CN106908815A - A kind of Northern Hemisphere tropospheric delay correction method based on sounding data - Google Patents

Abstract

The invention discloses a method for correcting the tropospheric delay in the northern hemisphere based on sounding data, comprising the following steps: S1: calculating the tropospheric delay of the sounding data at the station, denoted as ZTD ⁰ ; S2: utilizing the Hopfield model to calculate the tropospheric delay, denoted as ZTD (H); S3: On the basis of the Hopfield model formula, add the station latitude and annual cumulative day information, and establish a nonlinear equation; S4: take the tropospheric delay ZTD ⁰ calculated in step S1 as the true value, and use the least square method to determine the non-linear equation. The various coefficients of the linear equation are used to determine the final improved model equation and verify its accuracy. Compared with the traditional Hopfield model and Saastamoinen model, the invention effectively improves the calculation accuracy.

Description

A Northern Hemisphere Tropospheric Delay Correction Method Based on Sounding Data

technical field

The invention relates to the field of global navigation systems, in particular to a method for correcting the troposphere delay in the northern hemisphere based on sounding data.

Background technique

Tropospheric delay is the main reason that affects the positioning accuracy of satellite navigation, especially the accuracy in the elevation direction. At present, the main method of tropospheric delay correction is the model correction method. The model correction method establishes a functional relationship that can reflect the tropospheric delay based on different assumptions and influencing factors. The tropospheric delay correction model is an empirical formula obtained by analyzing meteorological data, and there are differences due to different analytical methods. According to whether meteorological parameters are required for model calculation, it can be divided into models requiring meteorological parameters and models without meteorological parameters. Zenith tropospheric delay models that require meteorological parameters mainly include Hopfield model, Saastamoinen model, etc. However, both the traditional Hopfield model and the Saastamoinen model do not consider the influence of the factors of the annual cycle change. The Saastamoinen model only considers the influence of the latitude factor, and the Hopfield model neither considers the latitude factor nor the factor of the annual cycle change. Accurate and reliable tropospheric delay model or by improving the existing tropospheric delay correction model to achieve the effect of local refinement, in order to improve the accuracy of regional tropospheric delay correction, which has very important practical significance for improving the accuracy and reliability of GNSS navigation and positioning .

Commonly used tropospheric delay empirical models with meteorological parameters are global tropospheric delay models established through the analysis of global atmospheric average meteorological data and global climate. In a local area or using regional meteorological data, the model accuracy of this type of model is poor, and the factors of latitude and annual cycle change are not considered, especially in areas with vast areas and complex environments. The correction effect is relatively limited.

Contents of the invention

Purpose of the invention: The purpose of the present invention is to provide a method for correcting the delay of the troposphere in the northern hemisphere based on sounding data that can solve the defects in the prior art.

Technical scheme: in order to achieve this goal, the present invention adopts following technical scheme:

The northern hemisphere tropospheric delay correction method based on sounding data of the present invention comprises the following steps:

S1: Calculate the tropospheric delay of the sounding data of the station, denoted as ZTD ⁰ ;

S2: Use the Hopfield model to calculate the tropospheric delay, denoted as ZTD(H);

S3: On the basis of the Hopfield model formula, increase the station latitude and annual cumulative day information, and establish a nonlinear equation;

S4: Taking the tropospheric delay ZTD ⁰ calculated in step S1 as the true value, use the least square method to determine the coefficients of the nonlinear equation, determine the final improved model equation and verify its accuracy.

Further, in the step S2, the tropospheric delay ZTD (H) calculated by the Hopfield model is shown in formula (1):

In formula (1), k ₁ , k ₂ , k ₃ are a group of meteorological constants related to the year, P ₀ is the air pressure of the station, T ₀ is the absolute temperature of the station, e ₀ is the water vapor partial pressure of the station, H _W is the height of the wet tropopause, and _HT is the height of the tropopause.

Further, the nonlinear equation established in the step S3 is as shown in formula (2):

ZTD＝ZTD(H)+f ₁ (doy)+g(φ) (2)

In formula (2), ZTD is the calculated value of tropospheric delay, ZTD(H) is the tropospheric delay calculated by the Hopfield model, f ₁ (doy) is the annual cumulative day function, and g(φ) is the latitude function.

Beneficial effects: the present invention proposes a method for correcting the troposphere delay in the northern hemisphere based on sounding data, which effectively improves the calculation accuracy compared with the traditional Hopfield model and Saastamoinen model.

Description of drawings

Fig. 1 is the information diagram provided by the sounding data of the specific embodiment of the present invention;

Fig. 2 is the tropospheric delay distribution of 7 DORIS stations of the embodiment of the present invention in 6 years;

Fig. 2 (a) is the tropospheric delay distribution of ARMa site 6 years of the embodiment of the present invention;

Fig. 2 (b) is the tropospheric delay distribution of the EVEb site 6 years of the embodiment of the present invention;

Fig. 2 (c) is the tropospheric delay distribution of GAVb site 6 years of the embodiment of the present invention;

Fig. 2 (d) is the tropospheric delay distribution of SAKb site 6 years of the embodiment of the present invention;

Fig. 2 (e) is the tropospheric delay distribution of BADb site 6 years of the embodiment of the present invention;

Fig. 2 (f) is the tropospheric delay distribution of the FAIb site 6 years of the embodiment of the present invention;

Fig. 2(g) is the 6-year tropospheric delay distribution of the SPJb site according to the embodiment of the present invention.

detailed description

The technical solution of the present invention will be further introduced below in conjunction with the accompanying drawings and specific embodiments.

