A method for constructing tropospheric delay mapping function based on mapping error modeling

Abstract

The present invention discloses a method for constructing a tropospheric delay mapping function based on mapping error modeling, which is suitable for radio measurement, especially for tropospheric delay correction in interferometric measurement. The method is as follows: first, the measured data of the tropospheric delay of the observation station before observation is processed, the observation elevation angle and the tropospheric line-of-sight delay are extracted, and the measured value of the tropospheric zenith delay is obtained through the constraint that the elevation angle is equal to 90°; secondly, the measured value of the mapping function is obtained through the measured value of the tropospheric zenith and the measured value of the line-of-sight; thirdly, the NMF model value of the mapping function is obtained through the station location information, the annual accumulation of observation time and the observation elevation; finally, the deviation between the mapping function model value and the measured value is modeled to obtain a mapping function error model, which can be superimposed with the classical model of the mapping function to obtain a comprehensive mapping function of the tropospheric delay. The present invention realizes high-precision tropospheric delay correction under low elevation conditions.

Description

Technical field:

[0001] The invention relates to a method for constructing a tropospheric delay mapping function based on mapping error modeling, and belongs to the field of space radio measurement. Technical background:

[0002] Tropospheric delay error is one of the important error sources in the field of space radio measurement. In measurement scenarios with high real-time requirements, the accuracy of the tropospheric delay model will directly affect the accuracy of the observations of radio measurements. For example, in very long baseline interferometry (VLBI), the deviation of the tropospheric delay model will introduce systematic errors in the final observations, thereby affecting the navigation and orbit determination performance of the detector. Tropospheric delay is generally modeled by the product of the zenith delay model and the mapping function. The function of the tropospheric delay mapping function is to map the zenith delay to the line-of-sight delay, based on which the radio observations are corrected for the medium. At present, the tropospheric delay model has a good correction effect at high elevation angles, but shows obvious errors at low elevation angles. This shows that the zenith delay model has a high accuracy, while the mapping function performance needs to be further improved under low elevation conditions. Summary of the invention:

[0003] The purpose of the present invention is to provide a method for constructing a tropospheric delay mapping function based on mapping error modeling based on the variation law of tropospheric delay and the mapping function model, so as to achieve high-precision tropospheric delay correction under low elevation angle conditions.

[0004] The present invention designs a method for estimating the measured zenith delay and extracting the measured mapping function based on the measured tropospheric delay data of the measuring station, and further obtains the mapping error relative to the classical tropospheric delay mapping function, models the mapping error, and obtains a comprehensive tropospheric delay function, which effectively reduces the deviation of the tropospheric delay model under low elevation angle conditions. The method of the present invention can be widely used in the medium link of radio measurement observation quantity, and can effectively improve the influence of medium error.

[0005] The present invention provides a method for constructing a tropospheric delay mapping function based on mapping error modeling. First, the measured data of tropospheric delay at a measuring station before observation are processed to extract the observation elevation angle and the tropospheric line-of-sight delay, and the measured value of the tropospheric zenith delay is obtained by constraining the elevation angle to be equal to 90°; secondly, the measured value of the mapping function is obtained through the measured value of the tropospheric zenith and the measured value of the line-of-sight; thirdly, the NMF model value of the mapping function is obtained through the measuring station location information, the annual accumulation of observation time and the observation elevation; finally, the deviation between the mapping function model value and the measured value is modeled to obtain a mapping function error model, which can be superimposed with the classical model of the mapping function to obtain a comprehensive mapping function of the tropospheric delay.

[0006] Furthermore, in the step (1), the measured data of tropospheric delay include observation time, observation elevation angle and tropospheric line-of-sight delay. With the elevation angle equal to 90° as a constraint, the tropospheric delay value is extracted, that is, the tropospheric zenith delay value. The measured values ​​obtained by screening are averaged to obtain the measured value of zenith delay.

[0007] Furthermore, in step (1), the measured value of the mapping function is obtained using formula (2),

[0008]

[0009] τ Trop Tropospheric line-of-sight delay, τ TropZTD is the tropospheric zenith delay, MF(el) is the mapping function, and el is the observation elevation angle.

[0010] Furthermore, in step (3), according to the observation elevation angle and observation time information obtained in step (1), the tropospheric delay mapping function model value is calculated according to formula (3);

[0011]

[0012] where a, b, c, a ht , b ht and c ht Mapping function parameters.

[0013] Furthermore, in step (4), the measured value and the model value of the mapping function obtained in steps (2) and (3) are subtracted to obtain a mapping deviation, and the mapping deviation is modeled by a trigonometric function of the observed elevation angle;

[0014]

[0015] where a 1 and a 2 is the model coefficient; the least squares processing of equation (4) is performed using the deviation value of the tropospheric delay mapping function to obtain the estimated value of the model coefficient.

