EP3047302A1

EP3047302A1 - Method and device for determining at least one sample-point-specific vertical total electron content

Info

Publication number: EP3047302A1
Application number: EP14781465.1A
Authority: EP
Inventors: Norbert Jakowski; Mohammad Mainul Hoque
Original assignee: Deutsches Zentrum fuer Luft und Raumfahrt eV
Current assignee: Deutsches Zentrum fuer Luft und Raumfahrt eV
Priority date: 2013-09-16
Filing date: 2014-09-15
Publication date: 2016-07-27
Also published as: DE102013218492B9; FR3010801B1; US10254409B2; WO2015036590A1; FR3010801A1; US20160282472A1; DE102013218492B3

Abstract

The invention relates to a device and to a method for determining at least one sample-point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4), wherein the sample-point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) indicates an electron content along a sample-point-specific vertical path (vW1, vW2, vW3, vW4), which extends through an Earth center point (M) and the corresponding sample point (S1, S2, S3, S4), wherein a first inclined total electron content is determined, wherein the first inclined total electron content indicates an electron content along an inclined beam path (SW), a first and at least one further sample point (S1, S2, S3, S4) are selected along the beam path (SW), an initial sample-point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) is determined for each sample point (S1, S2, S3, S4), an increment electron content is determined in dependence on the initial sample-point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) and a sample-point-specific vertical electron density distribution, wherein the increment electron content indicates an electron content of the increment associated with the sample point (S1, S2, S3, S4), wherein a further inclined total electron content is determined in dependence on the increment electron contents, wherein a sample-point-specific conversion function between the further inclined total electron content and the initial sample-point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) is determined, wherein the at least one sample-point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) is determined in dependence on the first inclined total electron content and the sample-point-specific conversion function.

Description

Method and device for determining at least one support point-specific vertical total electron content

The invention relates to a method and apparatus for determining at least one support point-specific vertical total electron content.

The electromagnetic radio waves of all satellite-based communication and / or navigation systems are subject to interaction with the plasma of the ionosphere. The interaction is dispersive, ie strongly frequency-dependent (proportional to 1 / f ² ) and practically insignificant at vibrational frequencies f greater than 10 GHz. In the L-band range used by the GNSS (Global Navigation Satellite Systems), the ionospheric propagation effects can not be neglected. Therefore, the knowledge of the current state of the ionosphere and the seizure of

Measures of error compensation of importance.

The basis of the position determination with GNSS are measurements of the code and

Carrier phase. The measured phase is determined by the phase length ^" " where n denotes the ionospheric refractive index and s the ray path (or propagation path) element. In geometric optics, the propagation of the radio wave is also determined by Fermat's principle (the principle of the shortest arrival) so that the propagation path can be found with the minimum of the phase length. This results in a refractive index n not equal to 1 to an extended beam path or

Runtime error compared to the comparison case of the propagation of the wave in a vacuum.

Ultimately, in a GNSS, the error is such that it is the one of the

Receiver of the signals detected distance between the satellite and the receiver falsified. In particular, a curvature of the

Radiation path and an interaction of the wave with the medium in question, which passes through the wave. However, the invention is not limited to GNSS.

The refractive index is subject to a complex non-linear relationship of different geophysical parameters, eg ionization state, magnetic field state, and l geometric parameter, eg elevation and / or azimuth. The first approximation of the refractive index causes range errors of the order of up to about 100 m, which can be eliminated in GNSS by means of two-frequency measurements. The corresponding methods are known. The higher-order errors in the refractive index (~ 1 / f ^m , m> 2) are on the order of up to several centimeters.

It has already been proposed, by measuring and evaluating signals received at different carrier frequencies (oscillation frequencies), to correct the first-order error (m = 2) and the error caused by the curved propagation path.

If there is only one single-frequency receiver, it is not easy and accurate

Error correction possible. In a one-frequency measurement, a code phase can be simplified by

Φ = ro + di + de Formula 1 where Φ is the code phase, ro is the distance between the transmitter and receiver, the ionospheric propagation error along the beam path, and the remaining range errors, such as. Watch error, called.

The ionospheric propagation error can be more than 100m, depending on the degree of ionization of the ionosphere. Therefore, a corresponding correction is desirable, especially in the aviation sector.

It is also known to perform an ionospheric correction as a function of so-called vertical ionosphere errors, the ionospheric error in the first approximation being proportional to a surface area related vertical

Total ionization of the ionosphere is. The vertical total ionization or the total vertical electron content is often referred to as TEC (total electron content). Here, the vertical ionospheric error serves as a reference for the calculation of an error along an arbitrarily oriented, through an elevation angle and azimuth

described beam path. As a rule, however, the real ionosphere is greatly simplified in this case. For example, In the absence of further information, it is assumed that the ionization is concentrated in a thin layer (thin-shell model). A

The corresponding transformation or mapping function will be referred to below as Thin Shell MF. Such a thin-shell MF is e.g. in the Yakovsky et.

al., "Relationship between GPS signal propagation errors and EISCAT observations", Ann. Geophysicae 14, pp. 1429-1436, Springer Verlag, 1996. Here also an ionosphere height of 350 km is described.