This specific embodiment discloses a method for correcting the tropospheric delay in the northern hemisphere based on sounding data, including the following steps:

S1: Calculate the tropospheric delay of the sounding data of the station, denoted as ZTD ⁰ , as follows:

This specific embodiment adopts the sounding data of 277 stations in the northern hemisphere in 2010. The latitude spans from 6.96°-82.5°, and the distribution area ranges from the tropics to the arctic circle. Taking station 78897 as an example, the sounding data provide different isobaric surface layer atmospheric characteristic layers and wind layer data, as shown in Figure 1. Atmospheric characteristic layer parameters include geopotential height (HGHT), air temperature (TEMP), dew point temperature (DWPT), and relative humidity (RELH), which are detected elements.

The tropospheric delay in the direction of the zenith can be expressed as the integral of the refractive index over the propagation path.

δ＝10 ^-6 ∫N(s)dS (1)

The refractive index N can be calculated according to the Smith-Weintarub equation and the values of air temperature (T), pressure (P) and water vapor pressure (e) provided by sounding data, using the following formula:

Considering the influence of the humidity component, when establishing the atmospheric refractivity model, a segmented function model is established with the height of 11km as the boundary. This specific embodiment adopts the following formula to carry out negative exponential function fitting, thus can obtain the atmospheric refractive index function model of segment:

The total delay function model for the troposphere is thus:

Among them, N(h ₀ ) in formula (4) is the ground refractive index, N(11000) is the refractive index at 11 km, h _T is the tropopause height, c ₁ and c ₂ are the refractive index attenuation coefficients, h ₀ is the station the elevation.

Fitting the refractive index of each layer below 11km calculated earlier, and using the least square method to solve the attenuation coefficient in formula (3). The initial refractive index and attenuation coefficient at 11km satisfying the least squares are calculated by fitting the refractive index of each layer above 11km. Use formula (4) to find the total delay of this station. The delay value δ is the tropospheric delay value calculated by using the sounding data of the station, that is, ZTD ⁰ .

S2: Use Hopfield to calculate the tropospheric delay, denoted as ZTD(H):

Among them, k ₁ , k ₂ , and k ₃ are a group of meteorological constants related to the year. In the formula, h ₀ , P ₀ , T ₀ , and e ₀ are the elevation, air pressure, absolute temperature, and water vapor partial pressure of the station respectively, and H _W is For the wet tropopause, Hopfield takes H _W as 11000m; _HT represents the height of the tropopause, that is, the atmospheric height where the refractive index is equal to 0. Some calculation results are shown in Table 1:

Table 1 Calculation results of sounding data and tropospheric delay deviation calculated by Hopfield

S3: On the basis of the Hopfield model formula, add the station latitude and annual cumulative day information, and establish a nonlinear equation, as shown in formula (6):

ZTD＝ZTD(H)+f ₁ (doy)+g(φ) (6)

In formula (6), ZTD is the calculated value of tropospheric delay, ZTD(H) is the tropospheric delay calculated by the Hopfield model, f ₁ (doy) is the annual cumulative day function, and g(φ) is the latitude function;

g(φ) is the cosine function of latitude, according to Taylor's formula, there is the following formula:

Among them, g′(φ), g″(φ), g ⁽ⁿ⁾ (φ) are the first-order, second-order and n-order derivatives of g(φ) respectively, and C is the Taylor remainder.

For the simplicity of the formula and the convenience of calculation, here n is taken as 3, and C is taken as a constant, let g′(φ), are a ₁ , a ₂ , and a ₃ respectively, then:

g(φ)＝a ₁ φ+a ₂ φ ² +a ₃ φ ³ +C (8)

Figure 2(a)—The seven DORS stations in Figure 2(g) cover the tropics to the boreal zone. It can be seen from Fig. 2 that the change of the annual period of the tropospheric delay is approximately a trigonometric function. We express the function of the annual period as a cosine function, that is, f ₁ (doy) is a cosine function, so the tropospheric delay model is improved as:

where doy is the cumulative day of the year. Since the initial phase of the cosine function cannot be determined, and it is difficult to obtain a5 in formula (9) during fitting, this paper changes formula (9) to The following formula to ensure the accuracy of the formula:

For the convenience of expressing the calculated coefficient, the latitude φ is replaced by In the end we get:

S4: Take the tropospheric delay ZTD ⁰ calculated in step S1 as the true value; use the least square method to determine the coefficients of the nonlinear equation, determine the final improved model equation and verify its accuracy.

