Positioning system

Abstract

An object of the present invention is to solve the conventional problem, that is, to provide a positioning system capable of obtaining coordinates of an observation point by appropriately correcting a tropospheric delay error even in a case where an altitude difference between a reference point and a meteorological office is relatively large.SOLUTION: A positioning system of the present invention is a system for obtaining coordinates of an observation point based on a reference point for satellite positioning while correcting an error associated with a tropospheric delay in satellite positioning, and includes meteorological data acquisition means, modified meteorological data calculation means, and tropospheric delay amount calculation means. The meteorological data acquisition means is means for acquiring meteorological data in the vicinity of the reference point, the corrected meteorological data calculation means is means for obtaining corrected meteorological data by correcting the meteorological data on the basis of an altitude difference between the reference point and the meteorological office, and the tropospheric delay calculation means is means for obtaining a tropospheric delay on the basis of the corrected meteorological data.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to technology relating to satellite positioning, and more specifically to a positioning system that determines the coordinates of an observation point after correcting for tropospheric delay errors in radio waves from a positioning satellite. [Background technology]

[0002] Construction infrastructure (hereafter referred to as "construction infrastructure"), which was intensively developed during the period of rapid economic growth, has already been significantly aging. In 2014, the Council for Social Capital Development compiled a "Recommendation for Full-Scale Implementation of Measures to Counteract Road Deterioration." Citing the example of the Sasago Tunnel disaster in 2012, the report sounded a warning that "in the near future, bridge collapses and other fatal incidents affecting human lives and social infrastructure will likely occur," and emphasized the importance of maintaining and managing construction infrastructure. Against this backdrop, the national government issued a ministerial ordinance amending the Road Act Enforcement Regulations, formulating periodic inspection guidelines that outline specific construction infrastructure inspection methods, key areas to look for in abnormalities, and photographs of case studies. For example, with regard to bridges, the government requires that bridges with a length of 2.0 meters or more, estimated to number approximately 700,000, undergo their first inspection within two years of their opening, followed by periodic inspections every five years.

[0003] Typical examples of construction infrastructure include road structures such as tunnels and bridges, as well as road slopes (including natural slopes and artificial slopes). The total length of roads in use in Japan exceeds 1.2 million km, including approximately 9,000 km of national expressways, and it is said that approximately 30% of these roads are located in mountainous areas, which means that a huge number of road slopes need to be maintained and managed.

[0004] Following the Hida River bus accident on National Highway 41 in 1968, advance traffic restrictions and road disaster prevention inspections were institutionalized, but road slope inspections have tended to be carried out only when large-scale slope disasters occur, such as the landslide accident on National Highway 56 in 1970 and the rockslide accident on National Highway 305 in 1989. However, in 1996, an 11,000m slope failure occurred near the entrance of the Toyohama Tunnel on National Highway 229. 3 Due to the rock collapse, emergency road disaster prevention inspections were carried out nationwide that year.

[0005] In recent years, road slope inspections have been carried out regularly (once every five years as a rule), and inspection results are recorded for each slope, and are carried out under a systematic system. For example, a stability survey sheet was introduced after the Naruto Rockfall Accident on National Highway 11 in 1990, and since 1996, when a comprehensive road disaster prevention inspection was carried out, a system has been introduced in which an overall evaluation consisting of "measures required," "medical record response," and "no measures required" is recorded on the stability survey sheet.

[0006] By inspecting road slopes in this way, it is possible to grasp the condition of each slope and consider subsequent countermeasures. However, as mentioned above, there are a large number of road slopes that require maintenance, so it is not realistic to conduct full-scale inspections frequently. Furthermore, current road slope inspections are based on an evaluation based on the inspector's visual findings, which means that the results are qualitative and vary depending on the inspector's experience and knowledge, which can be a problem.

[0007] In addition to inspecting road slopes, observations to monitor the movement of slopes at risk of collapse or showing signs of landslides (so-called dynamic observations) are sometimes carried out. For example, on slopes showing signs of landslides, observations using extensometers and punching plates, observations using borehole inclinometers, and measurements of ground surface displacement have been carried out. However, observations using extensometers and punching plates are only effective if they are installed along the landslide boundary (especially the head), and borehole extensometers are only effective if the landslide depth is accurately estimated, and there are also problems with installing them in multiple locations, as they are costly. In the first place, these observation methods can only be carried out on slopes where the landslide surface can be estimated to some extent, and cannot be used on slopes where the landslide surface cannot be estimated or on slopes at risk of collapse.

