GNSS receiver and method for estimating ionospheric delay.

Abstract

To provide a GNSS receiver and an ionosphere delay amount estimation method that calculate the ionosphere delay amount of a satellite transmitting only one wave with a small amount of processing.SOLUTION: A method includes calculating an ionosphere delay amount I of an L1 wave of a two-wave satellite, which is a satellite transmitting L1 and L2 waves (step 1). The method also includes analyzing the relationship between the ionosphere delay amount I of the L1 wave of each two-wave satellite and an elevation angle θ of each two-wave satellite using a single regression analysis or the like, and calculating and setting an ionosphere delay amount estimation function I=F(θ), which represents the relationship between both (step 2). The method further includes applying the elevation angle θ of a one-wave satellite, which is a satellite transmitting only the L1 wave, to the ionosphere delay amount estimation function I=F(θ) to estimate the ionosphere delay amount I of the one-wave satellite (step 3).SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] This invention relates to a technique for estimating ionospheric delay in a GNSS receiver. [Background technology]

[0002] In GNSS positioning, correcting for ionospheric delay—the delay caused by the decrease in propagation speed in the ionosphere—is crucial for achieving high-precision positioning. Hereafter, the ionospheric delay will be calculated using the distance obtained by multiplying the delay time in the ionosphere of the radio wave by the speed of light. Now, GNSS satellites include those that transmit only one L1 wave (hereinafter referred to as "single-wave satellites") and those that transmit two waves, an L2 wave with a different frequency from the L1 wave and an L1 wave (hereinafter referred to as "dual-wave satellites"). Furthermore, in GNSS receivers, the code pseudo-distance, which is the distance between the satellite and the GNSS receiver calculated from the propagation time of the positioning codes (PRN code, C / A code) transmitted by the satellite, is used for positioning. The following techniques are known for correcting the error in the ionospheric delay amount of this code pseudo-distance. In other words, a known technique for correcting the error in the ionospheric delay of the code pseudodistance for a single-wave satellite involves setting various parameters in the ionospheric delay calculation formula based on the Klobuchar model, which represents the relationship between local time (the time at the GNSS receiver position) and the ionospheric delay using a half-cosine wave, as shown in Figure 5, calculating the ionospheric delay, and then correcting the code pseudodistance obtained from the propagation time of the positioning code by the calculated ionospheric delay (for example, Non-Patent Document 1).

[0003] The parameters used in the formula for calculating the ionospheric delay based on the Klobuchar model include correction coefficients received from the satellite in navigation messages, magnetic latitude, satellite elevation angle, and local time. Furthermore, as a technique to correct the error in the ionospheric delay amount of the code pseudo-distance for dual-wave satellites, the frequency of the L1 wave is set to f , , , , L2 , , L1 ,

[0005] , , , , , , L1 , , L1 , ,

[0006] , , , , Let the frequency of the L2 wave be f L2 , P L1 is the code pseudorange obtained from the propagation time of the positioning code for the L1 wave, and P L2 is the code pseudorange obtained from the propagation time of the positioning code for the L2 wave. There is also a known technique for obtaining the code pseudorange P in which the error of the ionospheric delay amount is corrected by Equation 1 called ionosphere-free linear combination (for example, Patent Document 1).

[0004] γ(=(f L1 / f L2 ) 2 ) P=(P L2 -γ·P L1 ) / (1 - γ)...(Equation 1) Also, as a technique for correcting the error of the ionospheric delay amount of the code pseudorange for a single-frequency satellite, for each of the dual-frequency satellites, the ionospheric delay amount of the L1 wave is obtained by Equation 2 using the L1 wave and the L2 wave, and I L1 =(P L1 -P L2 ) / (1 - γ)...(Equation 2) Based on the ionospheric delay amount I L1 obtained by Equation 2, a correction coefficient for correcting the calculation formula of the ionospheric delay amount based on the Klobuchar model is obtained so that the calculation result is consistent. For a single-frequency satellite, the ionospheric delay amount is calculated using the calculation formula of the ionospheric delay amount corrected by the correction coefficient obtained by averaging the correction coefficients obtained for each dual-frequency satellite, and the code pseudorange obtained from the propagation time of the positioning code is corrected by the calculated ionospheric delay amount. There is also a known technique (for example, Patent Document 2).

