Beidou-based Antarctic ice dome elevation measurement method

Abstract

The invention provides a Beidou-based antarctic ice dome elevation measurement method, and solves the problem that the traditional method cannot obtain the high-precision altitude of the antarctic ice dome. The method comprises the following steps: firstly, erecting a Beidou base station at a South Pole ice dome test point, collecting original observation data of a Beidou satellite, and calculating accurate coordinates and geodetic height of the test point through a post-event precise point positioning technology; then, determining a gravity value of a test point by using ground gravity measurement equipment, reducing the gravity value of the test point to a geoid through various corrections such as instrument null drift, earth tide and atmospheric pressure, obtaining gravity anomaly of the test point in combination with a known normal gravity value of a reference ellipsoid surface, and converting the gravity anomaly into elevation anomaly through a formula; and finally, converting the geodetic height calculated by the test point into the altitude through the conversion relation between the geodetic height and the altitude, and checking and checking the initial altitude calculated by the global gravitational field model. The method can be widely applied to the fields of South Pole scientific research, resource development and the like.

Description

Technical Field

[0001] The present invention relates to a Beidou-based elevation measurement method for the Antarctic ice dome, which is used to determine the altitude of the Antarctic ice dome. Background Art

[0002] 98% of the entire Antarctic continent is covered by an ice sheet with an average thickness of 2,450 meters. Dome A is the ice dome farthest from the coastline in the Antarctic inland ice sheet and also the area with the highest altitude in the Antarctic inland ice sheet. The climatic conditions are extremely harsh, and it is known as the "Pole of Inaccessibility". In 2005, the 21st Chinese Antarctic Scientific Expedition team reached Dome A, the highest point of the Antarctic inland ice sheet measured by GPS, with an altitude of 4,093 meters. In 2020, China completed the Beidou-3 system and provided services to the world. It is of great significance to accurately measure the altitude of the Antarctic ice dome using the Beidou satellite navigation system.

[0003] Leveling is the main method for determining the altitude of ground points. However, due to the harsh Antarctic climate and the straight-line distance of 1,250 km between Kunlun Station and Zhongshan Station, the traditional leveling method of introducing the elevation of the tide gauge station at Zhongshan Station to Dome A of Kunlun Station by leveling is not applicable. The geoid model method is a common method for GNSS positioning equipment to obtain the altitude of ground points, that is, using geoid models such as EGM96 and EGM2008 to convert the geodetic height measured by GNSS into altitude. However, the accuracy of these models is limited, especially in the Antarctic region, where there are many blank areas. Therefore, the high-precision altitude of the Antarctic ice dome cannot be obtained by traditional methods. Summary of the Invention

[0004] In order to solve the problem of determining the altitude of the Antarctic ice dome, the present invention provides a Beidou-based elevation measurement method for the Antarctic ice dome.

[0005] The method mainly includes the following steps:

[0006] Step 1, select the visually highest point in the Antarctic ice dome, set up a Beidou reference station receiver, measure the instrument height, set the sampling rate to 1 Hz, and continuously collect and store data for more than 8 hours;

[0007] Step 2, export the collected data and parse it into the RINEX format, and perform post-processing PPP precise point positioning calculation to solve the accurate coordinates and geodetic height of the test point;

[0008] Step 3, calculate the elevation anomaly of the test point using the EGM2008 and EIGEN-6C4 global gravity field models respectively, and calculate the initial altitude of the test point through the conversion formula between geodetic height and altitude;

[0009] Step 4: Set up an absolute gravimeter at the to-be-determined point in Dome A, Antarctica, conduct absolute gravity measurement, and obtain the gravity value of the test point.

[0010] Step 5: After various corrections such as instrument zero drift, earth tides, and atmospheric pressure, reduce the gravity value of the test point to the geoid to obtain the gravity value of the geoid. Combine with the known normal gravity value on the reference ellipsoid surface to obtain the gravity anomaly between the geoid and the reference ellipsoid surface, and further calculate the distance between the geoid and the reference ellipsoid surface, that is, the height anomaly.

[0011] Step 6: Convert the geodetic height calculated at the test point to the altitude through the conversion relationship between the geodetic height and the altitude.

[0012] The method described in the present invention has the following advantages:

[0013] 1. By comprehensively adopting technologies such as Beidou high-precision positioning technology and gravity measurement technology, quickly obtain the altitude of Dome A, Antarctica.

[0014] 2. Adopt a globally unified reference surface, provide a more accurate global-scale altitude reference for Antarctic surveying and mapping geographical information, and have important value for more accurately predicting the impact of Antarctic glacier ablation on low-altitude areas.

