Method for calculating position in a satellite navigation receiver and program for calculating position.

Abstract

When using the precise orbital almanac, the precise orbital almanac for the previous or following day is not required. [Solution] In satellite navigation systems, precise orbital ephemeris, which contains accurate information about the time and orbit, is sometimes used. However, when using precise orbital ephemeris, there is a problem in that the accuracy of interpolation or extrapolation deteriorates when processing the beginning or end of the day. To avoid this, it was necessary to use the precise orbital ephemeris of the previous or next day. By appropriately interpolating or extrapolating the precise orbital ephemeris using the trend of changes in the broadcast orbital ephemeris, the accuracy of interpolation or extrapolation when processing the beginning or end of the day is improved, and the precise orbital ephemeris of the previous or next day becomes unnecessary.

Description

Technical Field

[0001] This invention relates to the calculation of positions in a satellite navigation receiver.

Background Art

[0002] A satellite navigation system that measures positions using artificial satellites is generally referred to as GNSS (Global Navigation Satellite System), and a representative example thereof is GPS (Global Positioning System) developed by the United States. In general, GNSS receives positioning signals transmitted by artificial satellites called navigation satellites with a satellite navigation receiver, measures the distance between the navigation satellite and the receiver, and thereby obtains the position where the receiver received the positioning signal by calculation. The position where the receiver received the positioning signal is simply referred to as the position of the receiver. The error with respect to the true position of the position obtained by calculation is called the positioning error, and the statistical state of the positioning error is called the positioning accuracy. Measuring a position is called positioning, and the calculation process therefor is called positioning calculation. The receiver may be referred to as a user station or a user receiver, and although a user originally means a person who uses the receiver, the receiver itself may also be called a user.

[0003] In order to calculate the position of a satellite navigation receiver, it is necessary to know the positions of the navigation satellites transmitting the positioning signals. However, the orbital information necessary for this is transmitted by the navigation satellites themselves by superimposing it on the positioning signals. Since the orbital information is created by prediction, it includes an error of about several meters, which becomes a factor of the positioning error when calculating the receiver position.

[0004] The timing of navigation satellites transmitting positioning signals is predetermined, and these signals are transmitted based on the time on their own clocks. High-precision atomic clocks are used for this purpose, but very slight time discrepancies are unavoidable, so satellite navigation receivers require information on the time indicated by the navigation satellite's clock. This information is transmitted by the navigation satellite itself as a transmitter clock error, included in the orbital information. Since the transmitter clock error is created by prediction, the timing of positioning signal transmission calculated using this error includes an error equivalent to several meters in distance, and this becomes a factor in positioning errors when calculating the receiver's position as an estimated error in the navigation satellite's transmitter clock error (simply called the clock error).

[0005] The information about the satellite's own clock and orbit transmitted by a navigation satellite is called the broadcast orbital ephemeris. By using the broadcast orbital ephemeris, a satellite navigation receiver can calculate the time and position coordinates of the navigation satellite's clock at any point in time within the validity period of the broadcast orbital ephemeris.

[0006] During the journey of a positioning signal to the ground, it passes through the ionosphere and troposphere, and delays occur as the radio signal passes through each region. These delays are called ionospheric propagation delay and tropospheric propagation delay, respectively. Therefore, when this radio signal is used as a positioning signal, these ionospheric and tropospheric propagation delays are factors contributing to positioning errors. The magnitudes of ionospheric and tropospheric propagation delays, converted to distance, are called ionospheric propagation delay amount and tropospheric delay amount, respectively.

[0007] In the field of GNSS, precise ephemeris are created and used for each navigation satellite as accurate information about its time and orbit. Precise ephemeris are often created at 15-minute or 5-minute intervals, and users can interpolate them to obtain the accurate time and position coordinates of each navigation satellite at any given point in time. Precise ephemeris are publicly available, for example, created by an international organization called IGS (International GNSS Service), and are used in fields of precise positioning such as surveying and geodesy.

[0008] Precise orbital ephemerides are generally created through post-mortem calculations, integrating measurement data from numerous receiving stations to obtain the most accurate information possible. This process also minimizes measurement errors such as ionospheric propagation delay and tropospheric propagation delay. The most accurate are the final ephemerides, which take approximately one to two weeks to create. Sometimes, ephemerides are provided with a delay of only a few days. Furthermore, near-real-time ephemerides, including predictions, are also created. The accuracy of these ephemerides decreases in this order, with the final ephemerides being the most accurate and the near-real-time ephemerides being the least accurate.

[0009] As of early 2026, GNSS systems available will include GPS, as well as GLONASS by Russia, Galileo by Europe, BDS by China, and QZSS (Quasi-Zenith Satellite System) by Japan. [Prior art documents] [Non-patent literature]

[0010] [Non-Patent Document 1] "What is a precise calendar?", Geospatial Information Authority of Japan press release, June 2023 (https: / / www.gsi.go.jp / common / 000250683.pdf) [Non-Patent Document 2] Qiao Yun, Research on Improving the Accuracy of GPS-Based Positioning, Master's Thesis, Tokyo University of Marine Science and Technology, September 2005 (https: / / www.denshi.e.kaiyodai.ac.jp / wp-content / uploads / pdf / content1 / kyo.pdf) [Overview of the project] [Problems that the invention aims to solve]

[0011] As described in Non-Patent Document 1 and paragraph

[0007] , precise orbital ephemeris have been created as accurate information on the clocks and orbits of navigation satellites and are publicly available for use. The electronic file of precise orbital ephemeris provided by IGS contains one day's worth of precise orbital ephemeris.