Therefore, firstly, the zenith tropospheric delay of the northern hemisphere radiosonde station is fitted according to formula (11), and the unknown parameters are solved using the least square method. The least squares method was used to solve the above six parameters, and part of the approximate true value of the troposphere calculated using sounding data was used as a fitting sample, and the rest was used to test the effect of the model. In this patent, the data of 20 stations per month are used to fit the coefficients, and the data of the remaining 635 stations are used for verification.

The average deviation BIAS and medium error RMSE are used as the basic standards for model comparison analysis and verification, and their calculation formulas are:

in: is the tropospheric delay calculated by equation (11), is the approximate true value of the troposphere calculated from sounding data, and N is the number of observation stations.

The coefficients of formula (11) are fitted, and finally the improved tropospheric delay model formula is obtained as:

Name the above model as HL model. In order to analyze the accuracy of the new HL model, calculate the accuracy of each month and the accuracy comparison between the corresponding Hopfield model and Saastamoine. Some results are shown in Table 2.

Table 2 Accuracy comparison of the three models

It can be seen from Table 2 that:

(1) The accuracy of Hopfield model and Saastamoinen model is almost the same. The average median errors of the two models are ±31.85mm and ±34.37mm respectively, and the difference between the median errors between the two models is within 4mm in each month. In terms of deviation, the total deviation of Hopfield model and Saastamoinen model at each site in the northern hemisphere is negative. It can be seen that the average degree of deviation between the Hopfield model and the approximate true value of the troposphere of the sounding data is smaller than that of the Saastamoinen model. The absolute value of the deviation of the Saastamoinen model in each day is about 5-7mm larger than that of the Hopfield model.

(2) Hopfield model, Saastamoinen model and HL model have obvious seasonality. The three were the smallest in March, respectively 20.11mm, 23.73mm, and 17.95mm, and reached the maximum in July, respectively, 43.54mm, 45.77mm, and 32.16mm. The three models all showed the following pattern: after the best accuracy appeared in March, the accuracy gradually deteriorated until the worst accuracy appeared in July-September, and then the accuracy improved again. The main reason for this phenomenon is that the tropospheric delay has obvious and stable annual cycle characteristics.

(3) The accuracy of the HL model is greatly improved compared with the Hopfield model and the Saastamoinen model. In order to compare the level of accuracy improvement more clearly, Table 4-8 shows the degree of accuracy improvement of the HL model relative to the Hopfield model and the Saastamoinen model. It can be seen that the accuracy of the HL model is higher than that of the traditional Hopfield model and Saastamoinen model. Except for March, the accuracy of the new model is more than 15% higher than that of the Hopfield model. On November 1st, the percentage of improvement is the largest, which is 27.5%. On July 1st, the amount of improvement is the largest, with an increase of 11.38mm, HL The overall accuracy of the model is 19.7% higher than that of the Hopfield model. The HL model is basically more than 20% higher than the Saastamoinen model, especially on May 1st, reaching 30.1%. Like the Hopfield model, the increase is the largest on July 1st, with an increase of 13.61mm. HL model An average improvement of 25.6% over the Saastamoinen model.

Table 3 Accuracy improvement of the HL model relative to the two models

From the above conclusions, it can be seen that the overall accuracy of the HL model is at the centimeter level, and both the total deviation and the medium error are better than the traditional Hopfield model and Saastamoinen model. At the same time, the model can better express the tropospheric delay. Non-linear change process. Therefore, for the northern hemisphere region, the delay value thereof can be calculated using the method proposed by the present invention.

Claims (3)

1. a method for correcting the delay of the northern hemisphere troposphere based on sounding data, is characterized in that: comprise the following steps: S1: Calculate the tropospheric delay of the sounding data of the station, denoted as ZTD ⁰ ; S2: Use the Hopfield model to calculate the tropospheric delay, denoted as ZTD(H); S3: On the basis of the Hopfield model formula, increase the station latitude and annual cumulative day information, and establish a nonlinear equation; S4: Taking the tropospheric delay ZTD ⁰ calculated in step S1 as the true value, use the least square method to determine the coefficients of the nonlinear equation, determine the final improved model equation and verify its accuracy. 2. the northern hemisphere tropospheric delay correction method based on sounding data according to claim 1, is characterized in that: in described step S2, the tropospheric delay ZTD (H) that Hopfield model calculates is as shown in formula (1): $\mathrm{<span\; class="notranslate">\; Z</span>}\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 273</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}}{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ In formula (1), k ₁ , k ₂ , k ₃ are a group of meteorological constants related to the year, P ₀ is the air pressure of the station, T ₀ is the absolute temperature of the station, e ₀ is the water vapor partial pressure of the station, H _W is the height of the wet tropopause, and _HT is the height of the tropopause. 3. the northern hemisphere tropospheric delay correction method based on sounding data according to claim 1, is characterized in that: the nonlinear equation set up in the described step S3 is as shown in formula (2): ZTD＝ZTD(H)+f ₁ (doy)+g(φ) (2) In formula (2), ZTD is the calculated value of tropospheric delay, ZTD(H) is the tropospheric delay calculated by the Hopfield model, f ₁ (doy) is the annual cumulative day function, and g(φ) is the latitude function.