CN116361714B - Non-isotropic horizontal troposphere delay classification method - Google Patents

Non-isotropic horizontal troposphere delay classification method Download PDF

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CN116361714B
CN116361714B CN202310635800.XA CN202310635800A CN116361714B CN 116361714 B CN116361714 B CN 116361714B CN 202310635800 A CN202310635800 A CN 202310635800A CN 116361714 B CN116361714 B CN 116361714B
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徐莹
周宏展
杨早早
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Shandong University of Science and Technology
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Abstract

The invention belongs to the technical field of global satellite navigation and positioning, and particularly discloses a method for classifying tropospheric delays in a horizontal direction, which takes non-isotropy into consideration. The method comprises the following steps: estimating troposphere delay data of different azimuth angles at each altitude in the altitude range to be classified; estimating non-isotropy values of different azimuth angles at each altitude according to troposphere delay data; combining the medium errors of troposphere delays at all the altitude angles, and constructing classification thresholds at different altitude angles based on the IGG-3; and judging the magnitude relation between the non-isotropic value and the absolute value of the classification threshold value, thereby realizing the horizontal direction classification of tropospheric delay. According to the method, the isotropy of the tropospheric delay in the horizontal direction is considered, quantitative analysis is realized by defining the non-isotropy value, and meanwhile, the IGG-3 is introduced to establish the classification threshold value, so that the horizontal direction classification of the tropospheric delay is well realized.

Description

Non-isotropic horizontal troposphere delay classification method
Technical Field
The invention belongs to the technical field of global satellite navigation and positioning, and particularly relates to a method for classifying tropospheric delays in a horizontal direction, which takes non-isotropy into consideration.
Background
Tropospheric delay, which is the effect of the change of speed and path of electromagnetic wave signals penetrating through neutral atmosphere, is one of the important error sources for high-precision navigation and positioning of global satellite navigation systems (Global Navigation Satellite System, GNSS). The estimation of high-precision tropospheric delay is of great importance to precision positioning, GNSS meteorology and the like. Generally, the tropospheric Delay in the zenith direction of the reference station is referred to as the zenith tropospheric Delay (ZenithTropospheric Delay, ZTD) and the remaining directions are referred to as the tropospheric Delay (SPD). In GNSS data processing, the SPD is typically obtained by multiplying ZTD by a mapping function. The troposphere delay mapping function is a key factor for improving the GNSS troposphere delay estimation precision, and the mapping function is used for connecting the ZTD with the SPDs in any direction so as to achieve the purpose of simplifying calculation.
NMF, GMF model and VMF series model are the most widely used and highest precision troposphere mapping function model at present. The modeling of the model is based on the principle of azimuthal symmetry about meteorological elements, i.e. the model is built on the basis of tropospheric isotropy. However, since the atmosphere is flowing, the water vapor motion also has high time-space variation characteristics, and the SPD can change with different azimuth angles, namely, the tropospheric delays in different directions above the measuring station can be different. It can be seen that the scheme of estimating tropospheric delay using a mapping function ignores the difference in tropospheric delay in different horizontal directions.
In the high-precision positioning algorithm process, a horizontal gradient term is generally introduced to correct errors of the mapping function due to neglecting differences of tropospheric delays of different azimuth angles. But the essence of the horizontal gradient correction is that the atmosphere is simply considered to be anisotropic, the first-order Fourier series of the SPD in the azimuth angle domain is expanded, the high-order terms are ignored, then the anisotropic components in the east-west direction and the north-south direction are calculated by using a parameter estimation method, and the anisotropic value is obtained by multiplying the anisotropic components by the corresponding horizontal gradient mapping function. The tropospheric delay is estimated by a method of combining a mapping function with a horizontal gradient function, while taking into account the difference in tropospheric delay in different horizontal directions, it does not coincide with the actual characteristics of tropospheric delay in the horizontal direction.
It can be seen that neither isotropy nor anisotropy accurately represents the actual characteristics of tropospheric delay in the horizontal direction.
