JP5550332B2 - Electron density estimation apparatus and electron density estimation method - Google Patents

Description

  The present invention relates to an electron density estimation apparatus and an electron density estimation method for estimating an ionospheric electron density distribution of a passage route by a plurality of different frequency signals transmitted from a satellite.

  Signals transmitted from satellites such as the satellite navigation system “Galileo”, GPS (Global Positioning System), and QZSS (Quasi Zenith Satellite System) are used for positioning observation points on the earth. . It is known that the pseudo-range difference between multiple frequency signals broadcast by these satellites is related to the number of electrons on the radio wave propagation path.

  A signal transmitted from the satellite toward the ground causes a propagation delay when passing through the ionosphere. This ionospheric propagation delay amount depends on the frequency of the propagated signal. Therefore, by receiving a plurality of frequency signals from the satellite, the total number of electrons (TEC: Total Electron Content) in the signal passing path can be obtained. When estimating the total number of electrons on the radio wave propagation path, a method using the pseudorange (code distance) difference depending on the transmission / reception times of multiple frequency signals or the difference in carrier phase pseudorange (phase distance) of multiple frequencies A method of using is known.

  Non-Patent Document 1 and Non-Patent Document 2 describe an IRI (International Reference Ionosphere) model that is an electron density model function in the ionosphere. Furthermore, Non-Patent Document 4 describes a Gallagher model that is also one of ionospheric electron density model functions. TEC can also be obtained by calculation using these model functions.

  Non-Patent Document 5 and Non-Patent Document 6 describe three-dimensional electron density estimation using satellite TEC by a tomographic method, and an algebraic reconstruction method called MART (Multiplicative Algebraic Reconstruction Technique) is applied. Yes. On the other hand, Non-Patent Document 7 describes electron density estimation by tomographic reconstruction using GSVD (Generalized Single Value Decomposition).

  Non-Patent Document 8 and Non-Patent Document 9 describe electron density calculation in which the ionosphere is regarded as a thin layer of spherical nuclei. Further, Non-Patent Document 10 describes a case where the electron density distribution in the three-dimensional direction is calculated in the height direction.

Dieter Biritza: “International Reference Ionsphere 2000”, Radio. Science, Vol. 36, Number 2, PP261-275, March / April, 2001 Dieter Bilitza, et, al. ,: “International Reference Ionsphere 1990”, November, 1990. A. Kompathy: 'Global Ionospheric Total Electro Mapping Mapping Using the Global Positioning System', UNB, Technical Report No. 188, Sep. 1997. Gallagher, D.C. L. , P.M. D. Craven, and R.M. H. Commfort, Global core plasma model, J. MoI. Geophys. Res. 105, A8, 18, 819-18, 833, 2000. Raymund, T .; D. Austin, J .; R. Franke, S .; J. et al. Liu, C .; H. Klobuchar, J .; A. , And Stalker, J .; ,: “Application of Computerized Tomography to the Investi- tion of Ionospheric Structures”, Radio Sci. 25 (5), 771-789, 1990. Stefan Schluer, et al. : “Monitoring the 3 Dimensional Ionospheric Electron Distribution based on GPS Measurements” K. Bhuyan, et al: “Tomographic structure of the Ionosphere using generalized single value decomposition”, Current Sci. , Vol 1.83, No. 9, 10 Nov. , 2002. Otsuka, Y. et al. , Et. al. : "A new technique for mapping of total electro content using GPS network in Japan," Earth Planets Space, 111-120, 2001. Ma, G .; , And T. Maruyama (2003), Derivation of TEC and estimation of instrumental biases from GEONET in Japan, Ann. Geophys. , 21, 2083-2093. Igarashi Kurayoshi, Saito Akinori, Otsuka Yuichi: “Comparative Analysis of TEC Derived from Standard Ionosphere Model (IRI) and TEC Observed with GPS Receiver Network”, 1st Symposium on the Use and Impact of the Ionosphere, pp24 -1-8, 2003.

  However, the methods described in Non-Patent Document 5 and Non-Patent Document 6 have a disadvantage that they can be applied only to a limited space region because the number of observed satellites is limited. In particular, the technique described in Non-Patent Document 5 uses a spatial average, and a valley of electron density in a specific height direction that the ionosphere has (part where the density between the E layer and the F layer becomes small). It is impossible to capture changes in the ionosphere height direction. Non-Patent Document 6 does not describe spatial averaging.