[0012] The precise orbital ephemeris is generally created for time points (called epochs) at 15-minute or 5-minute intervals, and it contains the time and position coordinates of each navigation satellite's clock at each time point. In order to calculate the position of a satellite navigation receiver, the time and position coordinates of the navigation satellite's clock at the time the receiver measures the distance using the positioning signal are necessary. Therefore, users need to appropriately interpolate the precise orbital ephemeris around the relevant time point. Non-patent document 2 uses an 11th-degree polynomial for this interpolation, and it is generally said that if using Lagrangian interpolation, a 7th-degree (8-point) or higher should be used.

[0013] In practice, the accuracy of interpolation of the precise ephemeris varies depending on the point in time being interpolated. That is, the desired accuracy can be obtained if there are sufficient epochs of the precise ephemeris before and after the target point in time. For 7th-order Lagrangian interpolation, a total of 8 epochs of precise ephemeris are used, with 4 epochs before and 4 after the target point in time.

[0014] Since the electronic files for the precise orbital ephemeris are created on a daily basis, processing at the beginning and end of each day becomes an issue. For example, consider a case where the precise orbital ephemeris is created at 15-minute intervals from 00:00 to 23:45 (information for 24:00 is included in the next day's electronic file).

[0015] For the first 15 minutes, there is only one epoch preceding it at 00:00, and 7 or more epochs are available from 00:15 onwards. For the next 15 minutes, there are only two epochs preceding it at 00:00 and 00:15, and 6 or more epochs are available from 00:30 onwards. The same applies to the following 15 minutes and beyond. In other words, during the time period before 00:45, a total of 8 precise orbital ephemeris epochs (4 before and 4 after) cannot be used.

[0016] Furthermore, for the last 15 minutes, there are no epochs after it, and more than 8 epochs are available for epochs prior to 23:45. For the 15 minutes prior to that, there is only one epoch after it, at 23:45, and more than 7 epochs are available for epochs prior to 23:30. For the 15 minutes prior to that, there are only two epochs after it, at 23:45 and 23:30, and more than 6 epochs are available for epochs prior to 23:15. The same applies to the 15 minutes prior to that. In other words, for the time period after 23:00, it is not possible to use the precise orbital ephemeris, which consists of 4 epochs before and 4 before, for a total of 8 epochs.

[0017] If it is not possible to use a precise orbital ephemeris of 8 epochs, 4 before and 4 after the point in time, interpolation is generally performed using only the available epochs. However, in this case, the interpolation accuracy deteriorates due to the asymmetry in the number of epochs before and after the point in time being interpolated, and because the order of the interpolation process is reduced.

[0018] If there is no epoch in the precise orbital ephemeris either before or after the point in time when the receiver measures the distance, such as at the end of the day, extrapolation is necessary, but the extrapolation accuracy in this case is generally significantly worse than that of interpolation.

[0019] One way to address this situation is to use the precise orbital ephemeris of the previous day or the following day, respectively, when processing the beginning or end of the day. By using the precise orbital ephemeris of the previous or following day and the precise orbital ephemeris of the current day consecutively, the above problems can be avoided.

[0020] However, in order to use the precise orbital ephemeris for the previous or next day, it is necessary to obtain that ephemeris in addition to the current day's ephemeris. This is time-consuming, and since it takes time for the ephemeris to be provided, the ephemeris for the following day may not yet be available.

[0021] As described above, when using the precise orbit ephemeris, there is a problem that the interpolation or extrapolation accuracy deteriorates when processing the time zone at the start or end of a day. To avoid this, there was an issue that it was necessary to use the precise orbit ephemeris of the previous day or the next day.

Means for Solving the Problem

[0022] To solve the above problem, when using the precise orbit ephemeris, it is sufficient if the interpolation or extrapolation accuracy does not deteriorate even when processing the time zone at the start or end of a day.

[0023] To improve the interpolation accuracy in a section where there is little data for the interpolation process, if the trend of data change in that section is known in advance, this can be utilized. The same applies to the case of extrapolation such as at the end of a day.

[0024] As information on the clock and orbit of a navigation satellite, the broadcast orbit ephemeris can also be used. Since the broadcast orbit ephemeris is transmitted by a navigation satellite, a satellite navigation receiver can naturally use it. For example, in IGS, the broadcast orbit ephemeris received on the ground is stored and is also publicly available for general use.

[0025] Generally, the broadcast orbit ephemeris has a valid time of about several hours, and in the case of GPS, it is usually set to a valid time of 4 hours. For example, the GPS broadcast orbit ephemeris with a valid time of 4 hours is valid within the range of ±2 hours from the reference time and is transmitted 2 hours before the reference time. In this case, since the orbit information is updated every 2 hours, usually, between 00:00 and 02:00 of a certain day, the orbit information valid within the range of 00:00 to 04:00 with the reference time set to 02:00 is transmitted, and between 02:00 and 04:00, the orbit information valid within the range of 02:00 to 06:00 with the reference time set to 04:00 is transmitted, and the same applies thereafter.

[0026] The broadcast orbit ephemeris is inferior in accuracy compared to the precise orbit ephemeris. However, this refers to the absolute values of the time and position coordinates of the navigation satellite's clock, and regarding the tendency of their changes, it has properties similar to those of the precise orbit ephemeris.

[0027] Therefore, by interpolating the precise orbit ephemeris using the tendency of the change of the broadcast orbit ephemeris, it is possible to prevent deterioration of the interpolation accuracy when processing the time zone at the beginning or end of a day. Also, including time zones other than these, functions used for interpolation processing can be simplified, such as reducing the degree of the function used for interpolation processing. The same applies to extrapolation.