[0008] In contrast, ground surface displacement measurement involves determining the coordinates of numerous observation points installed on a slope and monitoring slope movement by detecting displacement over time, which makes it possible to directly identify abnormalities and has the advantage that its effectiveness does not depend on the location of the instrument, as does the case with extensometers and borehole inclinometers.However, if observation points are to be positioned manually using a total station or similar, it requires a great deal of effort and cost.

[0009] Therefore, in recent years, slope monitoring has begun using a global navigation satellite system (GNSS), as disclosed in Patent Documents 1 and 2. By utilizing the inventions disclosed in Patent Documents 1 and 2, it is possible to monitor not only slopes that are at risk of collapse or show signs of a landslide, but also slopes where no particular movement is observed, and in addition, it is possible to grasp abnormalities directly and quantitatively, and has the advantage of not requiring the large effort and cost required by total station measurements.

[0010] It is known that errors occur in GNSS positioning due to several causes, and techniques for correcting these errors are widely used. Typical errors include errors due to the satellite clock and receiver clock, errors due to ionospheric delay, errors due to tropospheric delay, and errors due to multipath. Of these, errors due to tropospheric delay (hereinafter simply referred to as "tropospheric delay error") occur when radio waves from a positioning satellite are delayed as they pass through the troposphere. The troposphere contains both dry and moist air, so radio waves are refracted as they pass through the troposphere, resulting in corresponding delays. In particular, when there is a large difference in elevation between the observation point and the reference point, the radio wave transmission paths also differ significantly, resulting in increased tropospheric delay error.

[0011] To correct tropospheric delay errors, it is common to use the "modified Hopfield model," as shown in Patent Document 3. This modified Hopfield model uses the tropospheric delay (the amount of delay of radio waves in the troposphere), and this tropospheric delay is calculated based on a "dry term" that targets the dry atmospheric layer up to several tens of kilometers above ground, and a "wet term" that targets the moist atmospheric layer 2 to 3 km above ground. [Prior art documents] [Patent documents]

[0012] [Patent Document 1] Patent No. 7499363 [Patent Document 2] JP 2017-203650 A [Patent Document 3] JP 2008-051568 A Summary of the Invention [Problem to be solved by the invention]

[0013] As shown in Patent Document 3, meteorological data such as atmospheric pressure data, temperature data, and vapor pressure data are used to calculate the tropospheric delay. However, it is not so easy to obtain meteorological data appropriate for calculating the tropospheric delay, i.e., meteorological data appropriate for the target observation point. Of course, there is no problem if a measuring device for meteorological data is installed near a reference point used to observe the observation point. However, it is extremely difficult to install measuring devices near a reference point installed in a mountainous area, for example, and it also incurs costs for communicating the measurement data.

[0014] Therefore, in the past, the nearest meteorological station to the reference point was used, and the meteorological data measured there was used to calculate the tropospheric delay. However, the inventors of the present application discovered that in cases where there is a large difference in elevation between the observation point and the GNSS reference point, the conventional technology cannot accurately calculate the tropospheric delay. When the reference point is located significantly higher than the meteorological station, the meteorological conditions at the reference point and the meteorological station are different, so the modified Hopfield model using data from each meteorological station cannot obtain the tropospheric delay appropriate for the reference point or observation point.

[0015] The object of the present invention is to solve the conventional problems, that is, to provide a positioning system that can appropriately correct tropospheric delay errors and obtain the coordinates of an observation point even when the difference in altitude between the reference point and the meteorological station is relatively large. [Means for solving the problem]

[0016] The present invention focuses on the fact that meteorological data obtained from meteorological offices is corrected for a reference point and then tropospheric delay errors are corrected, and is an invention based on an idea that has not been seen before.