  Since the methods described in Non-Patent Document 8 and Non-Patent Document 9 calculate the electron density by regarding the ionosphere as a thin layer of a spherical nucleus as described above, it is possible to know the distribution in the three-dimensional height direction. Can not. Non-Patent Document 10 calculates the electron density distribution in the three-dimensional direction in the height direction, but does not refer to the spread in the horizontal direction, and obtains the electron density in the space with the spread in the latitude and longitude directions. Not. For these reasons, in the conventional literature, a method of handling a space portion that cannot be observed by a satellite such as GPS is insufficient.

  That is, the conventional technique cannot fully estimate the three-dimensional ionospheric electron density distribution. Since the technique in the prior art estimates the electron density by performing a spatial average, there are cases where it is determined that even a radio wave that normally passes is reflected. In addition, when the difference between the estimated space and other spaces is large, discontinuity occurs in the spatial electron density distribution change. As described above, the conventional method has a problem that a large error occurs when the radio wave propagation path is estimated using the electron density change rate as a result of the discontinuity in the electron density change.

  The present invention solves the above-mentioned problems of the prior art, and more accurately estimates the ionospheric electron density distribution in the three-dimensional height direction and the horizontal direction, and enables estimation of a space portion that cannot be observed by a satellite. It is an object to provide a density estimation device and an electron density estimation method.

In order to solve the above problems, an electron density estimation apparatus according to the present invention has one or more receivers that receive satellite signals transmitted from a plurality of positioning satellites, and uses positioning information included in the satellite signals. An electron density estimation device using a positioning system for obtaining position information, wherein the satellite signal passing path is based on a pseudorange and a carrier phase pseudorange from each of the one or more receivers to each of the plurality of positioning satellites. A total electron number calculating unit that calculates the total number of electrons, a space setting unit that sets a three-dimensional space for estimating electron density, and divides the three-dimensional space into a plurality of regions in the horizontal direction and the height direction , A first electron density estimator that estimates the electron density of each region divided by the space setting unit based on the total number of electrons calculated by the total electron number calculator, and the first electron density estimator Based on the electron density, extracts the electron density of the same height, characterized in that it comprises a second electronic density estimation unit that estimates by approximating the electron density distribution for each height using spherical harmonics.

In order to solve the above problems, an electron density estimation method according to the present invention has one or more receivers that receive satellite signals transmitted from a plurality of positioning satellites, and uses positioning information included in the satellite signals. An electron density estimation method using a positioning system for obtaining position information, wherein the satellite signal passing path is based on a pseudorange and a carrier phase pseudorange for each of the plurality of positioning satellites from each of the one or more receivers. A total electron number calculating step for calculating the total number of electrons, a three-dimensional space for estimating the electron density, and a space setting step for dividing the three-dimensional space into a plurality of regions in the horizontal direction and the height direction , A first electron density estimating step for estimating an electron density for each region divided by the space setting step based on the total electron number calculated by the total electron number calculating step; A second electron density estimating step for extracting an electron density at the same height based on the electron density estimated by the electron density estimating step and approximating an electron density distribution for each height using a spherical harmonic function; It is characterized by providing.

  According to the present invention, there are provided an electron density estimation apparatus and an electron density estimation method capable of estimating the ionospheric electron density distribution in the three-dimensional height direction and the horizontal direction more accurately and estimating a space portion that cannot be observed by a satellite. can do.

It is a block diagram which shows the structure of the electron density estimation apparatus of the form of Example 1 of this invention, and a positioning system. It is a detailed block diagram of the electron density estimation apparatus of the form of Example 1 of this invention. It is a flowchart figure which shows operation | movement of the electron density estimation apparatus of the form of Example 1 of this invention. It is a figure explaining the three-dimensional space setting by the three-dimensional electron density estimation space setting part in the electron density estimation apparatus of the form of Example 1 of this invention. It is a figure explaining the correction coefficient setting by the three-dimensional electron density estimation space setting part in the electron density estimation apparatus of the form of Example 1 of this invention.

  Hereinafter, embodiments of an electron density estimation apparatus and an electron density estimation method of the present invention will be described in detail with reference to the drawings.

  Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram illustrating configurations of an electron density estimation device 32 and a positioning system according to the first embodiment of the present invention. This electron density estimation device 32 has one or more satellite signal receivers 24 for receiving satellite signals transmitted from a plurality of positioning satellites (positioning satellites 10a, 10b, 10c), and positioning information contained in the satellite signals. Use a positioning system to obtain position information.

  First, the configuration of the present embodiment will be described. As shown in FIG. 1, the electron density estimation apparatus 32 and the positioning system of the present embodiment include a positioning satellite 10a, a positioning satellite 10b, a positioning satellite 10c, a satellite signal processing system 20, an ionosphere TEC / bias estimation, and a three-dimensional electron density estimation. A processing system 30 and an internet data processing system 40 are included. The positioning satellite 10a, the positioning satellite 10b, the positioning satellite 10c, and the satellite signal processing system 20 correspond to the positioning system of the present invention. Although a positioning system including the Internet data processing system 40 can be used, the Internet data processing system 40 is not necessarily essential and is additional. The satellite signal processing system 20, the ionosphere TEC / bias estimation processing system 30, and the Internet data processing system 40 are connected to each other via a communication line 50.

  The positioning satellite 10a, the positioning satellite 10b, and the positioning satellite 10c are navigation satellites such as GPS, Galileo, and Quasi-Zenith Satellite (QZSS), and transmit satellite signals having a plurality of frequencies.

  The satellite signal processing system 20 includes an antenna 22, a satellite signal receiver 24, and a satellite signal processing device 26. The satellite signal receiver 24 corresponds to the receiver of the present invention, and receives satellite signals of a plurality of frequencies transmitted from a plurality of positioning satellites (positioning satellites 10a, 10b, 10c) via the antenna 22. In addition, the satellite signal processing device 26 obtains position information using the positioning information included in the satellite signal.

  The ionosphere TEC / bias estimation / three-dimensional electron density estimation processing system 30 has an electron density estimator 32. Based on the received signal, the satellite position, the total ionosphere electron number (TEC) in the signal passing path, the inter-frequency bias, etc. calculate. The received data and processing results are transmitted to the data server system via the LAN and stored.

  The internet data processing system 40 includes a router 42, a GEONET collection data processing device 44, and an external internet network 46. The router 42 may be a switching hub. The Internet data processing system 40 is the ionosphere-related information published, the GPS observation data (GEONET data) published by the Geospatial Information Authority of Japan, and the IGS (International GPS Service for Geodynamics) that is publishing international observation results. It is a device that collects data etc. via the Internet. The results collected by the internet data processing system 40 are processed by the ionosphere TEC / bias estimation / three-dimensional electron density estimation processing system 30. The router 42 is provided in consideration of security and is a firewall.

  FIG. 2 is a detailed block diagram of the electron density estimation apparatus 32 according to the first embodiment of the present invention. As shown in FIG. 2, the electron density estimation device 32 includes a satellite TEC calculation unit 33, a TEC bias correction unit 34, an inter-frequency bias estimation unit 35, a three-dimensional electron density estimation space setting unit 36, an electron density model calculation unit 37, The provisional electron density estimation unit 38 and the three-dimensional electron density estimation unit 39 are included.

  The satellite TEC calculation unit 33, the TEC bias correction unit 34, and the inter-frequency bias estimation unit 35 correspond to the total electron number calculation unit of the present invention, and pseudo distances from each of one or more receivers to each of a plurality of positioning satellites. Based on the above, the total number of electrons in the satellite signal passage path is calculated. Specifically, the satellite TEC calculation unit 33 calculates the total number of electrons in the satellite signal passage path based on the pseudo distance from the satellite signal receiver 24 to each of the positioning satellites 10a, 10b, and 10c.

  The inter-frequency bias estimation unit 35 calculates the inter-frequency bias and outputs it to the TEC bias correction unit 34. Any method may be used for estimating the inter-frequency bias by the inter-frequency bias estimating unit 35, and a conventional method may be used.

  The TEC bias correction unit 34 performs correction using the inter-frequency bias estimated by the inter-frequency bias estimation unit 35, and calculates the final total number of electrons.

  The three-dimensional electron density estimation space setting unit 36 corresponds to the space setting unit of the present invention, sets a three-dimensional space for estimating the electron density, and divides the three-dimensional space into a plurality of regions.