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0006] [Non-Patent Document 1] Liu Xiu, "Research on Ionospheric Modeling Using Single-Frequency Pseudo-Distance Single-Person Positioning," [online], [Retrieved November 10, 2022], Internet <URL https: / / www.google.com / url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjsoICX3qL7AhUeBbkGHXvKDqIQFnoECBQQAQ&url=https%3A%2F%2Foacis.repo.nii.ac.jp%2F%3Faction%3Drepository_action_common_download%26item_id%3D1028%26item_no%3D1%26attribute_id%3D20%26file_no%3D1&usg=AOvVaw0iEDCYazgk1kt5wehSWoon> [Overview of the project] [Problems that the invention aims to solve]

[0007] The ionospheric delay calculated using the formula based on the Klobuchar model described above has low accuracy, resulting in significant errors in positioning measurements. On the other hand, by using the L1 and L2 waves of the aforementioned two-wave satellite to calculate the ionospheric delay of the L1 wave and correcting the ionospheric delay calculation formula based on the Klobuchar model, it is possible to estimate the ionospheric delay of a single-wave satellite with relatively good accuracy. However, this technology is computationally intensive because it requires obtaining and setting parameters for the ionospheric delay calculation formula based on the Klobuchar model, and performing calculations based on that formula, for both dual-wave satellites and single-wave satellites. This hinders real-time positioning.

[0008] Therefore, the present invention aims to accurately estimate the ionospheric delay amount for a satellite transmitting only one signal in a GNSS receiver using relatively low-load processing. [Means for solving the problem]

[0009] To achieve the above objective, the present invention provides a GNSS receiver for satellite positioning, which includes a dual-wave satellite that transmits both a first wave, which is a radio signal with a first frequency carrier wave frequency and a second wave, which is a radio signal with a second frequency different from the first frequency carrier wave frequency, and a single-wave satellite that transmits only the first wave, and for each of the multiple dual-wave satellites, the ionospheric delay amount of the first wave transmitted by the dual-wave satellite is determined using the first wave and second wave received from the dual-wave satellite. The system comprises: a two-wave satellite delay estimation means for estimating the ionospheric delay of the first wave of each of the two satellites estimated by the two-wave satellite delay estimation means; a correspondence calculation means for calculating a function that associates the elevation angle with the ionospheric delay based on the relationship between the ionospheric delay of the first wave of each of the two satellites estimated by the two-wave satellite delay estimation means and the elevation angle of the two satellites estimated by the two-wave satellite delay estimation means; and a one-wave satellite delay estimation means for estimating the ionospheric delay associated with the elevation angle of the one-wave satellite by the function as the ionospheric delay of the first wave of the one-wave satellite.

[0010] Here, such a GNSS receiver may be configured such that the corresponding calculation means calculates a linear equation as the function that represents the relationship between the elevation angle and the ionospheric delay, obtained by simple linear regression analysis on a data set whose elements are the ionospheric delay of the first wave of the two satellites estimated by the two-wave satellite delay estimation means, and the elevation angle of the two satellites estimated by the two-wave satellite delay estimation means, which are the elements of the ionospheric delay of the first wave.

[0011] Alternatively, in such a GNSS receiver, the function calculated by the corresponding calculation means may define an ionospheric delay amount corresponding to the elevation angle within each range of elevation angles. Furthermore, the GNSS receiver may be equipped with a correction means that, if the ionospheric delay amount of the first wave of the two satellites estimated by the two-wave satellite delay amount estimation means differs by a predetermined level or more from the reference ionospheric delay amount, which is the ionospheric delay amount associated with the elevation angle of the two satellites estimated by the two-wave satellite delay amount estimation means by the function, corrects the ionospheric delay amount of the first wave of the two satellites estimated by the two-wave satellite delay amount estimation means so that the difference between it and the reference ionospheric delay amount becomes smaller.

[0012] According to these GNSS receivers, the accuracy of estimating the ionospheric delay of the first wave of a single satellite can be improved by a relatively low-intensity process that only involves estimating the ionospheric delay of the first wave of a two-wave satellite, determining the correspondence between the elevation angle and the ionospheric delay, and then calculating the ionospheric delay corresponding to the elevation angle for a single satellite.