[0028] Specifically, first, from the time and position coordinates of the navigation satellite's clock according to the broadcast orbit ephemeris, at a plurality of epochs of the precise orbit ephemeris, by subtracting the time and position coordinates of the clock according to the precise orbit ephemeris, these differences at the plurality of epochs are obtained. By subtracting the result of interpolating or extrapolating this difference for the time point when the receiver measures the distance by the positioning signal from the time and position coordinates of the navigation satellite's clock according to the broadcast orbit ephemeris, new time and position coordinates of the clock regarding the navigation satellite are obtained. By such a procedure, interpolation or extrapolation of the precise orbit ephemeris can be performed using the tendency of the change of the broadcast orbit ephemeris.

[0029] Again, consider the case where the precise orbit ephemeris is created at 15 - minute intervals from time 00:00 to time 23:45.

[0030] For the first 15 minutes, there is only one epoch at time 00:00 before it, and for epochs after time 00:15, 7 or more can be used. The broadcast orbit ephemeris has valid information transmitted within the previous day until time 02:00, and the transmission of valid information within the range of time 00:00 to 04:00 starts at time 00:00. That is, the satellite navigation receiver is in a state where it can use the broadcast orbit ephemeris corresponding to 8 epochs from time 00:00 to 01:45.

[0031] For the next 15 minutes, there are only two epochs prior to it, at 00:00 and 00:15, and more than six epochs are available from 00:30 onwards. The broadcast orbit ephemeris contains information valid up to 02:00, which was transmitted the previous day, and the transmission of information valid within the time range of 00:00 to 04:00 began at 00:00. In other words, the satellite navigation receiver has access to broadcast orbit ephemeris corresponding to eight epochs from 00:00 to 01:45.

[0032] The same applies to the following 15 minutes and beyond. In other words, during the time period before 00:45, the precise orbital ephemeris of 8 epochs (4 before and 4 after) cannot be used, but the precise orbital ephemeris of 8 epochs from 00:00 to 01:45, and the corresponding broadcast orbital ephemeris, are available.

[0033] Therefore, for the time period before 00:45, the time and position coordinates of the navigation satellite's clock according to the broadcast ephemeris are subtracted from the time and position coordinates of the navigation satellite's clock according to the broadcast ephemeris for the eight epochs from 00:00 to 01:45 to obtain the difference for those eight epochs. By subtracting the result of interpolating this difference for the time when the receiver measured the distance using the positioning signal from the time and position coordinates of the navigation satellite's clock according to the broadcast ephemeris, new time and position coordinates for the navigation satellite are obtained. Through this procedure, interpolation of the precise ephemeris can be performed by utilizing the trend of change in the broadcast ephemeris.

[0034] Although this example uses 8 epochs, the same calculation can be performed using at least 2 epochs.

[0035] For the last 15 minutes, there are no subsequent epochs, and more than 8 epochs are available for use before 23:45. The broadcast orbit ephemeris transmission of information valid within the time range of 22:00 to 24:00 began at 22:00. In other words, the satellite navigation receiver is able to use the broadcast orbit ephemeris corresponding to the 8 epochs between 22:00 and 23:45.

[0036] For the preceding 15 minutes, there is only one epoch after that, at 23:45, and more than seven epochs are available for use before 23:30. The broadcast orbit ephemeris transmission of information valid within the time range of 22:00 to 24:00 began at 22:00. That is, the satellite navigation receiver is able to use the broadcast orbit ephemeris corresponding to the eight epochs from 22:00 to 23:45.

[0037] Furthermore, for the 15 minutes prior to that, there are only two epochs remaining, at 23:45 and 23:30, and more than six epochs are available before 23:15. The broadcast orbit ephemeris transmission of valid information within the time range of 22:00 to 24:00 began at 22:00. In other words, the satellite navigation receiver is in a state where it can utilize the broadcast orbit ephemeris corresponding to the eight epochs from 22:00 to 23:45.

[0038] The same applies to the 15 minutes prior to that time. In other words, during the time period after 23:00, the precise orbital ephemeris of 8 epochs (4 before and 4 after) cannot be used, but the precise orbital ephemeris of 8 epochs from 22:00 to 23:45, and the corresponding broadcast orbital ephemeris, are available.

[0039] Therefore, during the time period from 23:00 to 23:45, the time and position coordinates of the navigation satellite's clock according to the broadcast ephemeris are subtracted from the time and position coordinates of the clock according to the precise ephemeris for the eight epochs from 22:00 to 23:45 to obtain the difference for those eight epochs. This difference is then interpolated for the time when the receiver measured the distance using the positioning signal, and this result is subtracted from the time and position coordinates of the navigation satellite's clock according to the broadcast ephemeris to obtain the new time and position coordinates for the navigation satellite. Through this procedure, interpolation of the precise ephemeris can be performed by utilizing the trend of change in the broadcast ephemeris.

[0040] Although this example uses 8 epochs, the same calculation can be performed using at least 2 epochs.

[0041] For the time period after 23:45, the time and position coordinates of the navigation satellite's clock according to the broadcast ephemeris are subtracted from the time and position coordinates of the clock according to the precise ephemeris for the eight epochs from 22:00 to 23:45 to obtain the difference for those eight epochs. This difference is then extrapolated towards the time when the receiver measured the distance using the positioning signal, and this result is subtracted from the time and position coordinates of the navigation satellite's clock according to the broadcast ephemeris to obtain the new time and position coordinates for that navigation satellite. Through this procedure, extrapolation of the precise ephemeris can be performed by utilizing the trend of change in the broadcast ephemeris.