  The electron density model calculation unit 37 calculates an electron density model based on an ionosphere electron density model function such as the IRI model and Gallagher model as described above.

  The provisional electron density estimation unit 38 corresponds to the first electron density estimation unit of the present invention, and sets a three-dimensional electron density estimation space based on the total number of electrons calculated by the total electron number calculation unit (TEC bias correction unit 34). The electron density for each region divided by the unit 36 is estimated. In the present embodiment, the provisional electron density estimation unit 38 estimates the electron density using a MART technique as described in Non-Patent Document 5 or Non-Patent Document.

  The three-dimensional electron density estimator 39 corresponds to the second electron density estimator of the present invention, extracts the electron density at the same height based on the electron density estimated by the provisional electron density estimator 38, and performs spherical harmonics. Approximate and estimate the electron density distribution at each height using a function.

  Next, the operation of the present embodiment configured as described above will be described. FIG. 3 is a flowchart showing the operation of the electron density estimation apparatus 32 of the present embodiment. First, the satellite TEC calculation unit 33 calculates the total number of electrons in the satellite signal passage path based on the pseudorange and the carrier phase pseudorange for each of the plurality of positioning satellites from each of the one or more receivers (step S1). Specifically, the satellite TEC calculation unit 33 calculates the TEC of a satellite such as GPS from satellite receiver collection data installed over a wide range. Here, the satellite TEC calculation unit 33 according to the present embodiment performs signal propagation based on two-frequency signals (signals of L1 frequency (1575.42 MHz) and L2 frequency (1227.60 MHz) of the GPS satellite) broadcast from the satellite. Assume that the TEC of the route is calculated. A similar method can be used when broadcasting two different frequencies other than GPS.

Here, the pseudo distance between the positioning satellite 10a and the satellite signal receiver 24 is considered. The TEC of the satellite signal passing path is obtained based on satellite signals (indicated here by L1 and L2) transmitted from the positioning satellite 10a. First, the pseudorange (code distance, pseudorange) and the carrier phase pseudorange (phase distance) can be expressed as follows.

Here, ρ represents a distance (pseudo distance) due to a delay time. Φ represents a carrier phase distance. r indicates the true distance. c is the speed of light. Further, δt _u indicates a receiver time error, and δt ^s indicates a satellite time error. In this embodiment, the lower right subscript basically indicates a term related to the ground (receiver or the like), and the upper right subscript basically indicates a term related to the sky (satellite or the like). _{δtu, L1orL2 bias} indicates a receiver frequency dependent hardware dependent bias, and δt ^s _{L1orL2 bias} indicates a satellite frequency dependent hardware dependent bias. Further, I represents the ionospheric propagation delay amount, and T represents the tropospheric propagation delay amount. N _{L1orL2, amb} represents an integer uncertain value, and ε represents an observation error.

The satellite TEC calculation unit 33 can obtain the TEC by calculating the difference between the observation values of two frequencies (difference in delay time).

Here, f is a frequency. Λ represents a wavelength. _Δbias indicates an inter-frequency bias. TEC ^true indicates the true total number of electrons.

Next, the TEC bias correction unit 34 performs correction on the TEC using the inter-frequency bias _Δbias estimated in advance by the inter-frequency bias estimation unit 35 (step S2). First, the delay time difference between two frequencies after bias correction is expressed by the following equation.

Here, the equation (6) includes an indeterminate value (λ _L1 ΔN _{L1, amb} −λ _L2 ΔN _{L2, amb} ) that is unknown from the observed value. Therefore, the TEC bias correction unit 34 deletes the integer uncertain value by the following formula by combining the formulas (5) and (6). This technique is also described in Non-Patent Document 3.

Here, the subscript k indicates a data number. M represents the total number of samples that can be collected continuously. Further, TEC _{k, u} represents the total number of electrons (number / m ² ) on the propagation path of the satellite u.

  The electron density model calculation unit 37 calculates an electron density model based on the ionosphere electron density model function, and outputs the calculated electron density model to the three-dimensional electron density estimation space setting unit 36. The ionosphere model by the electron density model calculation unit 37 is described in, for example, Non-Patent Documents 1, 2, 4, and the like. Steps S1 and S2 (especially S1) correspond to the total electron number calculating step of the present invention.