[0013] Furthermore, the present invention also includes a dual-wave satellite delay estimation means that estimates the ionospheric delay amount of the first wave transmitted by a dual-wave satellite using the first wave and the second wave received from the dual-wave satellite, wherein a satellite that transmits both a first wave, which is a radio signal with a first frequency, and a second wave, which is a radio signal with a second frequency different from the first frequency, is defined as a dual-wave satellite, and a satellite that transmits only the first wave is defined as a single-wave satellite, and for each of a plurality of dual-wave satellites, the ionospheric delay amount of the first wave transmitted by the dual-wave satellite is determined using the first wave and the second wave received from the dual-wave satellite, and the dual-wave satellite The GNSS receiver also includes a correspondence calculation means that calculates a function that associates the elevation angle with the ionospheric delay amount based on the relationship between the ionospheric delay amount of the first wave of each of the two satellites estimated by the stellar delay amount estimation means and the combination of elevation angle and azimuth angle of the two satellites estimated by the two satellite delay amount estimation means, and a one-wave satellite delay amount estimation means that estimates the ionospheric delay amount associated with the combination of elevation angle and azimuth angle of the one-wave satellite by the function as the ionospheric delay amount of the first wave of the one-wave satellite.

[0014] With such a GNSS receiver, the accuracy of estimating the ionospheric delay of the first wave of a single satellite can be improved through relatively low-intensity processing, which involves estimating the ionospheric delay of the first wave of a two-wave satellite, determining the correspondence between the elevation angle and azimuth angle combination and the ionospheric delay, and then determining the ionospheric delay corresponding to the elevation angle and azimuth angle combination for a single satellite. [Effects of the Invention]

[0015] As described above, according to the present invention, a GNSS receiver can accurately estimate the ionospheric delay for a satellite that transmits only one wave using relatively low-load processing. [Brief explanation of the drawing]

[0016] [Figure 1] This is a block diagram showing the configuration of a GNSS receiver according to an embodiment of the present invention. [Figure 2] This figure shows the elevation angle and azimuth angle used in embodiments of the present invention. [Figure 3] This figure shows an example of a simple linear regression performed according to an embodiment of the present invention. [Figure 4] This figure shows the flow of the ionospheric delay correction process performed in an embodiment of the present invention. [Figure 5] This figure shows a well-known Klobuchar model. [Modes for carrying out the invention]

[0017] Embodiments of the present invention will be described below. Figure 1 shows the configuration of the GNSS receiver according to this embodiment. As shown in the figure, the GNSS receiver comprises an antenna 1, a radio unit 2, a received signal processing unit 3, a pseudo-distance calculation unit 4, an ionospheric delay correction unit 5, a positioning calculation unit 6 that calculates the current position of the GNSS receiver, an estimation function setting unit 7, and a satellite parameter management unit 8. The wireless unit 2 receives radio waves (L1 and L2 waves) transmitted by each satellite via the antenna 1 and sends the received signals to the received signal processing unit 3. The received signal processing unit 3 controls the radio unit 2 to acquire and track receivable radio waves, detect the phase of the carrier wave of the tracked radio wave, and measure the propagation time of the positioning code (PRN code, C / A code) carried by the tracked radio wave between the satellite and the GNSS receiver. Furthermore, the received signal processing unit 3 decodes the navigation message carried by the tracked radio waves and sends it to the satellite parameter management unit 8. The satellite parameter management unit 8 calculates and manages various satellite parameters such as the position, elevation angle, and azimuth angle of each satellite based on the satellite orbit information and satellite position information indicated by the navigation message received from the received signal processing unit 3, the internal clock of the GNSS receiver, and the current position of the GNSS receiver calculated by the positioning calculation unit 6.