[0042] Although this example uses 8 epochs, the same calculation can be performed using at least 1 epoch.

[0043] Let's explain this using mathematical formulas. Let B(T) be the coordinate value according to the broadcast orbital ephemeris at time T (either the time or position coordinate of the navigation satellite's clock), and let P(T1), P(T2), etc. be the coordinate values ​​according to the precise orbital ephemeris at times T1, T2, etc. (either the time or position coordinate of the navigation satellite's clock). The difference between these values ​​at time Ti, D(Ti), can be written as follows.

[0044]

number

[0045] Assuming the precise orbital ephemeris is accurate, D(Ti) will reflect the error contained in the broadcast orbital ephemeris at time Ti.

[0046] We obtain a function that approximates D(Ti) around time T, and call this F(T). Using F(T), we find the coordinate value P'(T) at time T by the following equation.

[0047]

number

[0048] This process removes the error component included in the broadcast orbital ephemeris. Since the trend of change in the broadcast orbital ephemeris between epochs remains, the precise orbital ephemeris is appropriately interpolated or extrapolated using the trend of change in the broadcast orbital ephemeris, so the receiver can use this P'(T) for position calculations.

[0049] This improves the accuracy of interpolation or extrapolation when processing the beginning or end of a day using the precise orbital ephemeris, eliminating the need for the previous or next day's precise orbital ephemeris. A similar effect can be achieved even if it is not the beginning or end of a day, but if for some reason some or all of the navigation satellite's precise orbital ephemeris is missing.

[0050] Furthermore, it is possible to reduce the order of the approximation function required to obtain a similar level of interpolation or extrapolation accuracy for time periods other than the beginning or end of the day.

[0051] Non-patent document 1 is a description of a precise orbital ephemeris and does not describe specific procedures for its use.

[0052] Non-patent document 2 describes a method for interpolating the precise orbital ephemeris for the purpose of using it in position calculations, and provides examples of differences from the broadcast orbital ephemeris. However, it does not mention interpolating the precise orbital ephemeris using the broadcast orbital ephemeris. Furthermore, it does not explain cases where extrapolation is required.

[0053] The invention according to claim 1 is a satellite navigation receiver that receives positioning signals transmitted by a plurality of navigation satellites that transmit positioning signals, measures the distance between them, and calculates the position at the time of the measurement, wherein the calculation of the position requires the time and position coordinates of each of the navigation satellites at the time of the measurement, and the satellite navigation receiver calculates the time and position coordinates of the navigation satellite's clock using the broadcast orbital ephemeris, which is information about the navigation satellite's own clock and orbit that the navigation satellite transmits superimposed on the positioning signal, for each of the navigation satellites, and then calculates the time and orbit of the navigation satellite's clock and orbit This is a method for calculating the position in a satellite navigation receiver, characterized by obtaining a difference between multiple points in time, where a precise ephemeris, which is accurate information about the path, is given, by subtracting the time and position coordinates of the navigation satellite's clock according to the precise ephemeris, and by subtracting the result of interpolating this difference between multiple points in time for the time of measurement from the time and position coordinates of the navigation satellite's clock at the time of measurement, calculated using the broadcast ephemeris, to obtain a new time and position coordinate for the navigation satellite, and then using this new time and position coordinate to calculate the position.

[0054] The invention according to claim 2 is a method for calculating the position in a satellite navigation receiver according to claim 1, characterized in that, during the interpolation, the difference between two time points in time for which precise orbital ephemeris are given before and after the time of measurement is linearly interpolated.

[0055] The invention according to claim 3 is a method for calculating the position in a satellite navigation receiver according to claim 1, characterized in that, during the interpolation, the difference between three or more points in time for which precise orbital ephemeris before and after the time of measurement is given is interpolated using a polynomial.

[0056] The invention according to claim 4 is a satellite navigation receiver that receives positioning signals transmitted by a plurality of navigation satellites that transmit positioning signals, measures the distance between them, and calculates the position at the time of the measurement, wherein the calculation of the position requires the time and position coordinates of each of the navigation satellites at the time of the measurement, and the satellite navigation receiver operates on each of the navigation satellites, using the broadcast orbital ephemeris, which is information about the navigation satellite's own clock and orbit that the navigation satellite transmits superimposed on the positioning signal, to calculate the time and position coordinates of the navigation satellite's clock and orbit This program calculates the position in a satellite navigation receiver, characterized by obtaining differences between multiple points in time, where a precise ephemeris, which is accurate information about the path, is provided. These differences are then interpolated for the measurement point, and the result is subtracted from the time and position coordinates of the navigation satellite's clock at the measurement point, calculated using the broadcast ephemeris, to obtain new time and position coordinates for the navigation satellite. The position is then calculated using these new time and position coordinates.

[0057] The invention according to claim 5 is a program for calculating the position in a satellite navigation receiver according to claim 4, characterized in that, during the interpolation, the difference between two time points in time for which precise orbital ephemeris are given before and after the time of measurement is linearly interpolated.

[0058] The invention according to claim 6 is a program for calculating the position in a satellite navigation receiver according to claim 4, characterized in that, during the interpolation, the differences at three or more time points before and after the time of measurement, for which precise orbital ephemeris are given, are performed using polynomial interpolation.