  Next, the three-dimensional electron density estimation space setting unit 36 sets a three-dimensional space for estimating the electron density, and divides the three-dimensional space into a plurality of regions. The operation of the three-dimensional electron density estimation space setting unit 36 corresponds to the space setting step of the present invention. Further, the three-dimensional electron density estimation space setting unit 36 sets an ionosphere electron density model value or an estimated value of the three-dimensional space to be estimated (step S3).

  Specifically, the three-dimensional electron density estimation space setting unit 36 divides the ionosphere in the three-dimensional space from the satellite to the point where the satellite receiver is arranged in the latitude / longitude / height directions, and calculates the ionosphere model value. The electron density is set in the region divided by use or at the position of the lattice point. The IRI models described in Non-Patent Documents 1 and 2 and the like cannot be set up to a space where satellites exist because the effective range is up to a height of 1000 km. Therefore, the three-dimensional electron density estimation space setting unit 36 adopts, for example, a method using GCPM (Global Core Plasma Model) described in Non-Patent Document 4 or a method of extrapolating about 400 km to 1000 km of the IRI model. Can do.

FIG. 4 is a diagram illustrating the three-dimensional space setting by the three-dimensional electron density estimation space setting unit 36 in the electron density estimation device 32 of the present embodiment. The three-dimensional electron density estimation space setting unit 36 of this embodiment divides the three-dimensional space into 12 regions (blocks) X1 to X12 as shown in FIG. The number of blocks. In FIG. 4, the signal passing path between the positioning satellites S1 to S4 and the satellite signal receivers Rx1 to Rx3 is represented by arrows. The relationship among the satellite, the TEC, and the electron density in FIG.

In the equation (9), X1 to X12 indicate the electron density of a region (mesh) obtained by dividing the space, and are unknown at this time. TEC ⁱ _j indicates the total number of electrons determined between the i satellite and the j receiver. For example, a thick arrow TEC ² ₁ in FIG. 4 indicates the total number of electrons in the signal passing path between the positioning satellite S2 and the satellite signal receiver Rx1. The TEC value output by the TEC bias correction unit 34 is substituted into the right side of the equation (9).

  Here, the determinant of Equation (9) is expressed as AX = E. A non-zero element (element represented by 1) in the matrix A indicates a mesh through which a signal between the i satellite and the j receiver has passed.

The value of the electron density actually set by the model is the value of one point in the mesh. Further, when the radio signal passes through each mesh, the radio wave may pass obliquely as well as when passing vertically through the mesh. In consideration of this effect, the three-dimensional electron density estimation space setting unit 36 substitutes a value represented by the following equation instead of 1 of the matrix A.

Here, dH _{i, j} indicates the size of the divided i, j mesh in the height direction. The conversion coefficient SF is a coefficient for correcting a signal incident from an oblique direction into a signal incident in the height direction. θ represents the incident elevation angle of the satellite radio wave received by the satellite receiver. FIG. 5 is a diagram for explaining the correction coefficient SF setting by the three-dimensional electron density estimation space setting unit 36 in the electron density estimation device 32 of the present embodiment.

The left side of the equation (12) indicates the TEC in the vertical direction in the i, j mesh. The TEC _{s on} the right side indicates the TEC in the radio wave direction passing through the i, j mesh. R in the equation (13) indicates the earth radius as shown in FIG. Further, h in the expression (13) indicates the height from the ground surface to the i, j mesh.

  Next, the provisional electron density estimation unit 38 estimates the electron density of the satellite signal passing path by the MART or GSVD method (step S4). Specifically, the provisional electron density estimator 38 is provided for each region divided by the three-dimensional electron density estimation space setting unit 36 based on the total number of electrons calculated by the total electron number calculator (TEC bias correction unit 34). Estimate the electron density. The operation of the provisional electron density estimation unit 38 corresponds to the first electron density estimation step of the present invention.

  In the present embodiment, the provisional electron density estimation unit 38 estimates the electron density by the MART or GSVD technique. However, in order to realize the present invention, it is not always necessary to use either technique, and the satellite signal reception is performed. It is only necessary to tentatively estimate the electron density of each region based on the observation values obtained by the machine.

The MART method is described in Non-Patent Documents 5 and 6 as described above, but will be briefly described here.