Before the present invention emerges, a method of estimating a tropospheric delay with high accuracy using an integration method (ray tracing method) has also been proposed. Based on NWP data, the method estimates SPDs of all azimuth angles under a certain altitude angle in the 2018 DOY196 UTC18 of the BJFS station by adopting a ray tracing method, and makes differences between the SPDs and average SPDs corresponding to all azimuth angles under the altitude angle, wherein SPD values under the azimuth angles of 180-360 degrees are similar, but SPD values under the azimuth angles of 30-150 degrees are obviously different, the maximum and minimum differences between SPDs corresponding to different azimuth angles can reach 15 cm, and the lower the altitude angle is, the larger the difference is. It is clear from this that the tropospheric delay is neither isotropic nor anisotropic, but not isotropic under conditions of high temporal-spatial variation characteristics of the fluidity of the atmosphere and the movement of water vapor. Although the integration method can estimate the tropospheric delay with high precision, the method is not easy to be applied to real-time positioning because real-time meteorological data are difficult to acquire.
Noun interpretation:
the isotropy of the tropospheric delay means that the physical, chemical, etc. properties of the object do not change due to the difference in metrology direction, also called homogeneity.
The anisotropy of tropospheric delay means that all or part of physical, chemical and other properties of an object change with the change of measurement direction, and the difference appears in different directions.
Non-isotropy of tropospheric delay means that at a certain altitude, the tropospheric delay at certain azimuths can be considered approximately equal, but at other azimuths the tropospheric delay is of greater variance.
Disclosure of Invention
The invention aims to provide a method for classifying tropospheric delays in a horizontal direction, which takes non isotropy into consideration, wherein the non isotropy of the tropospheric delays is quantitatively represented by the method of the non isotropy value, and meanwhile, a classification threshold function is established based on IGG-3 by combining the medium errors of the tropospheric delays at all height angles, so that classification of different properties (isotropy and non isotropy) of the tropospheric delays in the horizontal direction is realized.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for classifying delays of a horizontal troposphere considering non isotropy comprises the following steps:
step 1, estimating troposphere delay data of different azimuth angles at each altitude angle in an altitude angle range to be classified;
step 2, estimating non-isotropic values delta of different azimuth angles at each altitude angle according to the troposphere delay data obtained in the step 1, wherein the corresponding non-isotropic values delta exist at each azimuth angle at each altitude angle;
step 3, combining sigma at each height angle to determine a threshold function k.sigma at different height angles; wherein sigma is a medium error of tropospheric delay at a height angle where delta is located, and k is a three-section sliding window function constructed based on IGG-3;
and 4, judging the magnitude relation between the non-isotropy value delta of different azimuth angles at each altitude angle and the absolute value of the threshold function k.sigma, and realizing classification of different properties of tropospheric delay in the horizontal direction according to the magnitude relation.
The invention has the following advantages:
as described above, the present invention describes a method for classifying tropospheric delays in a horizontal direction taking into account non-isotropy, which breaks through the original theory of isotropy and anisotropy, takes into account the non-isotropy of tropospheric delays in a horizontal direction, and simultaneously introduces IGG-3 in order to establish classification thresholds for distinguishing two different properties of isotropy and non-isotropy of tropospheric delays in addition to quantitative analysis by defining a non-isotropy value, thereby realizing the horizontal direction classification of tropospheric delays of the present invention. The non-isotropy value is the basis of the troposphere delay classification method, and the classification threshold established based on IGG-3 well ensures continuity between azimuth angles with the same property after classification. The troposphere delay classification method provided by the invention is beneficial to establishing a troposphere delay correction model which is more close to the real condition of the atmosphere, improves the estimation precision of the troposphere delay, and reduces the influence of the troposphere delay on high-precision GNSS positioning. The classification method provided by the invention provides technical support for GNSS high-precision troposphere delay estimation, extreme weather forecast and the like.
Drawings
FIG. 1 is a flow chart of a method for classifying retardation of a horizontal troposphere in consideration of non-isotropy in an embodiment of the present invention.
Fig. 2 is a graph showing the value of the coefficient k in the embodiment of the invention.
FIG. 3 is a schematic diagram of a method for non-isotropic classification of tropospheric delay in an embodiment of the invention.
FIG. 4 is a plan view of an azimuthal categorization of a BAKE station by the method of the present invention for an altitude of 5-40 and an azimuth of 10-360.
FIG. 5 is a schematic diagram of a horizontal gradient model based on a non-isotropic classification method according to an embodiment of the present invention.