The simplifying assumption is made inter alia because in practice a distribution of the electron density along a ray path from the transmitter to the receiver is unknown. In the previously mentioned thin-shell model, it is assumed that the ionosphere is concentrated in a thin layer at a height of about 350 km to 400 km. By means of a geometric mapping function, assuming the thin shell model, a specific vertical total electron content at the intersection of the beam path with the thin ionosphere layer is then converted into an electron content along the beam path.

However, this is disadvantageously the normally changing

Electron density neglected along the ray path. Similarly, vertical and horizontal gradients of ionization are not considered. This can result in uncorrected residual errors of more than 10m.

Vertical total electronic content can be summarized into so-called TEC correction maps for different latitudes and longitudes. If the thin-shell model is used to create these TEC correction maps, systematic errors already occur during generation of the correction maps, which can continue to propagate and amplify during the inverse transformation. In

Augmentation systems such as WAAS and EGNOS must not exceed the specified thresholds in accordance with aviation safety standards. Thus, both the most accurate calculation possible of the vertical TEC Correction maps as well as the best possible use of these maps for the error correction on the inclinated beam paths desired.

The subsequently published DE 10 2013 208 040.9 describes a method and a

Apparatus for determining an error in the propagation of an electromagnetic wave in an atmosphere comprising electrically charged particles. The document describes that an electron content along a ray path from the transmitter to the receiver can be calculated as the sum of electron contents of a plurality of increments or segments of the ray path. In turn, the electron contents of the increments are determined as a function of a vertical electron density distribution. This vertical electron density distribution in turn is due to an analytically integrable physically realistic model of the vertical electron density distribution in the

Given ionosphere whose integral corresponds to the predetermined vertical electron content. A realistic description of the vertical electron density distribution provides, for example, the formula for the Chapman layer which can be derived from the Chapman theory.

K. Davies, "Ionospheric Radio", Peter Peregrinus Ltd, London, ISBN

086341 186X, pages (60-65,138), 1990 provides a realistic description of a vertical electron density distribution in the ionosphere.

The publication MM Hoque, "Higher order propagation effects and their corrections in precise GNSS positioning", Dissertation University Siegen, DLR research report 2009-09, ISSN 1434-8454, 2009, pages 218-224 describes an analytical solution of an integral over an electron density distribution ,

The technical problem arises of providing a method and device for more accurately determining at least one support point-specific vertical total electron content, the total vertical electron contents thus determined for more accurately determining a propagation error or an improved determination of a residual error of an electromagnetic wave in an atmosphere and thus also can be used for a more accurate position determination. It is a basic idea of the invention to consider a vertical electron density distribution in the determination of sample point-specific vertical total electron contents from, for example, measured electron content along a ray path from a transmitter to a receiver, wherein the support points are arranged along the ray path. This vertical electron density distribution can be given by an analytically integrable physically realistic model of the vertical electron density distribution in the ionosphere, whose integral to the given vertical

Electron content corresponds. A realistic description of the vertical

For example, electron density distribution provides the formula for the Chapman layer that can be derived from the Chapman theory. The method thus permits an inverse transformation of a total electron content of an incident beam path to at least one support point-specific vertical total electron content.

It proposes a method for determining at least one

support point-specific vertical total electron content.

The support point-specific vertical total electron content here denotes an electron content along a support point-specific vertical path which extends through a center of the earth and a corresponding interpolation point. The support point can be arranged at a predetermined height, in particular in an ionosphere. The height here can be measured against normal zero.

Furthermore, a first inclined total electron content is determined, wherein the first inclined total electron content denotes an electron content along an inclined beam path.

The included beam path refers to a beam path of an electromagnetic wave in the atmosphere, eg between a transmitter and a receiver. The beam path can be determined, for example, as a function of geometric parameters, for example an elevation angle and / or a zenith angle. In this case, it may mean in particular that the elevation angle of the beam path is at an intersection with the earth's surface is different from 90 °. In other words, the included beam path does not intersect the earth's surface vertically.

In this case, the first inclinated total electron content can be detected by sensors, in particular measured. Also, the first inclined total electron content may be determined depending on an error in the propagation of an electromagnetic wave along the beam path. For example, a runtime error of a radio signal can be detected. The propagation and propagation error can be detected or determined for example by means of a so-called two-frequency-based measurement. In a two-frequency-based measurement can be done by measurement and

Evaluation of signals on different carrier frequencies

(Vibration frequencies) were received, a propagation error can be determined. Depending on the propagation and transit error, then, in turn, e.g. depending on known relationships between runtime errors and

Electron content, the first inclined total electron content can be determined.

The vertex leading to the vertex-specific vertical to be determined

Total electron content corresponds, is preferably on the inclinated

Beam path. Thus, the sample point specific vertical path along which the sample point specific vertical electron content results cuts the beam path in the sample point.

Further, along the beam path, a first and at least one other

Base selected. At least one of the interpolation points can be arranged along the beam path between transmitter and receiver. Furthermore, a support point can be selected as the position of the transmitter or receiver. The support points thus divide the beam path into at least two increments.

Preferably, however, more than two vertices along the ray path are chosen, thereby dividing the ray path into more than two increments. Preferably, one of the support points is that support point which forms the intersection of the beam path and the support point-specific vertical path along which the support point-specific vertical total electron content to be determined is formed.

