WO2015139961A1

WO2015139961A1 - Method and system for correcting errors in satellite positioning systems and computer program products thereof

Info

Publication number: WO2015139961A1
Application number: PCT/EP2015/054516
Authority: WO
Inventors: Manuel Hernandez Pajares; Alberto GARCIA RIGO
Original assignee: Universitat Politècnica De Catalunya
Priority date: 2014-03-19
Filing date: 2015-03-04
Publication date: 2015-09-24

Abstract

The method comprising: determining, by a GNSS receiver (26), a position of a user and its corresponding time, said determining being performed by the computing of a pseudo-distance of the GNSS receiver (26) to each GNSS satellite (100, 101,..., 10n) in view thereof and by the receiving of a broadcasted navigation message within a subcarrier from a control segment of each GNSS satellite (100, 101... 10n), wherein said determined position is corrected by means of a remote server (20) that receives said determined position and corresponding time and computes at least positioning corrections to be applied thereof taking into account at least a delay error ε due to the ionospheric effects or any other predominant error of each of the GNSS satellites (100, 101... 10n).

Description

Method and system for correcting errors in satellite positioning systems and computer program products thereof

Field of the invention

The present invention generally relates to satellite positioning systems. In particular, the invention relates to a method, system and computer program products for correcting errors, particularly ionospheric errors, in satellite positioning systems.

Background of the invention

Nowadays, there is an increased interest in Global Navigation Satellite Systems (GNSS) with the modernization of the NAVigation Satellite Timing and Ranging Global Positioning System (NAVSTAR GPS). Moreover there is a renewed impulse to the Russian GLObal NAvigation Satellite System (GLONASS) and the deployment of new GNSS such as the European Global Navigation Satellite System (GALILEO) or the Chinese GNSS System (BeiDou). In the last years, the potential users with access to GNSS and the number of commercial applications based on GNSS have grown significantly, in fields such as precise navigation and timing, and ionospheric and tropospheric sounding, among others.

The GPS system is the most well-known GNSS. Regarding GPS architecture, one can distinguish between three main segments:

· Space segment: Consists of the GPS satellite constellation which is comprised at present of 24 satellites plus some on-orbit spares (Full Operational Capability, FOC), evenly distributed within 6 orbital planes with an inclination to the equator of the Earth of 55° and equally spaced 60°. Their orbits are near-circular with a semi- major axis of about 4.1 times the Earth radii (nominal orbits of around 20200km with respect the surface of the Earth). The orbital period is approximately 12 sidereal hours. This configuration guarantees a global 24-hour coverage with, at least, four satellites in view, which is the minimum number of satellites required to solve the position of a GPS receiver.

• Control segment: Consists of a network of ground stations, whose functions are:

- Control and keep the status and configuration of the satellite constellation.

- Predict satellites ephemeris and on-board clock evolution by solving the inverse problem with the directly gathered GPS measurements.

- Keep the GPS time scale.

- Periodically update the navigation message broadcast via the satellites. • User segment: Consists on the GPS receivers of all the users. The GPS receivers gather the GPS signal from the satellites and solve the navigation equations in order to obtain its own coordinates and clock error.

As previously said, GNSS are mainly constituted by a space segment of 24 satellites plus some on-orbit spares transmitting time marks on dual-frequency L-band electromagnetic carriers, which allows GNSS receivers, to measure the apparent travel time, i.e. the apparent or pseudo-distance (pseudorange, affected by effects changing the velocity of signals) to each GNSS satellite in view. This measured pseudorange, combined with the knowledge of the satellite position thanks to the information provided by the control segment of the GNSS satellites to the user, through a navigation message broadcast within a subcarrier, provides the equation, dependent on the user position and clock error, and which can be interpreted in first approximation as the equation of a sphere (hereinafter pseudo-sphere) containing the user.