[0016] Furthermore, in step (5), based on equation (4) and the classical tropospheric delay mapping function, the tropospheric delay zenith delay comprehensive mapping function can be obtained:

[0017] MF(el)=MF mdl (el)+ΔMF(el) (5).

[0018] Furthermore, in the step (4), a simple model based on trigonometric functions is used in the mapping error modeling process, but other more complex error models are also applicable, the only difference being the different mathematical processing in the modeling process.

[0019] Advantages of the present invention:

[0020] The present invention proposes a mapping function extraction method based on the measured tropospheric delay data of the measuring station, a modeling method of the tropospheric delay mapping error based on the observed elevation angle trigonometric function, and a method for constructing a comprehensive tropospheric delay mapping function based on the mapping error modeling, so as to achieve high-precision tropospheric delay correction under low elevation angle conditions and effectively reduce the tropospheric delay model deviation under low elevation angle conditions. The method of the present invention can be widely used in the medium delay correction link of radio measurement observation quantity, and can effectively improve the influence of medium error. Description of the drawings:

[0021] Figure 1 A process for constructing a comprehensive mapping function of tropospheric delay based on mapping error modeling;

[0022] Figure 2 Measured data of tropospheric delay and measured zenith delay;

[0023] Figure 3 Measured values ​​of tropospheric delay mapping function;

[0024] Figure 4 Tropospheric delay mapping function model value;

[0025] Figure 5 Tropospheric delay mapping function bias;

[0026] Figure 6 Tropospheric delay integrated mapping function bias;

[0027] Figure 7 Comparison of measured and modeled tropospheric delay on January 7, 2019. Specific implementation method:

[0028] In order to better illustrate the purpose and features of the present invention, the following is a detailed description with reference to the accompanying drawings and implementation examples. The construction process of the tropospheric delay comprehensive mapping function proposed in the present invention is as follows: Figure 1 shown.

[0029] The data used in the present invention are the measured data of tropospheric delay of a deep space station in my country on January 6 and 7, 2019. For other observation data, the modeling method is the same. Based on the data, detailed invention steps are given as follows.

[0030] (1) Obtaining the measured value of tropospheric delay zenith delay

[0031] Read the measured tropospheric delay data of a deep space station on January 6, 2019. The measured data includes observation time, observation elevation angle, and tropospheric line-of-sight delay. With the elevation angle equal to 90° as a constraint, extract the tropospheric delay value, which is the tropospheric zenith delay value. Figure 2 As shown in the figure. The measured values ​​obtained by screening are averaged to obtain the measured value of zenith delay. For this example, the measured value of zenith delay is about 2.2698m.

[0032] (2) Obtaining the measured value of the tropospheric delay zenith delay mapping function

[0033] The tropospheric line-of-sight delay is generally modeled as the product of the tropospheric zenith delay and a mapping function. The mapping function is a function of the observation elevation angle, as shown in equation (1), where τ Trop Tropospheric line-of-sight delay, τ TropZTD is the tropospheric zenith delay, MF(el) is the mapping function, and el is the observation elevation angle.

[0034] τ Trop =τ TropZTD ×MF(el) (1)

[0035] In step (1), the tropospheric line-of-sight delay and zenith delay values ​​have been obtained, from which the measured value of the mapping function can be obtained, as shown in formula (2):

[0036]

[0037] According to formula (2), the measured value of the mapping function can be obtained, as follows: Figure 3 shown.

[0038] (3) Obtaining the model value of the classic mapping function of tropospheric delay and zenith delay

[0039] According to the observation elevation angle and observation time information obtained in step (1), the classical tropospheric mapping function NMF is selected, as shown in formula (3), where a, b, c, a ht , b ht and c ht For the mapping function parameters, the relevant literature gives the calculation method.

[0040]

[0041] In the above formula, the values ​​of coefficients a, b, and c are different for different measuring station locations. The coefficient values ​​at typical latitudes are interpolated as shown in Table 1 to obtain the coefficient values ​​at the measuring station latitude. The interpolation method can be found in relevant literature. ht ,b ht ,c ht Gain experience points.

[0042] Table 1 NMF coefficients at typical latitudes

[0043]

[0044] Based on formula (3) and observation elevation angle and other information, the tropospheric delay mapping function model value can be further obtained, as shown in formula Figure 4 shown.