[0059] The invention according to claim 7 is a satellite navigation receiver that receives positioning signals transmitted by a plurality of navigation satellites that transmit positioning signals, measures the distance between them, and calculates the position at the time of the measurement, wherein the calculation of the position requires the time and position coordinates of each of the navigation satellites at the time of the measurement, and the satellite navigation receiver calculates the time and position coordinates of the navigation satellite's clock using the broadcast orbital ephemeris, which is information about the navigation satellite's clock and orbit that the navigation satellite transmits superimposed on the positioning signal, for each of the navigation satellites, and then calculates the time and orbit of the navigation satellite's clock and orbit This is a method for calculating the position in a satellite navigation receiver, characterized by obtaining a difference at one or more points in time by subtracting the time and position coordinates of the navigation satellite's clock according to the precise orbital ephemeris at one or more points in time for which accurate information, which is the precise orbital ephemeris, is given; subtracting the result of extrapolating this difference at one or more points in time toward the time of measurement from the time and position coordinates of the navigation satellite's clock at the time of measurement calculated using the broadcast orbital ephemeris to obtain new time and position coordinates for the navigation satellite; and performing the position calculation using these new time and position coordinates.

[0060] The invention according to claim 8 is a method for calculating the position in a satellite navigation receiver according to claim 7, characterized in that, during extrapolation, the difference at a point in time before or after the time of measurement for which a precise orbital ephemeris is provided is used as is.

[0061] The invention according to claim 9 is a method for calculating the position in a satellite navigation receiver according to claim 7, characterized in that, during extrapolation, the difference between two points in time, either before or after the time of measurement, for which a precise orbital ephemeris is given, is extrapolated by linear approximation.

[0062] The invention according to claim 10 is a method for calculating the position in a satellite navigation receiver according to claim 7, characterized in that, during extrapolation, the difference at three or more time points before or after the time of measurement for which a precise orbital ephemeris is given is extrapolated by polynomial approximation.

[0063] The invention according to claim 11 is a satellite navigation receiver that receives positioning signals transmitted by a plurality of navigation satellites that transmit positioning signals, measures the distance between them, and calculates the position at the time of the measurement, wherein the calculation of the position requires the time and position coordinates of each of the navigation satellites at the time of the measurement, and the satellite navigation receiver operates on each of the navigation satellites, using the broadcast orbital ephemeris, which is information about the navigation satellite's own clock and orbit that the navigation satellite transmits superimposed on the positioning signal, to calculate the time and position coordinates of the navigation satellite's clock and orbit This is a program for calculating the position in a satellite navigation receiver, characterized by obtaining a difference at one or more points in time by subtracting the time and position coordinates of the navigation satellite's clock according to the precise orbital ephemeris at one or more points in time for which accurate information, which is the precise orbital ephemeris, is given; subtracting the result of extrapolating this difference at one or more points in time toward the time of measurement from the time and position coordinates of the navigation satellite's clock at the time of measurement calculated using the broadcast orbital ephemeris to obtain new time and position coordinates for the navigation satellite; and using these new time and position coordinates to calculate the position.

[0064] The invention according to claim 12 is a program for calculating the position in a satellite navigation receiver according to claim 11, characterized in that, during extrapolation, it uses the difference at any point in time before or after the measurement time for which a precise orbital ephemeris is provided.

[0065] The invention according to claim 13 is a program for calculating the position in a satellite navigation receiver according to claim 11, characterized in that, during extrapolation, the difference between two time points in time, either before or after the time of measurement, for which a precise orbital ephemeris is given, is extrapolated by linear approximation.

[0066] The invention according to claim 14 is a program for calculating the position in a satellite navigation receiver according to claim 11, characterized in that, during extrapolation, the difference at three or more time points before or after the time of measurement, for which a precise orbital ephemeris is given, is extrapolated by polynomial approximation. [Effects of the Invention]

[0067] The inventions according to claims 1 to 6 are configured as described above, and by using the trend of changes in the broadcast orbital ephemeris to interpolate the precise orbital ephemeris, it is possible to prevent deterioration of interpolation accuracy when using the precise orbital ephemeris for processing the time period at the beginning or end of the day, thereby eliminating the need for the precise orbital ephemeris of the previous or next day. Furthermore, for time periods other than the beginning or end of the day, it is possible to reduce the order of the interpolation function required to obtain a similar level of interpolation accuracy.

[0068] The inventions described in claims 7 to 14 are configured as described above, and by utilizing the trend of changes in the broadcast orbital ephemeris to perform extrapolation of the precise orbital ephemeris, it is possible to prevent deterioration of extrapolation accuracy when using the precise orbital ephemeris for processing the beginning or end of the day, thereby eliminating the need for the precise orbital ephemeris of the previous or next day. Furthermore, for time periods other than the beginning or end of the day, it is possible to reduce the order of the extrapolation function required to obtain a similar level of extrapolation accuracy. [Brief explanation of the drawing]

[0066] [Figure 1] This diagram illustrates a first embodiment of the present invention and is a schematic diagram illustrating a method for calculating position and a program for calculating position in a satellite navigation system according to claims 1 to 6 of the present invention. [Figure 2] This diagram illustrates a second embodiment of the present invention and is a schematic diagram illustrating a method for calculating position and a program for calculating position in a satellite navigation system according to claims 7 to 14 of the present invention. [Modes for carrying out the invention]

[0067] Hereinafter, specific embodiments of the present invention will be described in detail with reference to the drawings. [Examples]

[0068] A first embodiment of this invention will be described in detail with reference to Figure 1.

[0069] The coordinate values ​​11(11a, 11b...) in the Precise Ephemeris schematically represent the coordinate values ​​of the navigation satellite in each epoch listed in the Precise Ephemeris. Here, the coordinate value refers to either the time or position coordinate of the navigation satellite's clock, or one of these scalar quantities.