Expression (14) is an expression indicating a MART algorithm. a _i represents the A matrix i row vector of the equation (10). _{Further, a ij} represents the ij component of the A matrix. X _j represents the j component of the X column matrix. Furthermore, E _i represents the i component of the E matrix in equation (9). Λ is a parameter that determines the degree of convergence.

  The provisional electron density estimator 38 uses the MART algorithm shown in the equation (14) to perform an iterative process until the value of the equation (14) converges, and is divided by the three-dimensional electron density estimation space setting unit 36. Estimate the electron density for each region. At that time, the provisional electron density estimation unit 38 uses the TEC value output from the TEC bias correction unit 34 as the value of the E matrix, and uses the model value calculated by the electron density model calculation unit 37 as the initial value of X. Use as a value.

  The provisional electron density estimation unit 38 cannot estimate the electron density in a space through which no signal passes.

When the GSVD method is adopted, the provisional electron density estimation unit 38 obtains the electron density by the following method. Note that Non-Patent Document 7 describes the GSVD method.

  L in the equation (15) is called a Tikhonov matrix. In the 0th-order Tikhonov normalization, L is a unit matrix. α is a normalization parameter and α> 0. L is a positive quadratic matrix (all eigenvalues are positive).

The electron density X satisfying the equation (15) can be expressed by the following equation.

  Next, the three-dimensional electron density estimation unit 39 approximates the electron density by a spherical harmonic function for each height (step S5). That is, the three-dimensional electron density estimation unit 39 extracts the electron density at the same height based on the electron density estimated by the provisional electron density estimation unit 38, and uses the spherical harmonic function to distribute the electron density at each height. Is approximated and estimated. The operation of the three-dimensional electron density estimation unit 39 corresponds to the second electron density estimation step of the present invention.

  Note that the three-dimensional electron density estimation unit 39 shows the characteristics of the present invention in its function and effect, and is different from the conventional method.

X in the equation (9) is a one-dimensional representation of a spatial mesh. The three-dimensional electron density estimation unit 39 extracts only the electron density at the same height from the electron densities estimated by the provisional electron density estimation unit 38.

In the equation (17), x = sin (θ). V indicates the electron density at a certain height. However, (theta) shows the latitude of a mesh and (phi) shows the longitude of a mesh. S _n and S _nm are Schmidt Seminormized Legendre functions. The Legendre function is shown in equation (20).

  Np represents the order of the Legendre function. The three-dimensional electron density estimation unit 39 approximates the electron density at the same height using equation (17). Thereby, the value of the electron density of the mesh which could not be obtained by the MART method can be obtained. In addition, the value obtained by GSVD can be corrected.

  That is, the three-dimensional electron density estimation unit 39 approximates the electron density with respect to a certain latitude / longitude (θ, φ) by a mesh component (17) in the height direction, and calculates a coefficient (α (H), β (H)) is obtained. By obtaining these coefficients (α (H), β (H)), the three-dimensional electron density estimation unit 39 designates latitude / longitude / height and uses the equation (17) to determine the height H at the height H. The electron density V (x, φ) can be calculated.

  Note that the conventional methods described in Non-Patent Document 8 and Non-Patent Document 9 focus only on a certain height, and do not obtain an electron density distribution for each height. Further, the technique described in Non-Patent Document 10 calculates the electron density distribution in the height direction, but does not calculate the electron density in a space having a spread in the latitude and longitude directions.

  When the electron density model value by the electron density model calculation unit 37 and the electron density value by the provisional electron density estimation unit 38 are greatly different from each other, the approximation by the three-dimensional electron density estimation unit 39 may not be appropriate. Therefore, the electron density estimation apparatus according to the present embodiment repeats the processing from step S3 by using the electron density at an arbitrary place obtained by the three-dimensional electron density estimation unit 39 as an initial value, so that the three-dimensional electron density estimation unit 39 The approximation accuracy can be improved.

Specifically, the three-dimensional electron density estimation unit 39 determines whether or not the value E in equation (22) is equal to or less than the threshold value ε (step S6). Here, the difference that is calculated by the equation (22) is estimated by the provisional electron density estimation unit 38, and the electron density X _k corresponding to the mesh satellite signal is passed, a three-dimensional electron density estimation unit 39 ( This is the sum of all the squares of the difference from the electron density V corresponding to this mesh among the electron density V obtained by the equation (17).

