4 is a histogram of combined hardware delays for a single station receiver and GNSS satellites for a day computed by the method of the present invention.
FIG. 5 is a graph of the change of the ionosphere vertical TEC of the Beidou No. 1 satellite calculated by the method provided by the invention along with time.
FIG. 6 is a graph of the vertical TEC of the single station ionosphere calculated by the method of the present invention over time.
Detailed Description
The preferred embodiments will be described in detail below with reference to the accompanying drawings. It should be emphasized that the following description is merely exemplary in nature and is not intended to limit the scope of the invention or its application.
Taking a certain station data supporting three-system GNSS observation as an example, the station data can simultaneously receive the data of the epochs, the pseudo ranges, the phases and the like of Beidou satellite, GPS satellite and GLONASS satellite constellations, and execute the following steps:
step 1: smoothing the differential pseudo range by using the differential phase observation of each GNSS satellite to obtain the ionized layer inclined TEC:
Figure BDA0001779581080000071
here, taking the Beidou satellite 1 (i ═ 1) as an example, the two carrier frequencies are f1＝1575.42MHz，f21227.6MHz, and 2.99792458 × 10 speed of light c8m/s, two phase observations at the time t ═ 1 are respectively
Figure BDA0001779581080000081
Figure BDA0001779581080000082
It is a geostationary satellite, which can be observed all day long, itThere are a total of 2733 observations within a day.
Figure BDA0001779581080000083
Wherein, i is 1,2, …,2733, N is 2733,
Figure BDA0001779581080000084
and
Figure BDA0001779581080000085
respectively representing pseudorange observations at time t for two frequencies for satellite number 1,
Figure BDA0001779581080000086
and
Figure BDA0001779581080000087
respectively, the phase observations of the two frequencies of satellite number 1 at time t. And smoothing the pseudo-range difference according to the phase difference to obtain an ionosphere tilt TEC observed value of the No. 1 satellite at the 1 st moment, wherein the value of the ionosphere tilt TEC observed value is about-34.35 TECU.
Fig. 1 shows a time-dependent change curve of an ionosphere oblique TEC observation value of a beidou satellite No. 1 obtained by a single-station multi-system hardware delay estimation method based on a local spherical symmetry hypothesis.
Step 2: here, the observation information of the beidou 1 satellite at the 1 st moment is still taken as an example, and is based on the station coordinates (the geographic latitude θ)018.35 °, geographic longitude λ0109.62 deg.), ground elevation and azimuth, respectively
Figure BDA0001779581080000088
And
Figure BDA0001779581080000089
the height of the penetration point from the ground is 450km, and the calculated geometric parameters are as follows:
(1) earth corner
Figure BDA00017795810800000810
Figure BDA00017795810800000811
(2) Geographic latitude of penetration point
Figure BDA00017795810800000812
Figure BDA0001779581080000091
(3) Geographic longitude of point of penetration
Figure BDA0001779581080000092
Figure BDA0001779581080000093
(4) Elevation angle of penetration point
Figure BDA0001779581080000094
Figure BDA0001779581080000095
Fig. 2 shows a distribution diagram of the ionosphere penetration point geographical latitude and longitude calculated by the method provided by the invention.
In step 3, according to the judgment condition of local spherical symmetry, two satellites meeting the condition are combined in pairs, still taking the Beidou satellite No. 1 (i is 1) as an example, the Beidou satellite No. 1 and the GPS satellite No. 25 (j is 36) form a first combination (k is 1) at the time of world time 06:43:50, and the local spherical symmetry condition is met by each parameter:
Figure BDA0001779581080000096
Figure BDA0001779581080000097
y1＝-19.26。
the observation equation at this time is as follows:
C01—G25：
Figure BDA0001779581080000098
all over the day, these two satellites satisfy the local spherical symmetry condition at a total of 86 times, and their observed equations at each time are averaged to obtain a simplified equation as follows:
C01—G25：
Figure BDA0001779581080000099
FIG. 3 is a diagram of the time-dependent elevation and azimuth of two satellites calculated by the method of the present invention. "C01" and "G25" in the figure represent the Beidou satellite 1 and the GPS satellite 25, respectively, which are satellite numbers represented in the form of three-digit bits "SNN", the initials "S" represent the satellite constellation, "C", "G" and "R" represent the Beidou, GPS and GLONASS satellite constellations, respectively, and the 2-3 characters represent the serial numbers of the satellites in that constellation. The portion where the two vertical dashed lines are sandwiched indicates the observed quantity satisfying the local spherical symmetry condition.