An increment or segment of the beam path thus denotes a part of the

Radiation path, which is located between a base and the adjacent along the beam path support point.

Further, for each of the bases selected along the beam path, an initial sample point specific vertical total electron content is determined. The initial

Support point-specific vertical total electron content here denotes a starting value or starting value for an electron content along a support point-specific vertical path, which is defined by a center of the earth and the corresponding

Base extends. Of course, this definition implies that the total vertical electron content should be along or in an electron content

designated support point-specific vertical column with a predetermined base, whose central longitudinal axis extends through the center of the earth and the corresponding support point.

The total vertical electron content may also be referred to as total electron content (TEC).

The total vertical electron content can be used as an integral of a support point-specific vertical electron density distribution to be explained in more detail below

Earth surface or the lower edge of the ionosphere are determined above about 50 km to infinity.

As explained in more detail below, the initial support point-specific vertical total electron contents may be previously known or determined based on models. In particular, these initial sample point-specific vertical

Total electron contents are determined independently of the previously determined first inclined total electron content. Further, depending on the initial sample point specific vertical total electron content and the sample point specific vertical

Electron density distribution determines an increment electron content, the

Increment electron content denotes an electron content of the increment associated with the support point. This increment may, for example, be the increment following the beam path to the corresponding support point.

In particular, the increment may denote the portion of the beam path between the corresponding support point and the support point adjacent to the beam path. This will also be referred to as neighbor base. The neighboring base of the first base can, for. B. be the other base. For the last interpolation point along the ray path, the increment refers to the portion of the ray path between the last interpolation point and an end point, for example the position of the transmitter or the receiver. A direction along the beam path may, for example, be oriented from the receiver to the transmitter, but also vice versa.

The support point-specific vertical electron density distribution describes the density distribution along the previously explained vertical path. If this electron density distribution is known, e.g. can be described or determined by a function, so also an electron content of a subsection of the previously explained vertical path between two different heights can be determined. If the ray path runs along the support point - specific vertical path, then the increment electron content of the increment between the

corresponding base and the neighboring base or the end point are determined. If, as in most cases, the support point-specific vertical path and the beam path include an angle of incidence, the electron content of the subsection of the vertical path can be converted into the increment electron content as a function of the angle of incidence or elevation angle, as explained in more detail below.

The support point-specific vertical electron density distribution allows the determination of the increment electron content, in particular exclusively, with knowledge of the previously discussed supporting point-specific vertical total electron content.

Then a further inclined total electron content depending on

Increment electron contents determined. For example, all of the incremental electron contents determined in this way can be added to a resulting electron content.

Thus, the method described in the aforementioned DE 10 2013 208 040.9 is thus carried out in order to determine the further inclined total electron content, independently of the determination of the first inclined total electron content. Here, the further inclined total electron content is along the same

Beam path as well as the first inclined total electron content determined.

With regard to the determination of the further included total electron content, reference may therefore be made in full to the disclosure of DE 10 2013 208 040.9. Also, the advantages cited in the document, in particular the improved and more accurate determination of an electron content of the beam path in comparison with the previously discussed thin-shell model, result.

Preferably, the beam path between the transmitter and the receiver is split into at least two increments. The number of increments may be determined depending on the elevation, the horizontal resolution of the vertical TEC data (e.g., readable from a TEC map) and the magnitude of the horizontal gradients. Depending on the number of increments, this results in a number of interpolation points along the beam path. For each interpolation point, the available reference information then becomes the respective reference point-specific vertical one

Total electron content determined, depending on this support point-specific vertical total electron content and the support point-specific vertical

Electron density distribution, an incremental electron content is determined, which denotes an electron content along the beam path between this support point and its neighboring base or the end point. The radiation path specific

Total electron content, which can also be referred to as inclinated total electron content, then results as the sum of all increment electron contents. It is possible to define vertices only at positions along the ray path between the transmitter and the receiver.

Furthermore, a support-point-specific conversion function between the further inclined total electron content and the initial support point-specific vertical total electron content is determined. Base point-specific here means that the conversion function is determined for each of the interpolation points, but in particular for the interpolation point, which forms the intersection between the inflected beam path and the vertical path along which the searched total vertical electron content results.

This conversion function can also be referred to as a mapping function and describes a relationship between the inclined total electron content and the initial support point-specific vertical total electron content.

Furthermore, the at least one support point-specific vertical total electron content as a function of the first inclined total electron content and the

base point specific conversion function is determined.

This results in an advantageous manner a more accurate determination of a

reference point-specific vertical total electron content, where the vertical

Coarse structure of the lonossphäre is considered. This in turn allows in

advantageously, the creation of more accurate TEC maps and thus also maps of the vertical run-time error, the vertical run-time error, e.g. depending on a previously known context, can be determined from the corresponding support point-specific vertical total electron contents of the TEC maps. These vertical propagation errors readable from the TEC map can then serve as a basis for the calculation of run-time errors along arbitrarily incident ray paths, e.g. by the method described in DE 10 2013 208 040.9. A TEC card, as explained in more detail below, provides information about a vertical one

Total electronic content depending on a latitude and longitude. In a further embodiment, the support point-specific conversion function is determined as the ratio between the further inclined total electron content and the initial support point-specific vertical total electron content,

in particular as a divison of the further inclined total electron content by the initial support point-specific vertical total electron content. As a rule, the further inclined total electron content is different from the first total electron content involved.