[0017] The positioning system of the present invention is a system that calculates the coordinates of an observation point based on a reference point for satellite positioning while correcting errors associated with tropospheric delay in satellite positioning, and includes a meteorological data acquisition means, a corrected meteorological data calculation means, and a tropospheric delay calculation means. The meteorological data acquisition means acquires "weather data (barometric pressure data, temperature data, and vapor pressure data from meteorological stations)" near the reference point. The corrected meteorological data calculation means corrects the meteorological data based on the elevation difference between the reference point and the meteorological station to calculate "corrected meteorological data (corrected barometric pressure data, corrected temperature data, and corrected vapor pressure data)." The tropospheric delay calculation means calculates the tropospheric delay based on the corrected meteorological data. The coordinates of the observation point are then calculated by performing baseline analysis using the tropospheric delay.

[0018] The positioning system of the present invention may also be configured such that the corrected meteorological data calculation means calculates corrected meteorological data as follows: corrected atmospheric pressure data is calculated from atmospheric pressure data, altitude difference, air density, and gravitational acceleration; corrected temperature data is calculated from temperature data, altitude difference, and temperature decrease rate; and corrected vapor pressure data is calculated from local water vapor pressure and local saturated water vapor pressure. Note that the local water vapor pressure is calculated from absolute humidity (a value obtained based on vapor pressure data) and corrected atmospheric pressure data, and the local saturated water vapor pressure is calculated from the corrected temperature data.

[0019] The positioning system of the present invention can also calculate the tropospheric delay based on two or more pieces of meteorological data. In this case, the meteorological data acquisition means acquires meteorological data from two or more meteorological stations. The corrected meteorological data calculation means calculates a weighted average for each piece of meteorological data according to the horizontal distance from the reference point to the meteorological station, and corrects the weighted average to calculate the corrected meteorological data. [Effects of the Invention]

[0020] The positioning system of the present invention has the following advantages. (1) Even if the difference in altitude between the reference point and the meteorological station is relatively large, for example, if the difference in altitude is 100 m or more, the coordinates of the observation point can be obtained by appropriately correcting the tropospheric delay error. (2) It can be implemented without installing meteorological data measuring equipment near the reference point, i.e., at a low cost comparable to that of conventional technology. (3) This is a monitoring technology that uses GNSS, and can monitor slopes that are at risk of collapse or show signs of landslides, as well as slopes where no particular movement is observed, and can also directly and quantitatively identify abnormalities. [Brief explanation of the drawings]

[0021] [Figure 1] A model diagram showing a situation where the reference point and observation point are located at a much higher position than the meteorological station. [Figure 2] 1 is a block diagram showing the main configuration of a positioning system according to the present invention; [Figure 3] A mathematical diagram showing the calculation formulas for "corrected atmospheric pressure data," "corrected temperature data," and "corrected vapor pressure data." [Figure 4] A mathematical diagram showing the calculation formula for "tropospheric delay." [Figure 5] A mathematical diagram showing the calculation formula for weighted average "corrected weather data." [Figure 6] FIG. 2 is a flowchart showing the main processing flow of the positioning system of the present invention. [Figure 7] (a) is a graph showing the change over time in observation point coordinates calculated without correction using the modified Hopfield model; (b) is a graph showing the change over time in observation point coordinates calculated based on the modified Hopfield model using meteorological data from meteorological offices near the reference point; (c) is a graph showing the change over time in observation point coordinates calculated based on the modified Hopfield model using meteorological data measured by equipment installed near the reference point; and (d) is a graph showing the change over time in observation point coordinates calculated by the present invention using meteorological data from meteorological offices near the reference point. DETAILED DESCRIPTION OF THE INVENTION

[0022] An example of an embodiment of the positioning system of the present invention will be described with reference to the drawings. The positioning system of the present invention can be implemented using a variety of objects as targets, but for convenience, the following description will be given assuming that the target is a slope (such as a natural slope or a slope). Note that a moving point installed on the target and used as an observation target will be referred to as an "observation point," and a fixed point installed near the target and used as a reference for GNSS positioning will be referred to as a "reference point."

[0023] The positioning system of the present invention is a technology for obtaining the coordinates of an observation point (hereinafter simply referred to as "observation point coordinates") by performing GNSS positioning, and obtains the observation point coordinates after correcting for tropospheric delay errors. This invention can be effectively implemented in cases where there is a large difference in elevation between the reference point and the meteorological station. Specifically, the positioning system of the present invention is preferably implemented in cases where the difference in elevation between the reference point and the meteorological station is 100 m or more.