FIG. 6 is a schematic diagram of a 17.5℃altitude SPD at time 2019 DOY001 UTC18 of a BAKE station of the RT-SPD, the MF-SPD with added horizontal gradient correction, and the SPD estimated based on the horizontal gradient model estimation of the classification method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and detailed description:
as shown in fig. 1, the present embodiment describes a method for classifying tropospheric delays in a horizontal direction taking into account non-isotropy, the method for classifying tropospheric delays in a horizontal direction taking into account non-isotropy, comprising the steps of:
step 1, troposphere delay data of different azimuth angles at each altitude angle (within a range of 0-360 degrees) in an altitude angle range to be classified are estimated, and the altitude angle range, the altitude angle, the sampling interval of the azimuth angles and the like can be determined according to requirements.
In this embodiment, the tropospheric delay data is estimated using meteorological parameters, for example by ray tracing.
And 2, estimating non-isotropy values delta of different azimuth angles at each altitude angle according to the troposphere delay data obtained in the step 1, wherein corresponding delta exists at each azimuth angle at each altitude angle.
The determination method of the non-isotropy value delta is as follows: the SPD of each azimuth of a certain altitude is made to differ from the average mean of the SPDs of the azimuth at that altitude, the difference being defined as the non-isotropic value delta.
The non-isotropy value delta is due to asymmetry and its expression is shown in formula (1):
Δ=SPD﹣meanspd （1）
where SPD denotes the tropospheric delay, and mean is the average of the SPDs at each azimuth at the altitude to be classified, i.e. the isotropy of the tropospheric delay due to the symmetry of the atmosphere.
The non-isotropy value delta is a quantized representation of the tropospheric delay non-isotropy. And, through Lilliefors hypothesis test, the non-isotropy value at a certain altitude angle is in conformity with the normal distribution.
The non-isotropic value delta inherits some of the characteristics of the SPD, e.g. delta increases exponentially with decreasing altitude, and it has been found experimentally that delta is on the order of 0.1mm at 40 ° altitude and reaches a maximum of dm at 5 ° altitude.
Since the non-isotropic value Δ defined in this embodiment removes the isotropic portion, the non-isotropic value Δ can better exhibit the change characteristics of the SPD in the horizontal direction at a certain altitude angle.
In order to implement the present invention, another key issue, in addition to the quantitative analysis by defining the non-isotropic value Δ, is how to determine a threshold to distinguish between the two different properties of isotropy and non-isotropy of the tropospheric delay.
Step 3, combining sigma at each height angle to determine a threshold function k.sigma at different height angles; where σ is the medium error in tropospheric delay at the altitude angle where Δ is located, and k is a three-segment sliding window function constructed based on IGG-3.
The method uses the function with continuity as the threshold value, and the threshold value with the function form of continuity can effectively detect abnormal values appearing in data, avoids the situation that the tropospheric delay on a certain azimuth angle shows other properties in the continuous range of the azimuth angle of the tropospheric delay showing the same properties, ensures that the azimuth angles where the tropospheric delay with the same properties after classification are kept continuous, and is beneficial to establishing a tropospheric delay estimation model closer to the real situation of the atmosphere.
For this purpose, the invention adopts the classification method of IGG-3 weight scheme to construct a three-section sliding window function k as a part of the threshold value. The IGG-3 right scheme divides the data into three types of effective information, usable information and harmful information through data quality, fully utilizes the effective information, limits the influence of the usable information and eliminates the harmful information, and is a scheme suitable for measuring data processing.
And constructing a three-section sliding window function k based on the IGG-3, wherein the expression of the three-section sliding window function k is shown in a formula (2).
（2）
Where |u| is the normalized residual,，e 0 for a first limiting threshold, e 1 Is a second limiting threshold.
According to a large number of repeated experiments, the value range of the I u I is about 0.3-3.8 in the height angle range of 40-5 degrees, so the first limiting threshold e is adopted in the embodiment 0 Second limiting threshold e 1 The method comprises the following steps of: e, e 0 =0.5，e 1 =2.0。
The graph of the value range of k is shown in fig. 2. In order to make the classification result not only be close to the actual characteristics of tropospheric delay, but also be convenient to establish a more accurate tropospheric delay estimation model by using the classification result, the maximum value of k is set to 0.8, the minimum value is set to 0.7, and the rest is set to a function form with continuity, so that effective information can be fully utilized, available information is limited, harmful information is eliminated, and continuity between azimuth angles with the same property after classification is realized.
Under certain conditions of space position, time and altitude angle, taking k times of the middle error sigma of the SPD at the altitude angle as a threshold value, quantitatively representing by using the non-isotropy value of the tropospheric delay, and classifying by combining the non-isotropy of the tropospheric delay.