And 4, step 4: for the Beidou satellite No. 1 in the step 3, a total of 8 satellites can form an observation equation with the Beidou satellite No. 1, which is sequentially G02, G14, G17, G19, G25, R06, R11 and R21, and the simplified equations are respectively as follows:
C01—G02：
Figure BDA0001779581080000101
C01—G14：
Figure BDA0001779581080000102
C01—G17：
Figure BDA0001779581080000103
C01—G19：
Figure BDA0001779581080000104
C01—G25：
Figure BDA0001779581080000105
C01—R06：
Figure BDA0001779581080000106
C01—R11：
Figure BDA0001779581080000107
C01—R21：
Figure BDA0001779581080000108
66 satellites were observed all day long, among them 13 Beidou satellites, 30 GPS satellites and 23 GLONASS satellites. A total of 256 satellite combinations are available. By combining all the observation equations, an equation set containing 66 unknowns can be obtained. This is an overdetermined system of equations that can be solved directly using the least squares method. The solution result is an optimal estimate of the combined hardware delays of the terrestrial receiver and the various GNSS satellites.
The combined hardware delays for a single station receiver and GNSS satellites within a day calculated according to the method provided by the invention are shown in the bar graph of fig. 4.
The diagonal TEC on the ground-to-GNSS satellite path can be obtained by directly subtracting this combined hardware delay from the observed diagonal TEC. Still taking the Beidou satellite No. 1 as an example, the tilted TEC thereof can be expressed as follows:
Figure BDA0001779581080000111
accordingly, from the transformation of the mapping function, the vertical TEC of the breakthrough point height can be obtained:
Figure BDA0001779581080000112
as shown in fig. 5, a graph of the change of the ionosphere vertical TEC of the beidou No. 1 satellite calculated according to the method provided by the present invention with time.
FIG. 6 is a graph of the vertical TEC of the single station ionosphere calculated by the method of the present invention over time.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. A single-station multi-system hardware delay estimation method based on a local spherical symmetry hypothesis is characterized by comprising the following steps:
step 1: receiving observation signals including Beidou, GPS and GLONASS satellite constellations by using a single-station GNSS multi-system receiver, and obtaining the ionized layer inclined TEC on each observation path by a phase smoothing pseudo range method;
step 2: calculating geometric information on each path, wherein the geometric information comprises the geographical latitude, the geographical longitude and the elevation of the position of a penetrating point above the station;
and step 3: on each epoch, when the difference of the elevation angle between two satellites is not more than 10 degrees and the difference of the azimuth angle is not more than 15 degrees, the two satellites are considered to accord with the geometric condition of local spherical symmetry, all satellite combinations which accord with the geometric condition of local spherical symmetry are screened out, and an observation equation is constructed;
and 4, step 4: solving the combined hardware delay of the receiver and each satellite in the observation equation by using a least square method; and obtaining the inclined TEC on the paths of the satellite and the receiver according to the combined hardware delay, and converting the inclined TEC into the vertical TEC of the penetration point position according to a mapping function.