  That is, the three-dimensional electron density estimation unit 39 calculates the difference between the electron density based on the estimated electron density distribution and the electron density estimated by the provisional electron density estimation unit 38 for each region, and calculates the difference calculated for each region. When the total square value is equal to or less than a predetermined threshold value ε, the estimated electron density distribution is determined to be a true value.

  When the value E of the equation (22) is larger than the threshold value ε, the process returns to step S3, and the value estimated by the three-dimensional electron density estimation unit 39 in the three-dimensional space by the three-dimensional electron density estimation space setting unit 36. Set V. Accordingly, the provisional electron density estimator 38 determines the three-dimensional electron density estimator when the sum of the squares of the differences calculated for each region by the three-dimensional electron density estimator 39 is larger than the predetermined threshold ε. Based on the electron density distribution estimated by 39, the electron density for each region is estimated again.

  As described above, the processing from step S3 to step S6 is repeated in the three-dimensional electron density estimation space setting unit 36, the provisional electron density estimation unit 38, and the three-dimensional electron density estimation unit 39, and the value E of equation (22) Is equal to or less than the threshold value ε, the three-dimensional electron density estimating unit 39 determines that the electron density close to the true value can be estimated, and ends the iterative process.

  As described above, the three-dimensional electron density estimation unit 39 can obtain the electron density that is smoothly approximated with respect to the same height using the equation (17). Next, the three-dimensional electron density estimation unit 39 performs processing for obtaining an electron density of an arbitrary height in the height direction when latitude / longitude is designated (step S7). In the present embodiment, the three-dimensional electron density estimation unit 39 interpolates using the function value obtained by the equation (17) in order to obtain the electron density of an arbitrary height. That is, the three-dimensional electron density estimation unit 39 estimates the electron density distribution at an arbitrary height by interpolating between adjacent regions using the estimated electron density distribution for each height.

  Note that the interpolation method is obtained by one-dimensional interpolation only in the height direction or three-dimensional interpolation using a mesh surrounding a place to be obtained.

First, the interpolation only in the height direction designated by latitude and longitude will be described. The three-dimensional electron density estimation unit 39 substitutes the latitude (θ) and longitude (φ) of the place to be obtained in the equation (17), and the electron density (V (x, φ, h ₁ ) in the mesh in the height direction, V (x, φ, h ₂ ),..., V (x, φ, h _max )) are obtained. Here, h ₁ indicates the height of the lowermost layer of the mesh, and h _max indicates the height of the uppermost layer of the mesh. The three-dimensional electron density estimator 39 obtains the electron density at the desired height by performing interpolation using a method in which the first-order differentiation and the second-order differentiation are continued in adjacent sections, such as spline interpolation using V.

Next, the interpolation by the mesh surrounding the place to be obtained will be described. The three-dimensional electron density estimation unit 39 obtains all mesh points by the equation (17) (V (x, φ, h ₁ ), V (x, φ, h ₂ ),..., V (x, φ, h _max )) 3D interpolation is performed. The three-dimensional electron density estimator 39 obtains the electron density at the desired height by performing interpolation using a method in which the first-order differentiation and the second-order differentiation are continued in adjacent sections, such as spline interpolation using V.

  As described above, according to the electron density estimation apparatus and the electron density estimation method according to the first embodiment of the present invention, the ionosphere electron density distribution in the three-dimensional height direction and the horizontal direction can be estimated more accurately, It is possible to estimate the space that cannot be observed.

  That is, in the electron density estimation apparatus and the electron density estimation method of the present embodiment, the three-dimensional electron density estimation unit 39 approximates the electron density distribution for each height using a spherical harmonic function, so that it is smooth in the horizontal direction. A connected electron density distribution can be obtained, and an electron density at an arbitrary latitude and longitude including a space that cannot be observed by a satellite such as GPS can be estimated.

  Furthermore, the electron density estimation apparatus and the electron density estimation method according to the present embodiment are configured so that the difference between the electron density based on the electron density distribution estimated by the three-dimensional electron density estimation unit 39 and the electron density estimated by the provisional electron density estimation unit 38 is obtained. Is calculated for each region, and whether or not the sum of the squares of the differences calculated for each region is equal to or smaller than a predetermined threshold value ε is determined as an arbitrary value obtained by the three-dimensional electron density estimation unit 39 The approximation accuracy of the three-dimensional electron density estimation unit 39 can be improved by repeating the processing from steps S3 to S6 with the electron density at the place as an initial value.