[0018] As described above, a satellite that transmits only one L1 wave is designated as a single-wave satellite, and a satellite that transmits two waves, an L2 wave with a different frequency from the L1 wave and an L1 wave, is designated as a dual-wave satellite. The pseudo-distance calculation unit 4 calculates the code pseudo-distance, which is the distance between the satellite and the GNSS receiver, from the propagation time of the positioning code carried by the L1 wave for single-wave satellites that are tracking the radio waves. For dual-wave satellites, the unit calculates the code pseudo-distance, which is the distance between the satellite and the GNSS receiver, from the propagation time of the positioning code carried by the L1 wave, and also calculates the code pseudo-distance, which is the distance between the satellite and the GNSS receiver, from the propagation time of the positioning code carried by the L2 wave.

[0019] The ionospheric delay correction unit 5 calculates a code pseudo-distance P for the two satellites tracking the radio waves by correcting the error in the ionospheric delay amount using Equation 3, and sends it to the positioning calculation unit 6. γ(=(f L1 / f L2 ) 2 ) P=(P L2 -γ·P L1 ) / (1-γ)...(Equation 3) However, f L1 The frequency of the L1 wave is f L2 The frequency of the L2 wave is P L1 For the L1 wave, the pseudo-code distance is calculated from the propagation time of the positioning code, P L2This represents the pseudo-code distance calculated from the propagation time of the positioning code for the L2 wave.

[0020] However, the ionospheric delay correction unit 5 may also smooth the code pseudo-distance P obtained by Equation 3 using a Hatch filter or the like, and then send it to the positioning calculation unit 6 after the change in pseudo-distance obtained from the carrier phase detected by the receiving processing unit. Furthermore, the ionospheric delay correction unit 5 also corrects the error in the ionospheric delay amount of the code pseudo-distance, which is calculated from the propagation time of the positioning code for the L1 wave, for the single-wave satellite that is tracking the radio waves, and sends the corrected code pseudo-distance to the positioning calculation unit 6. Details of the correction of the error in the ionospheric delay amount of the code pseudo-distance for this single-wave satellite will be described later.

[0021] The positioning calculation unit 6 then calculates the current position of the GNSS receiver using the code pseudo-distance of each satellite, which has been corrected by the ionospheric delay correction unit 5 for errors in the ionospheric delay amount, and various satellite parameters such as the position, elevation angle, and azimuth of each satellite, which are managed by the satellite parameter management unit 8. The following details the correction of the error in the ionospheric delay amount of the code pseudo-distance for the single-wave satellite mentioned above. The estimation function setting unit 7 sets the ionospheric delay amount I of the L1 wave for each of the two satellites tracking the radio waves at each point in time. L1 This is calculated using Equation 4. γ(=(f L1 / f L2 ) 2 ) I L1 =(P L1 -P L2 ) / (1-γ)...(Equation 4) Here, in equation 4, f L1 The frequency of the L1 wave is f L2 The frequency of the L2 wave is P L1 For the L1 wave, the code pseudo-distance is calculated from the propagation time of the positioning code, P L2 This represents the pseudo-code distance calculated from the propagation time of the positioning code for the L2 wave.

[0022] Alternatively, the estimation function setting unit 7 determines the ionospheric delay amount I of the L1 wave for each of the two satellites tracking the radio waves at each point in time. L1 The following calculation is performed: In other words, the provisional ionospheric delay amount of the L1 wave of the two-wave satellite is calculated from the code pseudo-distance calculated by the pseudo-distance calculation unit 4 using Equation 5. γ(=(f L1 / f L2 ) 2 ) Ip L1、k =(P L1、k -P L2、k ) / (1-γ)...(Equation 5) Here, in equation 5, P L1、t At time t, the pseudo-code distance for the L1 wave is calculated from the propagation time of the positioning code, P L2、t At time t, the pseudo-code distance for the L2 wave is calculated from the propagation time of the positioning code, and the IP L1、t This represents the hypothetical ionospheric delay of the L1 wave at time t, calculated using the code pseudodistance.

[0023] Furthermore, the change in the provisional ionospheric delay amount of the L1 wave is calculated using equation (6) from the carrier phase of the L1 wave and the carrier phase of the L2 wave detected by the received signal processing unit 3. dIφ L1、k =Iφ L1、k -Iφ L1、k-1 ...(Formula 6) Here, in equation 6, Iφ L1、t dIφ represents the hypothetical ionospheric delay of the L1 wave, as indicated by the carrier phase at time t. L1、t This represents the change in the hypothetical ionospheric delay of the L1 wave at time t.