[0024] Previously, the amount of tropospheric delay was calculated using the modified Hopfield model, using the data measured by the meteorological station nearest to the reference point. However, as shown in Figure 1, if the reference point and observation point are located significantly higher than the meteorological station, the transmission path of the radio waves from the positioning satellite ST will be significantly different, and the meteorological conditions at the reference point and the meteorological station will also be different. Therefore, the modified Hopfield model, which uses data from each meteorological station, will not be able to obtain the amount of tropospheric delay appropriate for the reference point or observation point.

[0025] Therefore, the positioning system of the present invention corrects the data measured by meteorological stations based on the elevation difference between the reference point and the meteorological station (hereinafter, particularly referred to as "reference point elevation difference"), and then calculates the tropospheric delay using a corrected Hopfield model. For convenience, the "barometric pressure data," "temperature data," and "vapor pressure data" measured by meteorological stations are collectively referred to as "weather data," and the data corrected based on the elevation difference are respectively referred to as "corrected barometric pressure data," "corrected temperature data," and "corrected vapor pressure data," and these are collectively referred to as "corrected meteorological data."

[0026] 2 is a block diagram showing the main components of the positioning system 100 of the present invention. As shown in this figure, the positioning system 100 of the present invention includes meteorological data acquisition means 101, corrected meteorological data calculation means 102, and tropospheric delay calculation means 103, and can also include coordinate calculation means 104, output means 105, meteorological data storage means 106, observation point coordinate storage means 107, etc.

[0027] Of the various means constituting the positioning system 100, the meteorological data acquisition means 101, the corrected meteorological data calculation means 102, the tropospheric delay calculation means 103, and the coordinate calculation means 104 can be manufactured as dedicated units, or a general-purpose computer device can be used. That is, the computer device executes calculation processing according to a predetermined program, thereby performing processing specific to each means. This computer device includes a processor such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit), memories such as ROM and RAM, and some also include input means such as a mouse and a keyboard, and a display, and can be configured, for example, as a personal computer (PC) or a server. If the computer device includes a display, the display can also be used as the output means 105.

[0028] The meteorological data storage means 106 and observation point coordinate storage means 107 can be configured as a storage device of a general-purpose computer (for example, a personal computer) or as a database server. When configured as a database server, they can be placed on a local network (LAN: Local Area Network) or as a cloud server that stores data via the Internet.

[0029] Below, each of the main elements constituting the positioning system 100 of the present invention will be described in detail.

[0030] (Mechanism for obtaining weather data) The weather data acquisition means 101 constituting the positioning system 100 is a means for acquiring weather data (barometric pressure data, temperature data, and vapor pressure data) from a meteorological station located near a reference point. When the weather data acquisition means 101 acquires weather data, it can be configured to receive weather data from a meteorological station via communication means (wireless or wired), to acquire weather data using portable storage means (such as a USB flash memory), or to have an operator input weather records (barometric pressure, temperature, and vapor pressure) on paper.

[0031] The weather data acquisition means 101 can be configured to acquire only the weather data of the weather station closest to the reference point elevation difference, or to select two or more weather stations based on predetermined conditions and acquire all of the weather data related to these weather stations. For example, it can select all weather stations within a predetermined range (e.g., 50 km), or a predetermined number of weather stations (e.g., four stations in order of proximity), or it can select weather stations based on these conditions and the condition that the elevation difference from the reference point is small (within a predetermined threshold). The weather data acquired here can be stored in the weather data storage means 106.

[0032] (Means for calculating corrected weather data) The corrected meteorological data calculation means 102 constituting the positioning system 100 is a means for calculating corrected meteorological data based on meteorological data and the reference point elevation difference. More specifically, the corrected meteorological data calculation means 102 calculates corrected atmospheric pressure data based on atmospheric pressure data, corrected temperature data based on temperature data, and corrected vapor pressure data based on vapor pressure data.

[0033] The corrected meteorological data calculation means 102 can calculate the corrected atmospheric pressure data by using the formula (1) shown in FIG. OBThe corrected atmospheric pressure data is obtained by subtracting the "pressure difference corresponding to the difference in reference point elevation (ρg△z)" from "

[0034] The corrected temperature data can be calculated by the corrected weather data calculation means 102 using the formula (2) shown in FIG. OB The corrected temperature data is obtained by subtracting the temperature difference (γ△z) corresponding to the difference in reference point elevation from the original temperature data.