Further, the at least one searched site specific vertical

Total electron content as the ratio between the first inclinated

Total electron content and the support point-specific conversion function determines, in particular as a division of the first inclined total electron content by the support point-specific conversion function.

This results in an advantageous manner a simple computational determination.

In another embodiment, the initial sample point specific is vertical

Total electron content previously known. Alternatively, the initial sample point-specific vertical total electron content can be determined model-based. The model-based determination can, in particular, be dependent on the one described at the outset

Thin-film model (thin-shell model).

Of course, however, other models can be used to determine a support point specific vertical total electron content.

Also, the initial sample point specific vertical electron content in

Depending on code and carrier phase measurements of global GNSS on two-frequency measurements are generated.

This advantageously results in a simple and reliable determination of start or output values for the proposed method. In a further embodiment, all initial sample point specific vertical electron contents are the same. This corresponds to an assumption of the spherical

Symmetry. This means that along e.g. the ionospheric trace of the inclined ray path (projection of the ray path into the thin spherical

ionospheric shell) the vertical TEC is constant.

Thus, the determination of a single is sufficient in an advantageous manner

base point specific vertical electron content as the starting point for the proposed method.

In another embodiment, initial sample point specific vertical

Total electron contents determined as a function of horizontal gradient information of the total vertical electron content. This horizontal

Gradient information may be known or determinable. In particular, these horizontal gradient information relate to a certain height, in particular the height of the interpolation points. Horizontal gradient information thus describes the difference between the vertical total electron contents of different interpolation points. Here, a horizontal gradient is clearly determined along a spherical surface.

For example, horizontal gradient information can be determined depending on a model. Thus, a priori information about horizontal TEC gradients can be introduced into the calculation via the model. If the model is trusted, this can improve the accuracy of the model

lead the proposed method. Also, horizontal gradient information, e.g. be determined from an existing TEC map of vertical TEC. Such a TEC card can be created for example by determining vertical TEC by means of the thin-film model explained in the introduction.

This also results in an improved accuracy of the proposed

Process. In another embodiment, the initial sample point specific vertical electron content is determined as a function of a TEC card, the TEC card providing information on a total vertical electron content depending on a latitude and longitude.

If a geographical latitude and latitude of a base can be determined, for example by projecting the base along the vertical path to the surface of the earth, the vertical axis can then be determined in dependence on the TEC map

Total electron content can be determined. Of course, if a vertex is not immediately assigned a value in the TEC card, it may be a vertical one

Total electron content depending on a value of at least one

nearest neighbor point are determined, wherein the neighboring point is assigned a corresponding value. This can be done for example by a

Interpolation be done.

Such a TEC card is available, for example, at http://swaciweb.dlr.de.

Here, the TEC map can be generated based on code and carrier phase measurements of global GNSS on two-frequency measurements.

This results in an advantageous manner an accurate knowledge of the vertical

Total electron content at the support points along the projection of the considered beam path, which in turn increases the accuracy of the proposed method. The proposed method may in this case serve to redetermine the TEC contained in the map.

In a further embodiment, the method is carried out for a plurality of interpolation points. Thus, advantageously, e.g. several values of a TEC card are redetermined.

Furthermore, the increment electron content can be dependent on a vertical

Increment electron content and a cutting angle between the beam path and the base point-specific vertical path. The vertical increment electron content refers to an electron content along the support point-specific vertical path between a height of the first support point and a height of the neighboring support point. As a result, the incidence or elevation angle of the beam path, which changes with height above the earth's surface, can be taken into account in an advantageous manner.

In particular, the intersection angle between the beam path and the support point-specific vertical path may be referred to as an angle enclosed by the beam path and a straight line perpendicular to the support point-specific vertical path that passes through the support point.

Thus, the vertical increment electron content can be determined by means of a geometric

Transformation formula can be converted to the ray path and can then be referred to as Strahlstrawegspezifischer Inkrementelektroneninhalt.

As the height of the support points above the surface of the earth changes, so does the previously explained cutting angle. Thus, the splitting of the beam path into several increments advantageously also results in a more precise geometric one

Conversion of a vertical increment electron content to a

ray path specific increment electron content.

In a further embodiment, the support point-specific

Electron density distribution model-based determined or described, in particular by an analytically integrable function.

In this case, the support-point-specific electron density distribution can be described, for example, by a function, in particular a function parameterized by one or more parameters. Preferably, a Chapman profile function is used here, which allows an analytically integrable physical description of the vertical electron density distribution. Such a Chapman profile function is described, for example, in K. Davies, "Ionospheric Radio", Peter Peregrinus Ltd, London, ISBN 086341 186X, pages (60-65,138), 1990. Parameters of a Chapman profile function are a solar zenith angle of the support point-specific vertical path, a maximum electron density, a height of the maximum electron density above sea level and a scale height of the neutral one

Atmosphere in the altitude range of the ionosphere.

The model-based support point-specific electron density distribution thus describes an electron density as a function of a height along the support point-specific vertical path over normal zero.