[0024] Here, since the carrier phase noise is small, if we ignore it, λ L1、 The wavelength of the L1 wave is λ L2、 The wavelength of the L2 wave is φ L1、t The phase of the L1 wave at time t is φ L2、t The phase of the L2 wave at time t is N L2 The unknown integer ambiguity of the L1 wave is N L2 As representing the unknown integer ambiguity of the L2 wave, Iφ L1、t ={λ L1 ( L1、t -N L1 )-λ L2 ( L2、t -N L2 )} / (1-γ) This can be expressed as, and while cycle slip does not occur, N L1 , N L2 Since it remains constant dIφ L1、k =Iφ L1、k -Iφ L1、k-1 ={λ L1 ( φ L1、k -φ L1、k-1 )-λ L2 ( L2、k -φ L2、k-1 )} / (1-γ) N L1 , N L2 Even if you don't know, dIφ L1、k It is possible to find this.

[0025] Then, at each point in time, the ionospheric delay I of the L1 wave is determined by equation 7, which represents the Hatch filter. I L1.k ={(M-1) / M)}(I L1.k-1 +dIφ L1.k )+(Ip L1.k / M)...(Formula 7) Here, in equation 7, L1.t represents the ionospheric delay of the L1 wave determined at time t, and M is the averaging constant.

[0026] The ionospheric delay amount I of the L1 wave was determined in this manner. L1.t This is the hypothetical L1 wave ionospheric delay Ip obtained using the code pseudodistance. L1.t This is the change in the ionospheric delay of the hypothetical L1 wave, dIφ, obtained using the carrier phase. L1.t This is the result of smoothing using the determined ionospheric delay amount I of the L1 wave. L1.t This is the hypothetical L1 wave ionospheric delay Ip obtained using the code pseudodistance. L1.t This removes the effects of the relatively large noise in the L1 and L2 waves that appear in the signal.

[0027] Note that the averaging constant M is a constant that determines the degree of this smoothing. Next, the estimation function setting unit 7 sets an ionospheric delay amount estimation function based on the relationship between the ionospheric delay amount I of the L1 wave determined for each dual-frequency satellite as described above L1 and the elevation angle of each dual-frequency satellite managed by the satellite parameter management unit 8. Here, as shown in FIGS. 2a and 2b, the elevation angle θ is the angle in the vertical direction with respect to the horizontal plane of the satellite ST as seen from the position CP of the GNSS receiver. The ionospheric delay amount estimation function is set as follows, for example. Now, let the elevation angle of the dual-frequency satellite i be θi, and the ionospheric delay amount I obtained for the dual-frequency satellite i L1 be Ii. Let θi represent the value of θ for the i-th data, and Ii represent the value of I for the i-th data, and a data group of (θ, I) is set. Then, by performing a simple regression analysis shown in Equation 8 of the data group, a relational expression based on a linear expression of the variable I and the variable θ is calculated, and set as the ionospheric delay amount estimation function I = F(θ).

[0028]

Equation

[0029] Here, as shown in FIG. 3, the relational expression I = F(θ) set as the ionospheric delay amount estimation function in this way is a linear expression that minimizes the sum of the squares of the errors between Ii and F(θi). Returning to FIG. 1, the ionospheric delay correction unit 5 corrects the error of the ionospheric delay amount of the code pseudo-range for each single-frequency satellite that is tracking the radio wave as follows. That is, first, the ionospheric delay correction unit 5 acquires the elevation angle managed by the satellite parameter management unit 8 of the single-frequency satellite. Then, using the acquired elevation angle of the single-wave satellite as the value of θ, the ionospheric delay I of the single-wave satellite is calculated using the set ionospheric delay estimation function. Therefore, when I=F(θ) as shown in Figure 3 is set, and an elevation angle of θx is acquired, the ionospheric delay Ix at position X is obtained as the ionospheric delay I.

[0030] Then, the calculated ionospheric delay I is the ionospheric delay I of the L1 wave of the 1-wave satellite. L1 It is estimated that the ionospheric delay amount I L1 The pseudo-code distance P is calculated from the propagation time of the positioning code carried by the L1 wave in minutes. L1 This value is corrected to obtain the code pseudo-distance P, and sent to the positioning calculation unit 6.