[0035] The corrected meteorological data calculation means 102 can calculate the corrected vapor pressure data by using the formula (3) shown in FIG. 3. That is, the "local estimated water vapor pressure e L " to "Locally estimated saturated water vapor pressure e LS The corrected vapor pressure data is obtained by dividing by the "locally estimated water vapor pressure e L " is obtained by equations (4) and (6) shown in Figure 3, and "field estimated saturated water vapor pressure e LS " can be obtained by equation (5) shown in Figure 3.

[0036] (Means for calculating tropospheric delay) The tropospheric delay calculation means 103 constituting the positioning system 100 is a means for calculating the tropospheric delay based on the corrected barometric pressure data, corrected temperature data, and corrected vapor pressure data. When the tropospheric delay calculation means 103 calculates the tropospheric delay, it can do so using equations (7) to (11) shown in FIG. 4. That is, the tropospheric delay is calculated by the sum of the "dry term" which is the first term on the right side of equation (7) and the "wet term" which is the second term. Note that the "dry air refractivity N" which constitutes the dry term dry」 is obtained by equations (8) and (10) shown in Fig. 4, and the refractive index of water vapor, N wet」 can be obtained by equations (9) and (11) shown in Figure 4.

[0037] As described above, the weather data acquisition means 101 can acquire only the weather data of the meteorological station closest to the reference point, or can acquire all the weather data related to two or more meteorological stations. When acquiring two or more weather data, the amount of tropospheric delay can be calculated using weighted averaged corrected weather data. More specifically, corrected weather data is calculated based on the weather data related to each meteorological station, and a weighted average value according to the horizontal distance from the reference point to the meteorological station is calculated using these multiple corrected weather data, and the amount of tropospheric delay is calculated using this weighted average value. For example, in FIG. 5, four meteorological stations are selected near the reference point, so first, four types of individual corrected weather data x i Then, the tropospheric delay is calculated using a weighted average value according to the horizontal distances d1 to d4 from the reference point to the meteorological station, that is, one piece of corrected meteorological data x (corrected pressure data, corrected temperature data, corrected vapor pressure data) obtained by equation (12) shown in Figure 5.

[0038] (Coordinate calculation means) The coordinate calculation means 104 constituting the positioning system 100 is a means for determining observation point coordinates by performing baseline analysis using various information contained in radio waves received from the positioning satellites ST. At this time, the phase data obtained from the positioning satellites ST is corrected by the amount of tropospheric delay, and the observation point coordinates are calculated by performing baseline analysis using the corrected phase data. The observation point coordinates calculated periodically here can be stored in the observation point coordinate storage means 107. The periodically calculated observation point coordinates can also be output to the output means 105, such as a display or printer, as a graph showing changes over time.

[0039] (Processing flow) The main processing of the positioning system 100 of the present invention will be described in detail below with reference to Fig. 6. Fig. 6 is a flow diagram showing an example of the flow of the main processing of the positioning system 100 of the present invention, in which the central column shows the processing to be performed, the left column shows input information required for that processing, and the right column shows output information resulting from that processing.

[0040] When calculating the observation point coordinates using the positioning system 100, first, meteorological data from a meteorological station near the reference point is acquired using the meteorological data acquisition means 101 (Step 201 in FIG. 6). Next, corrected meteorological data is calculated using the corrected meteorological data calculation means 102 (Step 202 in FIG. 6). As mentioned above, corrected atmospheric pressure data, corrected temperature data, and corrected vapor pressure data can be calculated using equations (1) to (6) shown in FIG. 3.

[0041] Once the corrected weather data is obtained, the tropospheric delay is calculated using the tropospheric delay calculation means 103 (Step 203 in Fig. 6). As mentioned above, the tropospheric delay can be calculated using equations (7) to (11) shown in Fig. 4. Once the tropospheric delay is obtained, the observation point coordinates are calculated using the coordinate calculation means 104 (Step 204 in Fig. 6), and are output to the output means 105, such as a display or printer, as a graph showing the change over time (Step 205 in Fig. 6).