And 4, judging the magnitude relation between the non-isotropy value delta of different azimuth angles at each altitude angle and the absolute value of the threshold function k.sigma, and realizing classification of different properties of tropospheric delay in the horizontal direction according to the magnitude relation.
When delta > |k.sigma|, the tropospheric delay at the azimuth angle corresponding to delta meeting the condition is forward non-isotropic; when delta is < - > k.sigma|, the tropospheric delay at the azimuth angle corresponding to delta satisfying this condition is reversely non-isotropic.
When-k.sigma| is less than or equal to delta is less than or equal to |k.sigma|, the tropospheric delay at the azimuth angle corresponding to delta meeting the condition is isotropic.
As shown in fig. 3, the vertical axis represents different properties, the horizontal axis represents non-isotropic values, the dotted gray stripe region represents a forward direction portion, the solid gray stripe region represents a reverse direction portion, and the solid black stripe region at the center represents a like direction portion.
Under the determined moment, the troposphere delay of each azimuth angle at different altitude angles of any measuring station can be classified according to the method, and technical support is provided for building a troposphere delay estimation model which is more fit with the actual characteristics of the atmosphere and is more accurate.
The following classification is performed in accordance with the above-described classification method using SPD with an azimuth angle of 10 ° to 360 ° as example data at day DOY00158 UTC18, 5 ° to 40 ° altitude, in the case of the BAKE station 2020 in the IGS station.
Fig. 4 shows the result of classifying example data according to the classification method and steps of the present invention. The polar coordinate system uses 0 m as a center, the polar axis thereof represents SPD (unit is m), and the polar angle represents azimuth angle.
In the figure, different circular curves represent SPDs with different height angles, the curve of the innermost circle is the SPDs with each azimuth at the height angle of 40 degrees, and the curve of the outermost circle is the SPDs with each azimuth at the height angle of 5 degrees. The dashed portion of each curve represents a reverse SPD, the dashed portion with a circular label represents a forward SPD, and the solid line represents a like SPD.
As can be seen from fig. 4, SPDs between 150 ° azimuth and 270 ° azimuth at each altitude of the BAKE station exhibit directionality, while SPDs exhibit reverse directionality between 330 ° and 90 ° azimuth, with SPDs exhibiting identity at the remaining azimuths.
After the classification method provided by the invention is applied to finish the classification of the SPD, the SPD with different properties (forward, isotropic and reverse) can be subjected to targeted modeling, so that the built model considers the isotropy of the SPD in the horizontal direction, but does not build a simple isotropic or anisotropic-based model, thereby being beneficial to estimating the real characteristics of the SPD which is more close to tropospheric delay and having higher precision, and further providing technical support in the fields of GNSS high-precision positioning, GNSS meteorology and the like.
In addition, in order to verify the effectiveness of the classification method provided by the invention, a non-isotropic horizontal gradient correction method based on tropospheric delay is established based on the classification method of the invention by combining a horizontal gradient correction model.
As shown in fig. 5, the non-isotropic horizontal gradient correction method based on tropospheric delay includes the steps of:
and firstly, carrying out difference between MF-SPD and RT-SPD with added horizontal gradient correction between the same azimuth angles at each altitude angle, and judging whether the maximum difference value (hereinafter referred to as the maximum difference value) between the two at each altitude angle is larger than 0.
Wherein for convenience of description, the RT-SPD scheme is taken as scheme 1, and the MF-SPD scheme is taken as scheme 2.
The mapping function used in scheme 2 is VMF1.
And classifying the data of the scheme 1 according to the classifying method provided by the invention, wherein the azimuth angle of the forward SPD is called a forward part, and the azimuth angle of the reverse SPD is called a reverse part.
If the maximum difference value at a certain altitude angle is greater than 0, it is explained that the estimated value of scheme 2 is greater than that of scheme 1, i.e. in the forward direction, the horizontal gradient causes the difference between the MF-SPD and the RT-SPD to increase. In this case, only VMF1 is used to estimate the SPD of the forward part, while the rest of the azimuth will be estimated according to scheme 2.
If the maximum difference at a certain altitude angle is smaller than 0, it is explained that the estimate of scheme 2 is smaller than that of scheme 1, i.e. in the reverse part, the horizontal gradient causes the difference between the MF-SPD and the RT-SPD to increase, in which case the SPD of the reverse part is estimated using VMF1 only, while the SPD will be estimated at the remaining azimuth angles according to scheme 2.