In this case, the model-based support point-specific electron density distribution, in particular at least one parameter of this electron density distribution, can be chosen such that an integral from zero to infinity over this support point-specific electron density distribution results in the above-explained and known vertical total electron content or deviates at most by a predetermined amount from this.

Knowledge of the vertical total electron content thus advantageously makes possible the most accurate model-based description possible

Electron density distribution. The determination of the vertical increment electron content explained above can then be carried out as a function of the model-based,

support point-specific electron density distribution. In particular, this vertical increment electron content can be determined as an integral from a height of the support point to a height of the neighboring support point above this electron density distribution.

Is used as a model-based support point-specific electron density distribution

Chapman profile function previously discussed selected, this integral can be determined in an advantageous manner and in sections as a function of the (known) vertical total electron content analytically. This is for example in MM Hoque, "Higher order propagation effects and their corrections in precise GNSS positioning", Dissertation University of Siegen, DLR Research Report 2009-09, ISSN 1434-8454, 2009, pages 218-224.

The model-based support point-specific electron density distribution in this case advantageously allows a good physical modeling of the vertical

Electron density distribution, which in turn allows a more accurate determination of an incremental electron content. This, in turn, allows, as previously explained, the more accurate determination of the propagation error.

Furthermore, at least one parameter of the support point-specific

Electron density distribution as a function of the support point-specific vertical

Total electron content can be determined. In this case, the previously explained relationship is used in an advantageous manner such that the integral from zero to infinity above the electron density distribution yields or estimates the previously known vertical total electron content. The at least one parameter may be, e.g. by a

appropriate parameter optimization, be chosen such that the value of

Integrals deviates as little as possible from the previously known vertical total electron content.

This advantageously enables a parameterization of the

Electron density distribution.

Furthermore, at least one parameter of the support point-specific

Electron density distribution fixed predetermined or model-based or metrologically determined. In particular, the at least one parameter can be determined prior to carrying out the method according to the invention.

The fixed determination of at least one parameter advantageously makes it possible to determine the vertical value without delay and thus in terms of time

Increment electron content except for a small residual error. By contrast, the model - based or metrological determination of at least one parameter allows the most realistic possible parameterization of the parameter

Electron density distribution, which leads to a more accurate determination of the propagation error.

In a further embodiment, the electron content along the beam path is additionally determined as a function of a plasma-sphere-related fraction.

Here, e.g. to the sum of all included increment electron contents

Correction term, which has a plasma-sphere-related proportion in the

Total electron content is quantified. The correction term, in addition to representing a plasma sphere-related fraction, also allows mapping of residual errors resulting from the description of the electron density distribution by the Chapman profile function, in particular the mapping of higher-order terms that may be present in the analytical description by the Chapman profile function.

Also, the plasmasphärenbedingte share, for example, an additional profile function for the vertical electron density profile of the plasma sphere above about 800 to 1000km are determined, the additional profile function can be added to the support point specific electron density distribution and mitintegriert. In this case, the plasma-sphere-related fraction is therefore used in the determination of the

Inkrementelektroneninhalts considered.

Alternatively, the plasma-sphere-related fraction can also be determined as a function of measurements.

This advantageously allows a further improved determination of the radiation path-specific electron content.

Next, a distance between a base and one along the

Radiation path adjacent base greater than 0 km and less than 10000 km. The distance may be in particular in a range of 20 km to 100 km. Here, distances between bases can be the same or different.

Also, a first interpolation point can be arranged at a predetermined height above normal zero, for example at a height greater than 50 km.

Further, the distance to the vertex adjacent to the beam path may be determined depending on an amount of the vertical total electron content and / or a horizontal gradient of the total vertical electron content and / or the elevation of the ray path.

Here, the horizontal gradient of the total vertical electron content may be mapped to the gradient along the projected ray path, where the ray path refers to a spherical layer as used in the use of the thin-shell mapping function. Here, the intersection of the beam path with this spherical layer, which is e.g. a layer usually fixed at a height of 350 or 400 km may be the so-called ionospheric puncture point

(lonospheric piercing point). Thus, the spherical layer may contain the ionosphere puncture point.

Alternatively, the information about the strength of the horizontal gradients may also be obtained from the given information, e.g. A TEC map can be derived by estimating the meridional and zonal gradients of the total vertical electron content in the environment between the geographic receiver and satellite position.

In this case, the greater the amount of the vertical total electron content and / or the gradient, the smaller the distance to the neighboring interpolation point.

Furthermore, a small vertical elevation usually has a large vertical one

Total electron content and a high gradient result, which requires a high increment. For example, the distance to the along the beam path adjacent

Base depending on a latitude of the base to be determined. With increasing geographical latitude of the bases may preferably increase a distance.

In this way, it can be taken into account in an advantageous manner that the vertical total electron content changes more in the region of small geographic latitudes than in the region of large geographical latitudes. Improvements achievable by the method are evident especially at small elevation angles.

Alternatively or cumulatively, the distance may be selected depending on a time of day and / or a magnitude of the solar activity.

Further proposed is a device for determining at least one support point-specific vertical total electron content. The device comprises at least one evaluation device. In this case, one of the methods explained above can be executed by means of the evaluation device. In particular, the device can be designed such that one of the methods explained above can be executed. In particular, the device may include means for determining the

previously discussed first incl. total electron content.