[0015] The present invention will be further described below in conjunction with the accompanying drawings of the specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is the flow chart of the method for measuring the altitude of Dome A, Antarctica based on Beidou of the present invention;

[0017] Figure 2 is the flow chart of the precise point positioning data quality control of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0018] In order to enable those of ordinary skill in the art to better understand the technical aspects of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0019] A method for measuring the altitude of Dome A, Antarctica based on Beidou, as shown in the attached Figure 1 figure, includes the following steps:

[0020] Step 1: Select the visually highest point in Dome A, Antarctica, set up a Beidou reference station receiver, measure the instrument height, set the sampling rate to 1 Hz, and continuously collect and store data for more than 8 hours.

[0021] Step 2: Export the collected data and parse it into the RINEX format, and perform post-processing PPP precise point positioning solution to solve the precise coordinates and geodetic height of the test point, as Figure 2 shown. Specifically as follows:

[0022] (1) Due to the complex satellite observation environment in the Antarctic region, the satellite elevation angle is relatively low, and the data quality is poor. Before performing precise point positioning solution, it is necessary to perform quality control on the original observation data, that is, use the MW combination and GF combination to detect cycle slips, and mark the satellite numbers and times when cycle slips occur. Specifically as follows:

[0023] 1) Construct the MW combination observation value L based on the pseudorange and carrier phase observation data of Beidou B1 and B3 frequency bands MW :

[0024]

[0025] In the formula, the subscripts 1 and 3 represent the frequency bands B1 and B3 respectively, represents the carrier phase observation value in cycles, P represents the pseudorange observation value in meters, f represents the frequency, and λ represents the wavelength.

[0026] Construct the cycle slip detection test quantity ΔL by differencing between epochs MW :

[0027] ΔL MW = L MW (i) - L MW (i - 1) (2)

[0028] When the test quantity ΔL MW meets the condition of being less than the set threshold, it is considered that a cycle slip has occurred. Considering the influence of the observation value sampling rate and the satellite elevation angle comprehensively, the threshold R MW (E, R) can be set according to the following formula, with the unit of cycle.

[0029]

[0030] In the formula, R represents the sampling rate, and E represents the satellite elevation angle.

[0031] 2) Construct the geometric-free distance GF combination based on the pseudorange and carrier phase observation data of Beidou B1 and B3 frequency bands:

[0032]

[0033] Construct the cycle slip detection test quantity ΔL by differencing between epochs MW :

[0034] ΔL GF = L GF (i) - L GF (i - 1) (6)

[0035] When the test quantity ΔL MWWhen it satisfies being less than the following threshold, cycle slips occur. Considering the influence of the observation value sampling rate and the satellite elevation angle comprehensively, the threshold R GF can be set according to the following formula, with the unit being meters.

[0036]

[0037] Similarly, in the formula, R represents the sampling rate, and E represents the satellite elevation angle.

[0038] (2) Establish the undifferenced observation equation using the observed BDS pseudorange and carrier phase observations:

[0039]

[0040] Among them, P i 、 are the pseudorange and carrier phase observations at frequency i respectively; c is the speed of light, and ρ is the geometric distance from the GNSS satellite to the receiver; dt s , dt r are the satellite clock error and the receiver clock error respectively; d trop , d ion are the tropospheric delay and the ionospheric delay respectively; λ i is the wavelength of the carrier at frequency i; N i is the unknown integer ambiguity at frequency i; ε P 、 are the observation noises of the pseudorange and carrier phase observations respectively; d other is other errors such as solid tide, relativistic effect, satellite and receiver phase center deviation and its variation, phase wrapping, and earth rotation.

[0041] (3) For the undifferenced observation equation, use precise products to fix the satellite orbit and clock error. The above undifferenced observation equation no longer considers the satellite orbit and clock error. The tropospheric dry component, satellite and receiver phase center deviation and its variation, and various errors such as solid tide are corrected through models. The tropospheric wet delay component is estimated through additional parameters. The ionospheric delay effect is eliminated by combining the ionosphere-free combination. Then the observation equation can be simplified as:

[0042]

[0043] In the formula, d tropw is the tropospheric wet delay component, N w is the ionosphere-free combination ambiguity, are the combined measurement noises of the pseudorange and carrier respectively.

[0044] (4) Let the parameter vector to be estimated be (X, Y, Z, T, d tropw , dN w , N1…N k) T Then the matrix form of the linearized equation is:

[0045]

[0046] Where M is the projection function, and in this invention, the GMF model is adopted. λ is the wavelength of the carrier ionosphere-free combination, k represents the satellite number, ranging from 1 to satellite k. λ is the wavelength of the specific frequency ionosphere-free combination. The pseudo-range to phase weight ratio is 1:10000. For the troposphere, since the troposphere is a continuous and slowly changing process, the segmented model is better than the constant parameter model. However, it still does not match the actual situation. In view of this, considering the relationship between adjacent troposphere segments, a random walk process can be used to simulate the troposphere noise, and its mean value is 0.