[0070] To calculate the position where a satellite navigation receiver receives a positioning signal, the time and position coordinates of the navigation satellite's clock at time T, when the receiver measures the distance using the positioning signal, are required. However, as illustrated by the coordinate values ​​11(11a, 11b...), the precise orbital ephemeris only provides coordinate values ​​for the epoch.

[0071] The coordinate values ​​12 from the broadcast orbit ephemeris schematically represent the coordinate values ​​of the navigation satellite calculated using the broadcast orbit ephemeris.

[0072] To calculate the position where a satellite navigation receiver receives a positioning signal, the receiver needs the time and position coordinates of the navigation satellite's clock at time T, when the receiver measures the distance using the positioning signal. Since the broadcast orbit ephemeris is a function of time, the satellite navigation receiver can calculate the coordinate values ​​for any time within the validity period of the broadcast orbit ephemeris, as illustrated by coordinate value 2.

[0073] By subtracting the coordinate values ​​11(11a, 11b...) from the precise orbital ephemeris from the coordinate values ​​12 from the broadcast orbital ephemeris, we obtain the difference 13(13a, 13b...) corresponding to each epoch of the precise orbital ephemeris.

[0074] For illustrative purposes, if we extract only difference 13(13a, 13b...) and plot it on the same time series so that its magnitude can be compared, it will look like difference 14(14a, 14b...).

[0075] A function that interpolates the difference 14(14a, 14b...) along the time axis can be obtained, for example, as interpolation function 15.

[0076] Since the interpolation function 15 can calculate the function value at any time, the function value 16 at time T when the receiver measures the distance using the positioning signal can be calculated. When the function value 16 is illustrated so as to be compared with the coordinate values ​​from the precise orbital ephemeris and the broadcast orbital ephemeris, it becomes the difference 17 at time T when the receiver measures the distance using the positioning signal.

[0077] A new coordinate value 18 is obtained by subtracting the difference 17 from the coordinate value 12 based on the broadcast orbital ephemeris. This is the result of interpolating the precise orbital ephemeris using the trend of changes in the broadcast orbital ephemeris for the time point T when the receiver measures the distance using the positioning signal, and the satellite navigation receiver according to the present invention uses this to calculate the position where the positioning signal was received.

[0078] For the interpolation function 15, if the difference 14(14a, 14b...) is obtained for two time points before and after time point T, it may be used as a linear interpolation.

[0079] For the interpolation function 15, if the difference 14(14a, 14b...) is obtained for three or more time points before and after time point T, it may be used as a polynomial interpolation.

[0080] Next, I will explain the operation.

[0081] The differences 13(13a,13b...) and 14(14a,14b...) between the broadcast orbital ephemeris and the precise orbital ephemeris correspond to D(Ti) in [Equation 1] and reflect the errors included in the broadcast orbital ephemeris at time Ti.

[0082] Interpolation function 15 corresponds to F(T) in [Equation 2] and is a function that interpolates D(Ti) around time T. That is, it reflects the error contained in the broadcast orbit ephemeris around time T.

[0083] The new coordinate value 18 obtained by subtracting the difference 7 from the coordinate value 2 from the broadcast orbital ephemeris corresponds to P'(T) in [Equation 2]. By subtracting the difference 7, the error component included in the broadcast orbital ephemeris is removed. Since the trend of change in the broadcast orbital ephemeris between epochs remains, the receiver uses this P'(T) in position calculations, thereby using a precisely interpolated orbital ephemeris that takes advantage of the trend of change in the broadcast orbital ephemeris.

[0084] This improves the interpolation accuracy of the precise orbital ephemeris when processing the beginning or end of a day. A similar effect can be obtained even if the precise orbital ephemeris for some or all of the navigation satellites is missing for any reason, even if it is not the beginning or end of a day.

[0085] Furthermore, it is possible to reduce the order of the interpolation function required to obtain a similar level of interpolation accuracy even during time periods other than the beginning or end of the day. [Examples]

[0086] A second embodiment of this invention will be described in detail with reference to Figure 2.

[0087] The coordinate values ​​21(21a, 21b...) in the precise orbital ephemeris schematically represent the coordinate values ​​of the navigation satellite in each epoch described in the precise orbital ephemeris. Here, the coordinate value refers to either the time or position coordinate of the navigation satellite's clock, or one of these scalar quantities.

[0088] To calculate the position where a satellite navigation receiver receives a positioning signal, the time and position coordinates of the navigation satellite's clock at time T, when the receiver measures the distance using the positioning signal, are required. However, as illustrated by the coordinate values ​​21(21a, 21b...), the precise orbital ephemeris only provides coordinate values ​​for the epoch.

[0089] The coordinate values ​​22 from the broadcast orbit ephemeris schematically represent the coordinate values ​​of the navigation satellite calculated using the broadcast orbit ephemeris.

[0090] To calculate the position where a satellite navigation receiver receives a positioning signal, the receiver needs the time and position coordinates of the navigation satellite's clock at time T, when the receiver measures the distance using the positioning signal. Since the broadcast orbit ephemeris is a function of time, the satellite navigation receiver can calculate the coordinate values ​​for any time within the validity period of the broadcast orbit ephemeris, as illustrated by coordinate value 22.

[0091] By subtracting the coordinate values ​​21(21a,21b...) from the precise orbital ephemeris from the coordinate values ​​2 from the broadcast orbital ephemeris, we obtain the difference 23(23a,23b...) corresponding to each epoch of the precise orbital ephemeris.

[0092] For illustrative purposes, if we extract only the difference 23(23a, 23b...) and plot it on the same time series so that its magnitude can be compared, it will look like difference 24(24a, 24b...).