[0031] However, the ionospheric delay correction unit 5 may also smooth the corrected code pseudo-distance P using a change in pseudo-distance determined from the carrier phase detected by the receiving processing unit by applying a Hatch filter or the like, and then send it to the positioning calculation unit 6. Here, the characteristic feature of the GNSS receiver processing in this embodiment is the processing part that estimates the ionospheric delay I of the single satellite, and the flow of this processing part is summarized in Figure 4. As shown in the diagram, in this flow, first, the ionospheric delay amount I of the L1 wave of each of the two satellites tracking the radio waves is calculated. L1 Calculate (Step 1). Next, the ionospheric delay amount I of the L1 wave of each of the two satellites L1 Step 2 involves analyzing the relationship between the elevation angle θ of each of the two satellites and calculating and setting an ionospheric delay estimation function I=F(θ) that represents the relationship between the two. Then, the elevation angle θ of the single-wave satellite is applied to the ionospheric delay estimation function I=F(θ), and the ionospheric delay I of the single-wave satellite is obtained. L1 Estimate (Step 3). Embodiments of the present invention have been described above. Here, according to the analysis using the GNSS measurement values for 24 hours at the Ishigaki Island electronic reference point conducted by the present inventors, in the positioning using the ionospheric delay amount of the first-wave satellite estimated based on the Klobuchar model, the maximum value of the offset error with respect to the true value was about 5.7 m. On the other hand, in the positioning using the ionospheric delay amount of the first-wave satellite estimated by the configuration shown in the above embodiment, the maximum value of the offset error with respect to the true value was about 1.1 m. It was confirmed that the estimation accuracy of the ionospheric delay amount was greatly improved by the application of this embodiment.

[0032] Therefore, according to this embodiment, by estimating the ionospheric delay amount of the L1 of the second-wave satellite and obtaining the ionospheric delay amount estimation function I = F(θ) representing the correspondence between the elevation angle and the ionospheric delay amount, and calculating the ionospheric delay amount according to the ionospheric delay amount estimation function I = F(θ) from the elevation angle for the first-wave satellite, it is possible to improve the estimation accuracy of the ionospheric delay amount of the first wave of the first-wave satellite by a relatively low-load process.

[0033] Here, in the above embodiment, the linear equation obtained by simple regression analysis was set as the ionospheric delay amount estimation function I = F(θ). However, the function to be set as the ionospheric delay amount estimation function I = F(θ) is the correspondence between the elevation angle θ and the ionospheric delay amount I obtained from the elevation angle θ of the second-wave satellite and the ionospheric delay amount I obtained for the second-wave satellite. L1 Any function may be used as long as it represents the correspondence.

[0034] For example, as the ionospheric delay amount estimation function I = F(θ), for each elevation angle range divided every predetermined angle (for example, 5 degrees), the ionospheric delay amount I corresponding to the elevation angle within the elevation angle range. L1 A function representing etc. may be used. In this case, as the ionospheric delay amount I corresponding to the elevation angle within the elevation angle range, in the linear equation obtained by simple regression analysis as described above, the ionospheric delay amount I corresponding to the elevation angle at the center of the elevation angle range, or the ionospheric delay amounts I obtained for each of the two second-wave satellites for the elevation angles within the elevation angle range. L1 The value at which the squared error is minimized with respect to I, or the median value of the ionospheric delay amounts I obtained for each of the two second-wave satellites for the elevation angles within the elevation angle range, etc. can be used.

[0035] Furthermore, the above describes the ionospheric delay estimation function as follows: ionospheric delay I with respect to elevation angle θ. L1 We defined a function I=F(θ) that determines the ionospheric delay amount I for a given combination of elevation angle θ and azimuth angle φ. L1 You may also define a function I = F(θ, φ) that determines this. Here, the azimuth angle φ is the angle measured from north to east of satellite ST as seen from the GNSS receiver position CP, as shown in Figures 2a and 2c. In this case, the ionospheric delay estimation function I=F(θ, φ) is set, for example, as follows, using the ionospheric delay I of the L1 wave determined for each of the two satellites and the elevation angle and azimuth angle of each of the two satellites managed by the satellite parameter management unit 8. Now, let's define the elevation angle of satellite i as θi, the azimuth angle of satellite i as φi, and the ionospheric delay amount I calculated for satellite i. L1 Let Ii be the value of θ for the i-th data point, φi be the value of φ for the i-th data point, and Ii be the value of I for the i-th data point. Thus, we set up a data set of (θ, φ, I).