The invention will be explained in more detail with reference to an embodiment. The figures show:

1 is a schematic representation of a segmented beam path,

2 shows a schematic flow diagram of a method for determining a further inclined total electron content,

Fig. 3 is a schematic flow diagram of the method according to the invention in a first embodiment and 4 shows a schematic flowchart of the method according to the invention in a further embodiment.

Hereinafter, like reference numerals designate elements having the same or similar technical features.

In the proposed method, a first inclined total electron content and a further inclined total electron content are determined, wherein the sought-after point-specific vertical total electron content vTEC1, vTEC2, vTEC3, vTEC4 is determined as a function of this inclinated total electron contents. In the

Explanations to FIG. 1 and FIG. 2 here also include a description of the determination of the further inclined total electron content.

In Fig. 1, a segmented beam path SW is shown schematically. The beam path SW extends between a transmitter Tx and a receiver Rx, the receiver Rx being arranged on a ground surface 1. Four support points S1, S2, S3, S4 are arranged by way of example along the beam path SW. In this case, the first interpolation point S1 is located at a first height h1 above the earth's surface 1, in particular above a defined level, for example normal zero, of the earth's surface 1. Correspondingly, the further interpolation points S2, S3, S4 are located at further heights h2, h3, h4, the heights h1, h2, h3, h4 increasing along the radiation path SW from the receiver Rx to the transmitter Tx. An end point of the beam path SW is formed here by the transmitter Tx.

Also shown are support point-specific vertical paths vW1, vW2, vW3, vW4. These vertical paths vW1, vW4 intersect both the corresponding support point S1, S4 and a center of the earth M.

Along these support point-specific vertical paths vW1,..., VW4, an initial vertical total electron content vTEC1, vTEC2, vTEC3, vTEC4 can be determined for each of these vertical paths vW1,. Here it is shown that the initial vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 are in a so-called TEC card 2 are included. In the TEC card 2, the initial total vertical electron contents vTEC1, vTEC2, vTEC3, vTEC4 are mapped into a spherical layer, the initial total vertical electron contents vTEC1, vTEC2, vTEC3, vTEC4 being dependent on a latitude and longitude of

Intersections of the vertical paths vW1, vW2, vW3, vW4 can be determined with this layer or with a ground surface 1 from the TEC card 2.

Further, it is assumed that a vertical electron density distribution along these vertical paths vW1, vW4 is described by a Chapman profile function according to ne (h) = NO ^■ exp (0.5 ^■ (1-z-sec x ^■ exp (-z))) Formula 2 where h is a height above normal zero, ne is the electron density, NO is a maximum electron density along the corresponding vertical path vW1, vW4, x is a solar zenith angle and z is given by z = (h-hO) / H Formula 3, where hO is a height of the maximum electron density NO and H a

Scale height of the neutral atmosphere called. The scale height H is defined by H = k ^■ T / m ^■ g where k denotes the Boltzmann constant, T the neutral gas temperature, m the molecular mass of the neutral gas and g the acceleration of gravity in the altitude range of the ionosphere.

An integral from zero to infinity over that given in formula 2

Electron density distribution results except for separately to be considered

Plasmasphärenanteile the illustrated in Fig. 1 initial vertical

Total electron content vTEC1, ... vTEC4.

In order now to determine an incremental electron content of an increment of the beam path SW, which is arranged between the adjacent support points S1, S4, a so-called vertical is generated in a first step Increment electron content determined. This is explained by way of example for the increment between the first two interpolation points S1, S2.

The vertical increment electron content is determined here as the integral of h1 to h2 above the electron density distribution given in formula 2.

This integral can, as in MM Hoque, "Higher order propagation effects and their corrections in precise GNSS positioning", Dissertation University Siegen, DLR Research Report 2009-09, ISSN 1434-8454, 2009, pages 218-224, analytically dependent of the initial vertical total electron content vTEC1.

In this calculation, the further parameters of the electron density distribution given by formula 2, in particular the scale height H and the height h0, can be determined as fixedly predetermined values or metrologically or model-based.

If the initial vertical total electron content vTEC1 is known, then the

previously explained analytical solution depending on the initial vertical total electron content vTEC1, but independent of the knowledge of the maximum electron density NO, take place.

Thus, the corresponding vertical increment electron content vlEC12 can be determined except for a small residual error ATEC.

The vertical increment electron content vlEC12 can vary depending on the

Elevation angle ß1 in a radwegspezifischen, inclinated

Increment electron content MEC12 between the first and the second interpolation point S1, S2 are converted. This can be done, for example

NEC12 = vlEC12 / (sqrt (1 - ((h1 + RE) ^■ cosβ1) / (h01 + RE)) ² )) Formula 4 In this case, h01 denotes the height of the maximum electron density NO along the first vertical path vW1 and RE denotes the earth radius.

In Fig. 1 it can be seen that the elevation angle ßi changes with increasing height h, where ε denotes an elevation angle of the beam path SW at the earth's surface 1.