The intersection of at least four of these pseudo-spheres, i.e. having simultaneous pseudorange measurements, y_; (i=l,...,m) of at least four satellites in view (m>=4), allows to solve, among others, the main four user unknowns, its 3D position, Xj (j=l,2,3), and its clock error (dt). To solve such model the distance is typically linearized, around to a raw position, x_OJ-, j=l,2,3 and the solution can be iterated if needed, i.e. when the raw initial position is very far from the actual one:

then

ΔΥ≡Υ- Υ₀ =Α ΔΧ (Eq.2) being Y=(yi,...,y_m)^T ,

Y₀ = f(X_Q), ΔΧ= X-X₀ in the basic GNSS positioning problem, and (A)^- = (5fi/5X_j)₀, i=l,...,m, j=l,..,n (n=4 in this basic model), is the Jacobean Matrix evaluated at the position guess.

The measured pseudorange is typically affected by other terms, among the distance and receiver clock error, which can be typically modelled in an accurate enough way, i.e. at sub- meter error level (for instance the satellite clock errors, provided by the control segment as well at meter-error level, tropospheric slant delay, modelled typically at 90% level, among others). However there exists one predominant term which affects the pseudorange measurements, and cannot be accurately corrected in mass-market GNSS receivers that presently work in a single frequency, the ionospheric delay generated by the free electrons, which are distributed -with high spatial and temporal variability- at heights between about 50 and beyond 2000 km, and can generate contributions of tens of meters to the pseudorange measurements.

In spite the user disposes of an ionospheric model, broadcast in the navigation message, this model [1] is too simple and typically corrects only the 50-70% of the ionospheric delay, with a remaining ionospheric error which can reach the level of few tens of meters, compromising seriously (after taking into account the geometric -Dilution Of Precision- augmenting error factor) the objective of a positioning error at few meters level.

Apart from that, the replacement of said non-accurate broadcast ionospheric corrections by more accurate ones coming from better and newer ionospheric models, that are fed with much more data and with more powerful computation strategies, such as the ionospheric tomography [2] , is not possible directly in the actual mass-market GNSS receivers, present in millions of computing devices such as smartphones. This is due to the present inability of accessing to the raw GNSS data, pseudorange measurements included. This problem impedes as well to properly correct any predominant source of range error, not only the typical ionospheric one, affecting the user position at a given moment (for instance an anomalous satellite clock correction provided by the control segment).

Therefore, there is a need in the art for a way to correct in more accurate way said errors, principally the ionospheric errors, in satellite positioning systems.

REFERENCES

[1] Klobuchar, J. A. et al.(1986), Design and characteristics of the GPS ionospheric time delay algorithm for single frequency users, IEEE Plans 1986 Position, Location and Navigation Symposium, Las Vegas, USA.

[2] Hernandez-Pajares, M., et al. (2011), The ionosphere: effects, GPS modeling and the benefits for space geodetic techniques, Journal of Geodesy, published on-line, 1-21, doi: 10.1007/s00190- 011-0508-5.

[3] GPS, I. (2000). 200C, "The Interface Control Document of the Global Position System", USA: ARINC Research corporation.

Disclosure of the Invention

The invention provides in a first aspect a method for correcting errors, particularly ionospheric errors, in satellite positioning systems comprising as commonly in the field:

a) computing, by a GNSS receiver that works in a single frequency and runs in a computing device such as a smartphone, a tablet, a PDA, or connected to a computer, among others of a user, at least a pseudo-distance, that is a distance affected by other effects that change the propagation velocity of the GNSS satellite signals such as the receiver and satellite clock errors, ionospheric electron content, tropospheric water vapor, relativistic terms, of the GNSS receiver to each GNSS satellite in view thereof, said computing being performed by means of the receiving of a time mark from each GNSS satellite and/or by means of the integrated Doppler effect, the so called carrier phase measurement of the pseudorange; b) receiving, by the GNSS receiver, from a control segment of each GNSS satellite system, a broadcast navigation message within a subcarrier; and

c) determining, by the GNSS receiver, a position of said user and a corresponding time by using said computed pseudo-distances and said received broadcast navigation message of steps a) and b).