[0045] (4) Modeling of tropospheric delay zenith delay mapping bias

[0046] The measured value and model value of the mapping function obtained in steps (2) and (3) are subtracted to obtain the mapping deviation, as Figure 5 As shown in . It can be seen that the mapping deviation increases significantly with the decrease of the observation elevation angle, which explains the phenomenon that the correction accuracy of the tropospheric delay model is higher at high elevation angles and the correction deviation is larger at low elevation angles. At the same time, it can be seen that the mapping deviation can be modeled by the trigonometric function of the observation elevation angle, as shown in formula (4), where a 1 and a 2 is the model coefficient

[0047]

[0048] use Figure 5 The model parameter estimation value can be obtained by performing the least squares processing on equation (4) using the deviation value of the delay mapping function in the troposphere. 1 =-0.0882; a 2 =0.1252.

[0049] (5) Construction of comprehensive mapping function of tropospheric delay

[0050] Based on formula (4) and the classical tropospheric delay mapping function, the tropospheric delay zenith delay comprehensive mapping function can be obtained, as shown in formula (5).

[0051] MF(el)=MF mdl (el)+ΔMF(el) (5)

[0052] Figure 6 The deviation between the comprehensive mapping function of tropospheric delay and the measured value is given. It can be seen that Figure 5 ,The mapping function deviation is significantly reduced in the low elevation angle region, and still remains near 0 in the high elevation angle region.

[0053] Verification of the comprehensive mapping function of tropospheric delay and zenith delay:

[0054] The data of January 7, 2019 are used for verification. The observed data are read to obtain the measured value of the tropospheric line-of-sight delay and the observation elevation angle. The tropospheric zenith delay value obtained in step (1), the tropospheric delay zenith delay comprehensive mapping function obtained in step (5), and the observation elevation angle on January 7, 2019 can be used to obtain the tropospheric delay model value, as shown in the following figure: Figure 7As shown. It can be seen that after the mapping function is corrected, the tropospheric delay model value is more consistent with the measured value, especially under low elevation conditions, the tropospheric delay deviation is significantly reduced relative to the classic mapping function model. For the detector observation arc, 20190107 is approximately 11:30-20:10, and the model value proposed by the present invention is closer to the measured value and has a smaller deviation. In this observation arc, the mean square value of the tropospheric delay deviation corresponding to the classic mapping function is approximately 0.797m, while the mean square value of the deviation of the mapping function proposed by the present invention is approximately 0.418m, which is a relative improvement of about 47.58%; at an elevation angle of 10°, the tropospheric delay model deviation is reduced from approximately -0.945m of the initial model to approximately 0.03m, which illustrates the effectiveness of the mapping function proposed by the present invention.

Claims

1. A method for constructing a tropospheric delay mapping function based on mapping error modeling, characterized in that: (1) The measured data of tropospheric delay at the observation station are processed before observation to extract the observation elevation angle and tropospheric line-of-sight delay, and the measured value of tropospheric zenith delay is obtained by constraining the elevation angle to 90°; (2) Obtaining the measured value of the tropospheric delay zenith delay mapping function through the measured value of the tropospheric delay zenith delay and the measured value of the line of sight; In the step (2), the measured value of the mapping function is obtained using formula (2): τ Trop Tropospheric line-of-sight delay, τ TropZTD is the tropospheric zenith delay, MF(el) is the mapping function, and el is the observation elevation angle; (3) Obtain the NMF model value of the mapping function through the station location information, the annual accumulation of observation time and the observation elevation angle; (4) Model the deviation between the mapping function model value and the measured value to obtain the mapping function error model, which is then superimposed with the classical model of the mapping function to obtain the comprehensive mapping function of tropospheric delay; In the step (4), the measured value and the model value of the mapping function obtained in steps (2) and (3) are subtracted to obtain a mapping deviation, and the mapping deviation is modeled by a trigonometric function of the observed elevation angle; Where a1 and a2 are model coefficients. The estimated values ​​of the model coefficients can be obtained by performing least squares processing on equation (4) using the deviation value of the tropospheric delay mapping function. Based on equation (4) and the classical tropospheric delay mapping function, the tropospheric delay zenith delay comprehensive mapping function can be obtained: MF(el)=MF mdl (el)+ΔMF(el)(5).

2. The tropospheric delay mapping function based on mapping error modeling according to claim 1, characterized in that: In the step (1), the measured data of tropospheric delay include observation time, observation elevation angle and tropospheric line-of-sight delay. With the elevation angle equal to 90° as a constraint, the tropospheric delay value is extracted, that is, the tropospheric zenith delay value. The zenith delay measured value can be obtained by averaging the screened measured values.

3. The tropospheric delay mapping function based on mapping error modeling according to claim 1, characterized in that: In the step (3), according to the observation elevation angle and observation time information obtained in the step (1), the tropospheric delay mapping function model value is calculated according to formula (3); where a, b, c, a ht , b ht and c ht Mapping function parameters.

4. The tropospheric delay mapping function based on mapping error modeling according to claim 1, characterized in that: In the step (4), other complex error models may be used in the process of mapping error modeling.

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