[0093] The function that extrapolates the difference 24(24a,24b...) in the time axis direction can be obtained, for example, as the extrapolation function 25.

[0094] Since the extrapolation function 25 allows us to calculate the function value at any given time, we can calculate the function value 26 at time T when the receiver measures the distance using the positioning signal. When the function value 26 is illustrated in a way that allows us to compare it with the coordinate values ​​from the precise orbital ephemeris and the broadcast orbital ephemeris, it becomes the difference 27 at time T when the receiver measures the distance using the positioning signal.

[0095] A new coordinate value 28 is obtained by subtracting the difference 27 from the coordinate value 22 based on the broadcast orbital ephemeris. This is the result of extrapolating the precise orbital ephemeris using the trend of changes in the broadcast orbital ephemeris for the time point T when the receiver measures the distance using the positioning signal, and the satellite navigation receiver according to the present invention uses this to calculate the position where the positioning signal was received.

[0096] For the extrapolation function 25, if the difference 14(14a, 14b...) is obtained for either the time before or after time T, that difference may be used as is.

[0097] For the extrapolation function 25, if the difference 14(14a, 14b...) is obtained for any two time points before or after time point T, it can be used as a linear approximation.

[0098] For the extrapolation function 25, if the difference 14(14a, 14b...) is obtained for three or more time points before or after time point T, it may be used as a polynomial approximation.

[0099] Next, I will explain the operation.

[0100] The differences 23(23a,23b...) and 24(24a,24b...) between the broadcast orbital ephemeris and the precise orbital ephemeris correspond to D(Ti) in [Equation 1] and reflect the errors included in the broadcast orbital ephemeris at time Ti.

[0101] Extrapolation function 25 corresponds to F(T) in [Equation 2] and is a function that approximates D(Ti) around time T. That is, it reflects the error contained in the broadcast orbit ephemeris around time T.

[0102] The new coordinate value 28 obtained by subtracting the difference 27 from the coordinate value 22 based on the broadcast orbital ephemeris corresponds to P'(T) in [Equation 2]. By subtracting the difference 27, the error component included in the broadcast orbital ephemeris is removed. Since the trend of change in the broadcast orbital ephemeris between epochs remains, the receiver uses this P'(T) in position calculations, thereby using a precisely extrapolated orbital ephemeris that takes advantage of the trend of change in the broadcast orbital ephemeris.

[0103] This improves the extrapolation accuracy of the precise orbital ephemeris when processing the beginning or end of a day. A similar effect can be obtained even if the precise orbital ephemeris for some or all of the navigation satellites is missing for any reason, even if it is not the beginning or end of a day.

[0104] Furthermore, this method allows for a reduction in the order of the extrapolation function required to achieve a similar level of extrapolation accuracy, even during time periods other than the beginning or end of the day. [Industrial applicability]

[0105] The method for calculating position in a satellite navigation system and the program for calculating position according to the present invention can be used for positioning and surveying at fixed points. Furthermore, if a precise orbital ephemeris including predictions is used, it can be widely used in positioning systems, guidance systems, and the like for moving objects. [Explanation of symbols]

[0106] 11(11a,11b...) Coordinate values ​​based on the precise orbital ephemeris. 12. Coordinate values ​​based on the broadcast orbit ephemeris. 13(13a,13b...) Difference between the precise orbital ephemeris and the broadcast orbital ephemeris. 14(14a,14b...) Difference between the precise orbital ephemeris and the broadcast orbital ephemeris. 15 Interpolation Functions 16. Function value at time point T 17 Difference at time point T 18 New coordinate values ​​at time point T 21(21a,21b...) Coordinate values ​​based on the precise orbital ephemeris. 22 Coordinate values ​​based on the broadcast orbit ephemeris 23(23a,23b...) Difference between the precise orbital ephemeris and the broadcast orbital ephemeris. 24(24a,24b...) Difference between the precise orbital ephemeris and the broadcast orbital ephemeris. 25 Extrapolation Functions 26. Function value at time point T 27 Difference at time point T 28 New coordinate values ​​at time point T

Claims

1. It receives positioning signals transmitted by multiple navigation satellites that transmit positioning signals, and measures the distance between them. In a satellite navigation receiver that calculates the position at the time of the measurement, The calculation of the position requires the time and position coordinates of each of the navigation satellites' clocks at the time of the measurement. The aforementioned satellite navigation receiver is For each of the aforementioned navigation satellites, Using the broadcast orbital ephemeris, which is information about the navigation satellite's own clock and orbit that the navigation satellite transmits superimposed on the positioning signal, the time and position coordinates of the navigation satellite's clock are calculated from the time and position coordinates of the navigation satellite. At multiple points in time for which a precise ephemeris, which is accurate information about the navigation satellite's clock and orbit, is provided, the difference between those multiple points in time is obtained by subtracting the time and position coordinates of the navigation satellite's clock according to the precise ephemeris. The result of interpolating the differences at these multiple points in time with respect to the measurement time is, By subtracting the time and position coordinates of the navigation satellite's clock at the time of the measurement, calculated using the broadcast orbital ephemeris, a new time and position coordinates for the navigation satellite are obtained. The position is calculated using these new time and position coordinates. A method for calculating position in a satellite navigation receiver, characterized by the following:

2. During the interpolation, the difference between two points in time, before and after the measurement point, for which precise orbital ephemeris are given, is linearly interpolated. A method for calculating position in a satellite navigation receiver according to claim 1, characterized in that