The further inclined total electron content along the ray path SW then results as the sum of all radiation path-specific, inclinated increment electron contents ilEC, wherein the last increment is arranged between the fourth support point S4 and the end point. Also, an estimated total residual error may be added to the sum describing higher order terms due to the analytic

Description of Formula 2 may be present.

It is also possible to the previously explained sum of the inclinated

Increment electron contents ilEC a plasma-sphere-related fraction P

hinzuzuaddieren. This plasma sphere fraction P can be dependent on

geophysical parameters such as e.g. a time of day, a latitude and a measure of solar activity and / or other parameters. Thus, the estimated and previously explained total residual error can be modified with a tuning factor such that the plasma sphere fraction approximately

Takes into account.

The scale height H (see, for example, Formula 3) may be given as a fixed predetermined parameter. However, it is also possible that the scale height H is determined model-based. In this case, the scale height can be determined, for example, as a function of a season, a solar activity and / or further parameters.

The height h0 of the maximum electron density can be set, for example, to 350 km and the scale height H to 70 km. FIG. 2 shows a schematic flowchart for determining a further inclined total electron content.

In a first step S1, a ray path SW (see FIG. 1) is selected, along which the further inclined total electron content is to be determined. Likewise, positions of a receiver Rx and a transmitter Tx are determined.

In a second step S2, the selected beam path SW is calculated as a function of the coordinates determined in the first step S1.

In a third step S3, a number of increments and the positions of the interpolation points S1,... S4 are set. This can vary depending on

Accuracy requirements are made. It can be considered that the accuracy increases with increasing number of increments. In this step, the calculation of the local elevation angle βi at the interpolation points may expediently also be carried out.

In a fourth step S4 parameters of the Chapman profile function (see formula 2) are determined. Further, for each vertical path vW1, ... vW4, the total vertical electronic electron content vTEC1, ... vTEC4 is determined, e.g. from the previously explained TEC card. Thus, the included increment electron contents ilEC first order can be calculated. So for every increment between the

Support points S1, ... S4 determines the increment electron content ilEC.

In a fifth step S5, the beam path-related overall residual error for the inclined increment electron content from the model approach is then estimated.

In a sixth step S6, all increment electron contents ilEC and the total residual errors are added up to a resulting electron content. This corresponds to the sought additional total electron content. FIG. 3 shows a schematic flowchart of the method according to the invention in a first embodiment. In an initial state AZ, an already determined first inclined total electron content is present. This first inclinated

Total electron content, for example, via a measurement directly or in

Dependence on measured transit time errors of radio signals along the

Beam path SW (see Fig. 1) are determined.

In a method step VS1, the determination of a plurality of initial vertical total electron contents vTEC1,... VTEC4 takes place. These can be used, for example, in

Dependence of the above-explained thin-film model can be determined. In a first state Z1, information is thus available about these initial vertical

Total electron contents vTEC1, ... vTEC4. In a further method step VS2, the determination of the further inclined total electron content takes place. In the further method step VS2, for example, the method explained in FIG. 2 can be carried out.

In a second state Z2, the further inclined total electron content is thus determined.

In a further method step VS3, a support point-specific

Conversion function as ratio between the further inclinated

Total electron content and the initial total vertical electron content vTEC1, ... vTEC4 for which a new value is to be determined. In this ratio, the further included total electron content forms the numerator and the corresponding initial vertical total electron content vTEC1,... VTEC4 the denominator.

If, for example, the first vertical total electron content vTEC1 is to be determined (and replace the value of the initial first total electron content vTEC1), the further inclined total electron content forms the numerator and the first initial total vertical electron content vTEC1 forms the denominator.

In a third state Z3 is thus the support point-specific conversion function in front.

In a further method step VS4, the support point-specific vertical total electron content vTEC1, vTEC2, vTEC3, vTEC4 is then dependent on the first inclined total electron content and the support point-specific

Conversion function is determined. The support point-specific vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 determined in this way may differ from the initial vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 and replace them subsequently. Thus, the TEC card 2 (see FIG. 1) can be renewed or updated.

In this ratio, the first included total electron content forms the numerator and the sample point specific conversion function the denominator.

If, for example, the first vertical total electron content vTEC1 is to be determined (and replace the value of the initial first total electron content vTEC1), the first inclined total electron content forms the numerator and the conversion function specific to the first interpolation point forms the denominator.

In a final state EZ there is thus a new value for the vertical

Total electron contents vTEC1, vTEC2, vTEC3, vTEC4.

FIG. 4 shows a schematic flow diagram of the method according to the invention in a further embodiment. It is assumed that information about the vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 (see FIG. 1) is already known. These can therefore be used to determine the initial support point-specific total electron content vTEC1 vTEC4. In an initial state AZ, these previously known information on the vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 are present, for example in the form of a TEC card 2 (see FIG. 1) or in the form of a model. In a method step VS1, the determination of the further inclined total electron content takes place. In this Method step VS1, for example, the method explained in FIG. 2 can be carried out.

In a first state Z1, therefore, the further inclined total electron content is determined.

In a further method step VS2, a support point-specific conversion function is determined for each interpolation point S1,... S4 as the ratio between the further inclined total electron content and the corresponding previously known vertical total electron content vTEC1,... VTEC4.

In a second state Z2 are thus the support point-specific

Conversion functions.