Furthermore, the boundaries of SPDs of different properties will be smoothed.
Taking a 5-40 DEG altitude angle and a 10-360 DEG azimuth SPD at the moment of a BAKE station 2019 DOY001 UTC18 as an example, a scheme 3 (an SPD estimated based on a horizontal gradient model of the classification method of the invention) is constructed, and in combination with schemes 1 and 2 mentioned in the implementation steps of the model, the validity of the model is verified and the accuracy of the model is evaluated, wherein the scheme 1 is taken as a reference.
Fig. 6 shows SPD (17.5 ° altitude) estimated by a BAKE station according to three schemes. In the figure, the polar axis of the polar coordinate system represents the SPD value (in m, 7.590 m at the pole, 7.620 m at the outermost boundary), and the polar angle represents the azimuth angle.
The pattern formed by combining three points with different densities is the result of scheme 1, and the densities of the points from dense to sparse respectively represent the reversibility, the homopolarity and the forward direction; the diagonal line graph shows the results of scheme 2; the graph filled in by black represents the results of scheme 3.
For a 17.5 altitude, the maximum difference between scheme 2 and scheme 1 is less than 0, so the reverse portion (10 ° -120 ° azimuth) uses VMF1 alone to estimate SPD, with the rest of the azimuths being estimated according to scheme 2.
As can be seen from fig. 6, scheme 3 is significantly closer to scheme 1 than scheme 2, and its estimation is more accurate.
From quantitative analysis, when using scheme 1 as a reference, the RMS of scheme 2 was 6.1 mm and the RMS of scheme 3 was 3.9 mm, and it can be seen that scheme 3 based on the classification method of the present invention has an accuracy improved by about 36% compared to scheme 2.
The non-isotropic classification method of tropospheric delay as proposed by the present invention was demonstrated to be effective by this experiment.
The method provides a new modeling thought and technical support for establishing the troposphere delay correction model which is high in precision and more close to the real condition of the atmosphere, and has important research significance and application value in the aspects of GNSS meteorology, GNSS high-precision positioning and the like.
The foregoing description is, of course, merely illustrative of preferred embodiments of the present invention, and it should be understood that the present invention is not limited to the above-described embodiments, but is intended to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

Claims (2)

1. A method for classifying retardation of a troposphere in a horizontal direction considering non-isotropy is characterized in that,
the method comprises the following steps:
step 1, estimating troposphere delay data of different azimuth angles at each altitude angle in an altitude angle range to be classified;
step 2, estimating non-isotropy values delta of different azimuth angles at each altitude angle according to the troposphere delay data obtained in the step 1; wherein a corresponding non-isotropic value delta exists at each azimuth at each altitude;
in the step 2, the expression of the non-isotropy value delta is as shown in formula (1):
Δ=SPD﹣meanspd （1）
wherein SPDs represent tropospheric delay, and meanspd is the average value of SPDs of azimuth angles at altitude to be classified;
step 3, combining sigma at each height angle to determine a threshold function k.sigma at different height angles; wherein sigma is a medium error of tropospheric delay at a height angle where delta is located, and k is a three-section sliding window function constructed based on IGG-3;
in the step 3, the expression of the three-section sliding window function k is shown in formula (2);
（2）
where |u| is the normalized residual,，e 0 for a first limiting threshold, e 1 Is a second limiting threshold;
step 4, judging the magnitude relation between the non-isotropy value delta of each azimuth angle at each altitude angle and the absolute value of the threshold function k.sigma, and realizing classification of different properties of tropospheric delay in the horizontal direction according to the magnitude relation;
in the step 4, the classification process of the different properties of the tropospheric delay in the horizontal direction is as follows:
when delta > |k.sigma|, the troposphere delay at the azimuth angle corresponding to delta meeting the condition is positive; when delta is minus k-sigma, the tropospheric delay at the azimuth angle corresponding to delta meeting the condition is reverse;
when the absolute value of the k and the absolute value of the sigma is less than or equal to the absolute value of the delta, the troposphere delay at the azimuth angle corresponding to the delta meeting the condition shows the same polarity.
2. The method of classifying a horizontal tropospheric delay in consideration of non-isotropy as claimed in claim 1,
in the step 1, tropospheric delay data is estimated by using meteorological parameters by a ray tracing method.
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