3. During the interpolation, the difference between three or more points in time for which precise orbital ephemerides are given, before and after the measurement point, is interpolated using polynomial interpolation. A method for calculating position in a satellite navigation receiver according to claim 1, characterized in that

4. It receives positioning signals transmitted by multiple navigation satellites that transmit positioning signals, and measures the distance between them. In a satellite navigation receiver that calculates the position at the time of the measurement, The calculation of the position requires the time and position coordinates of each of the navigation satellites' clocks at the time of the measurement. The satellite navigation receiver operates as follows: For each of the aforementioned navigation satellites, Using the broadcast orbital ephemeris, which is information about the navigation satellite's own clock and orbit that the navigation satellite transmits superimposed on the positioning signal, the time and position coordinates of the navigation satellite's clock are calculated from the time and position coordinates of the navigation satellite. At multiple points in time for which a precise ephemeris, which is accurate information about the navigation satellite's clock and orbit, is provided, the difference between those multiple points in time is obtained by subtracting the time and position coordinates of the navigation satellite's clock according to the precise ephemeris. The result of interpolating the differences at these multiple points in time with respect to the measurement time is, By subtracting the time and position coordinates of the navigation satellite's clock at the time of the measurement, calculated using the broadcast orbital ephemeris, a new time and position coordinates for the navigation satellite are obtained. The position is calculated using these new time and position coordinates. A program for calculating the position in a satellite navigation receiver, characterized by the above features.

5. During the interpolation, the difference between two points in time, before and after the measurement point, for which precise orbital ephemeris are given, is linearly interpolated. A program for calculating the position in a satellite navigation receiver according to claim 4, characterized in that

6. During the interpolation, the difference between three or more points in time for which precise orbital ephemerides are given, before and after the measurement point, is interpolated using polynomial interpolation. A program for calculating the position in a satellite navigation receiver according to claim 4, characterized in that

7. It receives positioning signals transmitted by multiple navigation satellites that transmit positioning signals, and measures the distance between them. In a satellite navigation receiver that calculates the position at the time of the measurement, The calculation of the position requires the time and position coordinates of each of the navigation satellites' clocks at the time of the measurement. The aforementioned satellite navigation receiver is For each of the aforementioned navigation satellites, Using the broadcast orbital ephemeris, which is information about the navigation satellite's own clock and orbit that the navigation satellite transmits superimposed on the positioning signal, the time and position coordinates of the navigation satellite's clock are calculated from the time and position coordinates of the navigation satellite. At one or more points in time for which a precise ephemeris, which is accurate information about the navigation satellite's clock and orbit, is provided, the difference at that one or more points in time is obtained by subtracting the time and position coordinates of the navigation satellite's clock according to the precise ephemeris. The result of extrapolating the difference at one or more time points toward the time of the measurement is, By subtracting the time and position coordinates of the navigation satellite's clock at the time of the measurement, calculated using the broadcast orbital ephemeris, a new time and position coordinates for the navigation satellite are obtained. The position is calculated using these new time and position coordinates. A method for calculating position in a satellite navigation receiver, characterized by the following:

8. In the extrapolation process, the difference at a point in time, either before or after the measurement time, for which a precise orbital ephemeris is provided, is used as is. A method for calculating position in a satellite navigation receiver according to claim 7, characterized in that

9. During the extrapolation process, the difference between two points in time, either before or after the measurement point, for which a precise orbital ephemeris is provided, is extrapolated using linear approximation. A method for calculating position in a satellite navigation receiver according to claim 7, characterized in that

10. During the extrapolation process, the difference at three or more points in time, either before or after the measurement point, for which a precise orbital ephemeris is provided, is extrapolated using polynomial approximation. A method for calculating position in a satellite navigation receiver according to claim 7, characterized in that

11. It receives positioning signals transmitted by multiple navigation satellites that transmit positioning signals, and measures the distance between them. In a satellite navigation receiver that calculates the position at the time of the measurement, The calculation of the position requires the time and position coordinates of each of the navigation satellites' clocks at the time of the measurement. The satellite navigation receiver operates as follows: For each of the aforementioned navigation satellites, Using the broadcast orbital ephemeris, which is information about the navigation satellite's own clock and orbit that the navigation satellite transmits superimposed on the positioning signal, the time and position coordinates of the navigation satellite's clock are calculated from the time and position coordinates of the navigation satellite. At one or more points in time for which a precise ephemeris, which is accurate information about the navigation satellite's clock and orbit, is provided, the difference at that one or more points in time is obtained by subtracting the time and position coordinates of the navigation satellite's clock according to the precise ephemeris. The result of extrapolating the difference at one or more time points toward the time of the measurement is, By subtracting the time and position coordinates of the navigation satellite's clock at the time of the measurement, calculated using the broadcast orbital ephemeris, a new time and position coordinates for the navigation satellite are obtained. The position is calculated using these new time and position coordinates. A program for calculating the position in a satellite navigation receiver, characterized by the above features.

12. In the extrapolation process, the difference at a point in time, either before or after the measurement time, for which a precise orbital ephemeris is provided, is used as is. A program for calculating the position in a satellite navigation receiver according to claim 11, characterized in that

13. During the extrapolation process, the difference between two points in time, either before or after the measurement point, for which a precise orbital ephemeris is provided, is extrapolated using linear approximation. A program for calculating the position in a satellite navigation receiver according to claim 11, characterized in that

14. During the extrapolation process, the difference at three or more points in time, either before or after the measurement point, for which a precise orbital ephemeris is provided, is extrapolated using polynomial approximation. A program for calculating the position in a satellite navigation receiver according to claim 11, characterized in that

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