[0042] (Demonstration results) To verify the effectiveness of the positioning system 100 of the present invention, the inventors of the present application conducted a demonstration test to determine the coordinates of actual observation points using various methods. Figure 7 shows the results, including a graph illustrating the changes in observation point coordinates over time. Figure 7(a) shows a case in which observation point coordinates were determined without correction using the modified Hopfield model. Figure 7(b) shows a case in which observation point coordinates were determined based on the modified Hopfield model using meteorological data from a meteorological station near the reference point. Figure 7(c) shows a case in which a measuring device was installed near the reference point, and meteorological data measured by the measuring device was used to determine the observation point coordinates based on the modified Hopfield model. Figure 7(d) shows a case in which observation point coordinates were determined using meteorological data from a meteorological station near the reference point using the positioning system 100 of the present invention. The elevation difference between the observation point and the meteorological station (reference point elevation difference) in this demonstration test was approximately 370 m.

[0043] It was confirmed that during the period in which the demonstration test was conducted (the period shown in the graph of FIG. 7), almost no changes in the observation points were observed. However, in the cases of FIG. 7(a) and FIG. 7(b), it is inferred that there were changes in the observation points, and therefore it is difficult to say that the analysis was accurate. In contrast, in the case of FIG. 7(c), which used meteorological data, which are essentially measured values, the displacement generally remained near zero during the period, and it is inferred that there were no changes in the observation points, so it can be said that the analysis was accurate. Furthermore, in the case of FIG. 7(d), which used the positioning system 100 of the present invention, similar to FIG. 7(c), the displacement generally remained near zero during the period, and it is inferred that there were no changes in the observation points, so it can be said that the analysis was accurate. [Industrial Applicability]

[0044] The positioning system of the present invention can be used for a variety of positioning targets, including natural slopes, cut slopes, embankment slopes, and other slopes, as well as civil engineering structures such as bridges, dams, and retaining walls. Considering that the present invention can prevent accidents caused by slopes, such as collapses and landslides, and can also detect abnormalities in construction infrastructure such as bridges in advance, it can be said to be an invention that can be used not only industrially but also is expected to make a great contribution to society. [Explanation of symbols]

[0045] 100 Positioning system of the present invention 101 (Positioning System) Meteorological Data Acquisition Method 102 (Positioning System) Corrected Meteorological Data Calculation Means 103 Tropospheric delay calculation method (for positioning systems) 104 (Positioning system) coordinate calculation means 105 (Positioning system) output means 106 (Positioning System) Meteorological Data Storage Means 107 (Positioning system) observation point coordinate storage means ST positioning satellite

Claims

1. A system for correcting errors due to tropospheric delay in satellite positioning and determining the coordinates of an observation point based on a reference point for satellite positioning, a meteorological data acquisition means for acquiring atmospheric pressure data, temperature data, and vapor pressure data from meteorological stations located near the reference point; a corrected meteorological data calculation means for correcting the atmospheric pressure data, the temperature data, and the vapor pressure data based on the elevation difference between the reference point and the meteorological station, thereby obtaining corrected atmospheric pressure data, corrected temperature data, and corrected vapor pressure data; a tropospheric delay calculation means for calculating a tropospheric delay based on the corrected atmospheric pressure data, the corrected temperature data, and the corrected vapor pressure data; determining the coordinates of the observation point by performing a baseline analysis using the tropospheric delay amount; A positioning system characterized by:

2. the corrected meteorological data calculation means calculates the corrected atmospheric pressure data from the atmospheric pressure data, the altitude difference, the air density, and the gravitational acceleration; The corrected meteorological data calculation means calculates the corrected temperature data from the temperature data, the altitude difference, and the temperature decrease rate, Furthermore, the corrected meteorological data calculation means calculates a local water vapor pressure from the absolute humidity obtained based on the vapor pressure data and the corrected atmospheric pressure data, and calculates a local saturated water vapor pressure from the corrected air temperature data, and then calculates the corrected vapor pressure data from the local water vapor pressure and the local saturated water vapor pressure.

2. The positioning system according to claim 1.

3. the meteorological data acquisition means acquires the atmospheric pressure data, the temperature data, and the vapor pressure data related to two or more of the meteorological stations; the corrected meteorological data calculation means calculates weighted average values ​​of the atmospheric pressure data, the temperature data, and the vapor pressure data in accordance with the horizontal distance from the reference point to the meteorological station, and corrects the weighted average values ​​to calculate the corrected atmospheric pressure data, the corrected temperature data, and the corrected vapor pressure data.

2. The positioning system according to claim 1.

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