In a further method step VS3, a detected or determined first inclined total electron content is then considered, in order then to determine for each support point S1, S4 a new support point-specific vertical total electron content vTEC1, vTEC2, vTEC3, vTEC4 as a function of the first inclined total electron content and the support point-specific conversion function. These new support point-specific vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 are in a final state EZ.

In FIG. 4, a dashed arrow PF indicates that these newly determined support point-specific vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 are used in an initial state AZ for a new run of the proposed method as initial support point-specific vertical total electron contents vTEC1, vTEC2, vTEC3, vTEC4 can be.

The method thus also serves to create as accurate as possible TEC correction maps. The method can be used very well anywhere where the most accurate TEC maps are to be created. Of course, this applies to the scientific field for ionosphere research but also to information and data services such as the DLR Ionospheric Weather Service SWACI. For aeronautical applications as well, these TEC maps can provide appropriate corrections for determining transit times, eg in the currently operating Space Based Augmentation Systems (SBAS) such as the WAAS (Wide Area Augmentation System) in the USA and EGNOS (US Pat. European Geostationary Overlay Service) in Europe.

Simulations have shown that the proposed method can achieve significantly smaller deviations from the correct vertical TEC values along different beam paths than when using the thin-film model.

Claims

claims

1 . Method for determining at least one sample point specific vertical electron content (vTEC1, vTEC2, vTEC3, vTEC4), wherein the

vertex-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) denotes an electron content along a support point-specific vertical path (vW1, vW2, vW3, vW4) that extends through a center of the earth (M) and the corresponding interpolation point (S1, S2, S3, S4 ), wherein

a first inclined total electron content is determined, wherein the first inclined total electron content denotes an electron content along an inclined beam path (SW),

a first and at least one further support point (S1, S2, S3, S4) is selected along the beam path (SW),

for each support point (S1, S2, S3, S4), an initial support point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) is determined,

- depending on the initial support point-specific vertical

Total electron content (vTEC1, vTEC2, vTEC3, vTEC4) and a

support point-specific vertical electron density distribution

Incrementelektroneninhalt is determined, wherein the increment electron content denotes an electron content of the support point (S1, S2, S3, S4) associated increment,

- wherein a further inclinated total electron content depending on

Increment electron content is determined

- whereby a support point-specific conversion function between the further inclined total electron content and the initial support point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) is determined,

- Wherein the at least one support point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) depending on the first inclinated

Total electron content and the support point specific conversion function is determined.

2. The method according to claim 1, characterized in that the support point-specific conversion function as a ratio between the further inklinierten

Total electron content and the initial support point-specific vertical

Total electron content (vTEC1, vTEC2, vTEC3, vTEC4) is determined, wherein the at least one support point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) as a ratio between the first inclinated

3. The method according to any one of the preceding claims, characterized in that an initial support point specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) is previously known or model-based determined.

4. The method according to any one of the preceding claims, characterized in that all initial support point-specific vertical total electron contents (vTEC1, vTEC2, vTEC3, vTEC4) are the same.

5. The method according to any one of claims 1 to 4, characterized in that initial support point-specific vertical total electron contents (vTEC1, vTEC2, vTEC3, vTEC4) are determined in dependence on horizontal gradient information of the total vertical electron content.

6. The method according to any one of claims 1 to 5, characterized in that initial support point-specific vertical total electron contents (vTEC1, vTEC2, vTEC3, vTEC4) are determined in dependence of a TEC card (2), the TEC card (2) information to a total vertical electron content (vTEC1, vTEC2, vTEC3, vTEC4) depending on a latitude and longitude.

7. The method according to any one of the preceding claims, characterized in that the method for a plurality of interpolation points (S1, S2, S3, S4) is performed.

8. The method according to any preceding claim, characterized in that the support point-specific electron density distribution is determined or described model-based.

9. The method according to any one of the preceding claims, characterized in that the electron content along the beam path (SW) is additionally determined as a function of a plasmasphärebedingten portion.

10. Device for determining at least one reference point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4), wherein the

vertex-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) denotes an electron content along a support point-specific vertical path (vW1, vW2, vW3, vW4) that extends through a center of the earth (M) and the corresponding interpolation point (S1, S2, S3, S4 ), wherein the

Device comprises at least one evaluation device, wherein by means of the evaluation device

a first inclinated total electron content can be determined, wherein the first inclined total electron content denotes an electron content along an inclined beam path (SW),

a first and at least one further interpolation point (S1, S2, S3, S4) can be selected along the beam path (SW),

for each support point (S1, S2, S3, S4), an initial support point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) can be determined,

- depending on the initial support point-specific vertical

Total electron content (vTEC1, vTEC2, vTEC3, vTEC4) and a

support point-specific vertical electron density distribution

Inkrementelektroneninhalt is determinable, wherein the Inkrementelektroneninhalt an electron content of the support point (S1, S2, S3, S4) associated

Increments denotes

wherein a further inclinated total electron content can be determined as a function of the increment electron contents,

- Where a support point specific conversion function between the other including the total electronic electron content and the initial sample point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4), the at least one sample point-specific vertical total electron content (vTEC1, vTEC2, vTEC3, vTEC4) being dependent on the first one

Total electron content and the support point specific conversion function is determinable.