  Moreover, the electron density estimation apparatus and the electron density estimation method of the present embodiment interpolate between adjacent regions using the electron density distribution for each height estimated by the three-dimensional electron density estimation unit 39, and at an arbitrary height. Since the electron density distribution is estimated, it is possible to obtain a smoothly connected electron density distribution not only in the horizontal direction but also in the height direction, and the unique height direction possessed by the ionosphere that was difficult to reproduce by conventional methods The electron density peak (E layer or F layer) can be reproduced.

  The electron density estimation apparatus and the electron density estimation method according to the present invention can be used for an electron density estimation apparatus that estimates the ionospheric electron density distribution of a passage route by a plurality of different frequency signals transmitted from a satellite.

10a, 10b, 10c Positioning satellite 20 Satellite signal processing system 22 Antenna 24 Satellite signal receiver 26 Satellite signal processing device 30 Ionosphere TEC / bias estimation / three-dimensional electron density estimation processing system 32 Electron density estimation device 33 Satellite TEC calculation unit 34 TEC Bias correction unit 35 Inter-frequency bias estimation unit 36 3D electron density estimation space setting unit 37 Electron density model calculation unit 38 Provisional electron density estimation unit 39 3D electron density estimation unit 40 Internet data processing system 42 Router 44 GEONET collection data processing device 46 External Internet Network 50 Communication Line S1, S2, S3, S4 Positioning Satellite Rx1, Rx2, Rx3 Satellite Signal Receiver

Claims (4)

An electron density estimator using a positioning system that has one or more receivers that receive satellite signals transmitted from a plurality of positioning satellites and that obtains position information using positioning information included in the satellite signals,
A total electron number calculator that calculates the total number of electrons in the path of the satellite signal based on the pseudorange and carrier phase pseudorange for each of the plurality of positioning satellites from each of the one or more receivers;
A space setting unit that sets a three-dimensional space for estimating electron density and divides the three-dimensional space into a plurality of regions in the horizontal direction and the height direction ;
A first electron density estimating unit that estimates an electron density for each region divided by the space setting unit based on the total number of electrons calculated by the total electron number calculating unit;
A second electron density obtained by extracting an electron density at the same height based on the electron density estimated by the first electron density estimating unit and approximating an electron density distribution for each height using a spherical harmonic function; An estimation unit;
An electron density estimation apparatus comprising: The second electron density estimation unit calculates a difference between the electron density based on the estimated electron density distribution and the electron density estimated by the first electron density estimation unit for each region, and calculates the difference calculated for each region. The electron density distribution estimated when the sum of squares is less than or equal to a predetermined threshold value is determined to be a true value,
The first electron density estimator determines whether the second electron density estimator determines the sum of the squares of the differences calculated for each region by the second electron density estimator and the second electron density estimator. 2. The electron density estimation apparatus according to claim 1, wherein the electron density for each region is estimated again based on the estimated electron density distribution.   The second electron density estimation unit estimates an electron density distribution at an arbitrary height by interpolating between adjacent regions using the estimated electron density distribution at each height. Item 3. The electron density estimation apparatus according to Item 2. An electron density estimation method using a positioning system that has one or more receivers that receive satellite signals transmitted from a plurality of positioning satellites and that obtains position information using positioning information included in the satellite signals,
A total electron number calculating step of calculating a total number of electrons of a passage path of the satellite signal based on a pseudorange and a carrier phase pseudorange for each of the plurality of positioning satellites from each of the one or more receivers;
A space setting step of setting a three-dimensional space for estimating the electron density and dividing the three-dimensional space into a plurality of regions in the horizontal direction and the height direction ;
A first electron density estimating step for estimating an electron density for each region divided by the space setting step based on the total number of electrons calculated by the total electron number calculating step;
A second electron density obtained by extracting an electron density at the same height based on the electron density estimated in the first electron density estimating step and approximating an electron density distribution for each height using a spherical harmonic function; An estimation step;
An electron density estimation method comprising:

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