2. The method for estimating hardware delay of single station and multiple systems based on local spherical symmetry hypothesis according to claim 1, wherein in the step 1, the calculation formula of the ionosphere tilted TEC is:
Figure FDA0002829255800000011
where the superscript i denotes the GNSS satellite number, the subscript t denotes the time of day, the subscripts 1 and 2 denote the two carriers of the GNSS, the subscript obs denotes the observations,
Figure FDA0002829255800000012
the unit of an ionosphere oblique TEC observation value on an observation path of the GNSS receiver from the ith satellite to the ground at the time t is TECU, and 1TECU is 1.0 multiplied by 1016Electron/m2C is the speed of light, f1And f2Respectively representing the two carrier frequencies of the GNSS satellites,
Figure FDA0002829255800000021
and
Figure FDA0002829255800000022
phase observations at time t of carrier frequencies No. 1 and No. 2 of the ith satellite respectively,
Figure FDA0002829255800000023
and
Figure FDA0002829255800000024
the corresponding pseudo-range observations are respectively represented, and N is the number of observation samples of the ith satellite in a continuous observation arc.
3. The method for single-station multi-system hardware delay estimation based on the local spherical symmetry hypothesis as claimed in claim 1, wherein in step 2, the calculation formula of the geographical latitude, the geographical longitude and the elevation of the penetration point position above the station is as follows:
Figure FDA0002829255800000025
Figure FDA0002829255800000026
Figure FDA0002829255800000027
wherein the content of the first and second substances,
Figure FDA0002829255800000028
and
Figure FDA0002829255800000029
respectively the geographical latitude and the geographical longitude of the ith satellite at the point of penetration height at time t,
Figure FDA00028292558000000210
is the elevation angle relative to the GNSS satellites at the point of penetration,
Figure FDA00028292558000000211
then in elevation on the ground with respect to the GNSS satellites,
Figure FDA00028292558000000212
is the azimuth, R, of the GNSS satellite relative to the stationEIs the average radius of the earth, z is the height at which the ionosphere penetration points are located,
Figure FDA00028292558000000213
is the earthThe angle of the corner is such that,
Figure FDA00028292558000000214
θ0and λ0Respectively, the geographical latitude and longitude of the ground station.
4. The local sphere symmetry assumption-based single-station multi-system hardware delay estimation method according to claim 2, wherein in step 3, for any two satellites i and j observed at time t and meeting the local sphere symmetry condition, the observation equation between them is as follows:
Figure FDA0002829255800000031
wherein, i and j respectively represent satellite numbers,
Figure FDA0002829255800000032
and ft jRespectively representing the mapping functions of the ith and jth satellites at time t,
Figure FDA0002829255800000033
is the combined hardware delay of the receiver and the satellite, which is the receiver hardware delay BRHardware delay B from ith satelliteiTo sum, i.e.
Figure FDA0002829255800000034
To reduce computational redundancy, the simplified equation after averaging all the moments is as follows:
Figure FDA0002829255800000035
where T represents the number of observation samples for this satellite combination,
Figure FDA0002829255800000036
and
Figure FDA0002829255800000037
respectively representing the average values of the mapping functions in the ith and jth satellite combinations.
5. The method for single-station multi-system hardware delay estimation based on the local spherical symmetry hypothesis as claimed in claim 4, wherein in step 4, a combination formed by satellites numbered i and j is denoted as a combination numbered k, and simplified equations of the satellite combinations can be combined into a sparse matrix form as follows:
Figure FDA0002829255800000038
wherein M represents the number of combined hardware delays to be solved, K represents the number of satellite combinations, bmDenotes the combined hardware delay, y, of the m-th satellite and the receiverkRepresents the combined observations of satellites numbered i and j in combination k:
Figure FDA0002829255800000039
Figure FDA00028292558000000310
from the element fkiThe K M dimensional matrix is a sparse matrix with each row having only two non-zero elements, the row index K indicating the serial number of the satellite combination, the column index i indicating the satellite numbered i, fkiRepresenting the mean value of the mapping function of the satellite i in the combination k, represented by the element bmThe formed M × 1-dimensional vector is an unknown quantity and can be solved by a least square method.
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