[0036] Then, using the multiple regression analysis shown in Equation 9 of the data set, a linear relationship is calculated between the variable I and the combination of variables θ and φ, and this is set as the ionospheric delay estimation function I=F(θ, φ).

[0037]

number

[0038] By considering the azimuth angle in addition to the elevation angle in this way, we can expect to further improve the accuracy of estimating the ionospheric delay I of a single-wave satellite. Furthermore, in the above embodiments, the ionospheric delay estimation function F, such as I=F(θ) or I=F(θ,φ), is used to determine the ionospheric delay I of the L1 wave of a single-wave satellite. L1Although it was used only for estimating the ionospheric delay and calculating the code pseudo-distance P of a single-wave satellite corrected for errors in ionospheric delay, the ionospheric delay estimation function was used for the ionospheric delay I of the L1 wave of a two-wave satellite. L1 It may also be used for estimating the distance and for calculating the code pseudo-distance P of a dual-wave satellite after correcting for errors in ionospheric delay.

[0039] For example, the ionospheric delay I calculated using Equation 4 for the L1 wave of a dual-wave satellite is the ionospheric delay I of a dual-wave satellite obtained from the ionospheric delay estimation function F. L1 If it differs by more than a predetermined level, the ionospheric delay amount I calculated by Equation 4 L1 The ionospheric delay I is obtained from the ionospheric delay estimation function F. L1 Correction is made to the ionospheric delay amount I calculated using Equation 4. L1 The ionospheric delay I is obtained from the ionospheric delay estimation function F. L1 You can also correct it in a direction that approaches the desired value.

[0040] And when such a correction is made, the corrected ionospheric delay amount I can be calculated without using Equation 3. L1 The code pseudo-distance P of the two satellites will be calculated using this method, correcting for errors in the ionospheric delay. Furthermore, similar to what was shown above for the L1 wave, the ionospheric delay amount I of the L2 wave is also shown for the L2 wave. L2 To estimate the ionospheric delay, we set an ionospheric delay estimation function G of I=G(θ) or I=G(θ,φ), and the ionospheric delay I of the L2 wave of the dual-wave satellite. L2 It may also be used for estimating the distance and for calculating the code pseudo-distance P of a dual-wave satellite after correcting for errors in ionospheric delay.

[0041] For example, for the L2 wave of a dual-wave satellite, P in Equation 4 L1 and P L2 The ionospheric delay amount I can be obtained using the L2 wave delay calculation formula, which is the formula with the terms swapped. L2 However, the ionospheric delay I of the two satellites can be obtained from the ionospheric delay estimation function G. L2 If it differs by a certain level or more, the ionospheric delay amount I obtained by the above L2 wave delay calculation formula is L2 The ionospheric delay I is obtained from the ionospheric delay estimation function G. L2Correction is made, or the ionospheric delay amount I obtained by the above L2 wave delay calculation formula is L2 The ionospheric delay I is obtained from the ionospheric delay estimation function G. L2 You can adjust it to move closer to the target.

[0042] And when such a correction is made, the corrected ionospheric delay amount I can be calculated without using Equation 3. L2 The code pseudo-distance P of the two satellites will be calculated using this method, correcting for errors in the ionospheric delay. [Explanation of symbols]

[0043] 1... Antenna, 2... Wireless unit, 3... Received signal processing unit, 4... Pseudo-distance calculation unit, 5... Ionospheric delay correction unit, 6... Positioning calculation unit, 7... Estimation function setting unit, 8... Satellite parameter management unit.