[0047] (5) Calculate the precise space rectangular coordinates (X, Y, Z) of the test point through static Kalman filtering, and convert them to longitude and latitude (B, L) and geodetic height H 大地高 .

[0048] Step 3: Calculate the height anomaly of the test point using the EGM2008 and EIGEN-6C4 global gravity field models respectively, and calculate the normal height of the test point.

[0049] (1) Calculate the initial height anomaly ξ according to the EGM2008 and EIGEN-6C4 gravity field models:

[0050]

[0051] Where GM is the geocentric gravitational constant; a is the semi-major axis of the reference ellipsoid, and are the fully normalized disturbing potential coefficients of degree n and order m, is the fully normalized associated Legendre function of degree n and order m, r is the geocentric radius vector of the test point, γ is the normal gravity value of the calculation point, λ is the geocentric longitude, and θ is the geocentric latitude.

[0052] (2) Convert the geodetic height to the normal height H 正常高 :

[0053] H 正常高 = H 大地高 - ξ (13)

[0054] Step 4: Set up an absolute gravimeter at the fixed point on the Antarctic ice dome, conduct absolute gravity measurement, and measure the gravity value g of the test point by taking the average of multiple measurements;

[0055] Step 5: Convert the normal height to the orthometric height (altitude):

[0056]

[0057] Among them, γ is the normal gravity value of the calculation point.

[0058] The present invention has the following characteristics:

[0059] (1) Set up a Beidou reference station at the Dome A test point in Antarctica, and use the post-precision point positioning technology to calculate the accurate coordinates and geodetic height of the test point;

[0060] (2) Set up an absolute gravimeter at the Dome A test point in Antarctica to measure the gravity value of the test point, and then obtain the gravity anomaly and height anomaly of the test point;

[0061] (3) Comprehensively use ground gravity measurement and global gravity field model to calculate the height anomaly of the test point;

[0062] (4) Use the EGM2008 and EIGEN-6C4 global gravity field models to calculate the initial height anomaly of the test point, as a check for the gravity anomaly obtained from ground gravity measurement, making the measured elevation of Dome A in Antarctica more accurate and reliable.

Claims

1. A Beidou-based method for measuring the elevation of the Antarctic ice dome, characterized in that: The following steps are involved: (1) A BeiDou base station was set up at the Antarctic ice dome test site, and the precise coordinates and geodetic height of the test site were calculated using post-precision point positioning technology; (2) Set up an absolute gravimeter at the Antarctic ice dome test site to perform absolute gravity measurements and obtain the gravity value at the test site; The gravity value of the test point is converted to the geoid to obtain the gravity value of the geoid; Combined with the known normal gravity value of the reference ellipsoid, the gravity anomaly between the geoid and the reference ellipsoid is obtained, and the distance between the geoid and the reference ellipsoid is further calculated, that is, the elevation anomaly of the test point. (3) The geoid height obtained in step (1) and the elevation anomaly calculated in step (2) are integrated to convert the geoid height calculated at the test point into the altitude through the conversion relationship between the geoid height and the altitude.

2. The method for measuring the elevation of Dome A in Antarctica based on Beidou according to claim 1, wherein: In step (2), after various corrections such as instrument zero drift, earth solid tide, atmospheric pressure, etc., the gravity value of the test point is converted to the geoid to obtain the gravity value of the geoid.

3. A Beidou-based elevation measurement method for Dome A in Antarctica according to claim 1, characterized in that: The elevation anomaly of the test point is calculated using the EGM2008 and EIGEN-6C4 global gravity field models, and the initial altitude of the test point is calculated using the conversion formula between geodetic height and altitude. The initial altitude of the test point is used as an anomaly check for the altitude obtained by ground gravity measurement in step (3).

4. A Beidou-based elevation measurement method for Dome A in Antarctica according to claim 1, characterized in that: The post-precision point positioning technology described in step (1) includes: 1) using the observation value MW and LG combination method to preliminarily process the original observation value, eliminate the gross error data, and if there is a cycle slip, segment the data and add an ambiguity parameter; 2) based on the residual of the post-observation value of the root mean square filter, perform hypothesis testing to determine the gross error and cycle slip; 3) when processing the data, comprehensively consider the influence of factors such as satellite cut-off altitude angle, tropospheric mapping function, and tidal load on the positioning result.

5. A Beidou-based elevation measurement method for Dome A in Antarctica according to claim 1, characterized in that: In step (1), the sampling rate of the BeiDou base station receiver is set to 1 Hz, and data is continuously collected and stored for more than 8 hours.

6. The method for measuring the elevation of Dome A in Antarctica based on Beidou according to claim 5, wherein: The collected data are exported and parsed into RINEX format, and PPP precise point positioning solution is performed afterwards to solve the precise coordinates and geodetic height of the test point.

Images