Claims

1. A GNSS receiver for satellite positioning, A satellite that transmits both a first wave, which is a radio signal with a first frequency carrier wave frequency, and a second wave, which is a radio signal with a second frequency different from the first frequency carrier wave frequency, is defined as a two-wave satellite, and a satellite that transmits only the first wave is defined as a one-wave satellite. A two-wave satellite delay estimation means estimates the ionospheric delay of the first wave transmitted by a multiple two-wave satellite using the first wave and the second wave received from the two-wave satellite. Correspondence calculation means calculates a function that associates the elevation angle with the ionospheric delay amount, based on the relationship between the ionospheric delay amount of the first wave of each of the two satellites estimated by the two satellite delay amount estimation means and the elevation angle of the two satellites estimated by the two satellite delay amount estimation means. A GNSS receiver characterized by having a single-wave satellite delay estimation means that estimates the ionospheric delay amount, which is associated with the elevation angle of the single-wave satellite by the function, as the ionospheric delay amount of the first wave of the single-wave satellite.

2. A GNSS receiver according to claim 1, The corresponding calculation means is characterized by calculating a linear equation as the function that represents the relationship between the elevation angle and the ionospheric delay, obtained by performing a simple linear regression analysis on a data set of data whose elements are the ionospheric delay of the first wave of the two satellites estimated by the two-wave satellite delay estimation means and the elevation angle of the two satellites estimated by the two-wave satellite delay estimation means.

3. A GNSS receiver according to claim 1, The GNSS receiver is characterized in that the function calculated by the corresponding calculation means defines an ionospheric delay amount corresponding to the elevation angle within each range of elevation angles.

4. A GNSS receiver according to claim 1, 2, or 3, A GNSS receiver characterized by having a correction means that corrects the ionospheric delay amount of the first wave of a two-wave satellite estimated by the two-wave satellite delay amount estimation means so that the difference between the first wave ionospheric delay amount of the two-wave satellite estimated by the two-wave satellite delay amount estimation means and the reference ionospheric delay amount, which is the ionospheric delay amount associated with the elevation angle of the two-wave satellite estimated by the two-wave satellite delay amount estimation means by the function, to a predetermined level or more.

5. A GNSS receiver for satellite positioning, A satellite that transmits both a first wave, which is a radio signal with a first frequency carrier wave frequency, and a second wave, which is a radio signal with a second frequency different from the first frequency carrier wave frequency, is defined as a two-wave satellite, and a satellite that transmits only the first wave is defined as a one-wave satellite. A two-wave satellite delay estimation means estimates the ionospheric delay of the first wave transmitted by a multiple two-wave satellite using the first wave and the second wave received from the two-wave satellite. The two-wave satellite delay estimation means estimates the ionospheric delay amount of the first wave of each of the two satellites, and the correspondence calculation means calculates a function that associates the elevation angle with the ionospheric delay amount based on the relationship between the ionospheric delay amount of the first wave and the combination of elevation angle and azimuth angle of the two satellites estimated by the two-wave satellite delay estimation means. A GNSS receiver characterized by having a single-wave satellite delay estimation means that estimates the ionospheric delay amount, which is associated with a combination of elevation angle and azimuth angle of the single-wave satellite by the aforementioned function, as the ionospheric delay amount of the first wave of the single-wave satellite.

6. A method for estimating the ionospheric delay in a GNSS receiver that performs satellite positioning, A satellite that transmits both a first wave, which is a radio signal with a first frequency carrier wave frequency, and a second wave, which is a radio signal with a second frequency different from the first frequency carrier wave frequency, is defined as a two-wave satellite, and a satellite that transmits only the first wave is defined as a one-wave satellite. For each of a plurality of two-wave satellites, a two-wave satellite delay estimation step is performed to estimate the ionospheric delay amount of the first wave transmitted by the two-wave satellite using the first wave and the second wave received from the two-wave satellite. A correspondence calculation step is performed to calculate a function that associates the elevation angle with the ionospheric delay amount, based on the relationship between the ionospheric delay amount of the first wave of each of the two satellites estimated in the two-wave satellite delay amount estimation step and the elevation angle of the two satellites estimated in the two-wave satellite delay amount estimation step. A method for estimating ionospheric delay, characterized by comprising: a single-wave satellite delay estimation step, which estimates the ionospheric delay amount, which is associated with the elevation angle of the single-wave satellite by the function described above, as the ionospheric delay amount of the first wave of the single-wave satellite.

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