Particularly, and on contrary of the known proposals in the art, the method of the first aspect corrects said determined position of the user by further performing following steps: d) receiving, by a remote server to which said user connects at a given time, either automatically or manually by the user, or by a set of programs installed and running inside the user computing device itself, the determined position x', being x'= (χι',χ₂' ,Χ3 '), and corresponding time of step c); and

e) computing, by said remote server, or by the set of programs inside the user computing device, at least positioning corrections 5x'to be applied to said determined position x' taking into account at least a delay error ε due to the ionospheric effects or any other predominant error of each of the GNSS satellites, typically given in previous step b).

In accordance with an embodiment, the remote server further transmits the correction of the determined position of the user to the GNSS receiver for future potential positions and sets of GNSS satellites in view, from the prediction of the predominant error, e.g. the ionospheric one, for instance in the next few hours. The user then uses the transmitted correction of the determined position to obtain an improved position.

In addition, user positioning and clock corrections δΧ', being δΧ'=(δχ', 5dt), are computed by approximating the ionospheric delay by a broadcast value provided in the navigation message, or any other broadcast correction showing a predominant error, minus a more accurate value of the correction term showing predominant error for the pseudorange of each GNSS satellite and taking them as pseudo observations, being ε such difference, so that: (δχ', 5dt)= (A'WAy'A'W · ε is the corresponding impact on the user solution, e.g. positioning and time domain, where: (A)^- = (5fi/5X_j)₀ , i=l ,...,m, j=l,..,n, is the Jacobean Matrix evaluated at the position guess, corresponding to a linearized model of the GNSS observations or Y:

(X-X₀)=Y_o + A ΔΧ and W is a weighting matrix.

The determined position x' and a clock error dt of the GNSS receiver are also properly corrected, termed as X'=(x', dt), in accordance with an embodiment, subtracting this correction directly computed in the n-D user solution space (including positioning and clock error, n>4): X'- δΧ'= Χ₀+(Α'λνΑ) Α'λν·(ΔΥ+ε)- (A'WA^A'W · ε = Χ₀+(Α'λνΑ) Α'λν·ΔΥ = X, so that the user can directly correct the unknowns X' including position, and sometimes velocity, from the effect of the remaining range error ε, for instance of ionospheric origin, thanks as well to the use of a projector P= (A'WAy'A'W corresponding to a same modelling and set of GNSS satellites in view.

In accordance with an embodiment, the determined position comprises a geographical location including at least coordinates x and y which are perpendicular to each other.

Furthermore, said determined position, according to another embodiment, further includes a z coordinate which is perpendicular to both of said x and y coordinates.

Alternatively, in yet another embodiment, the determined position comprises a geographical area, said geographical area being of a certain radius including the user. For instance, said certain radius may include a distance up to 10 Km, or to any maximum expected user displacement distance depending on the type of user such as pedestrian, car, bike, during the time comprised by the predicted precise values of the predominant error, provided to the user.

According to a second aspect, there is provided a system for correcting errors, particularly ionospheric errors, in satellite positioning systems, the system including: a set of GNSS satellites and a GNSS receiver running in a computing device of a user and being configured to:

- compute a pseudo-distance of the GNSS receiver to each one of said GNSS satellite in view thereof, said computing being performed by means of the receiving of a time mark from each GNSS satellite and/or by means of the integrated Doppler effect, the so called carrier phase measurement of the pseudorange;

- receive from a control segment of the GNSS, a broadcast navigation message within a subcarrier of each GNSS satellite; and

- determine a position of said user and a corresponding time by using said computed pseudo-distance and said received broadcast navigation message.

The system of the second aspect in a characteristic manner further comprises a remote server to which said user connects at a given time being configured to:

- receive from the GNSS receiver said determined position x' and corresponding time thereof; and

- compute at least positioning corrections δ ' to be applied to said determined position taking into account at least a delay error or ε due to the ionospheric effects or any other predominant error of each of the GNSS satellites.

The system of the second aspect is adapted to implement the method of the first aspect.

The subject matter described herein can be implemented in software in combination with hardware and/or firmware, or a suitable combination of them. For example, the subject matter described herein can be implemented in software executed by a processor. According to a third aspect there is provided a computer program product comprising computer executable software stored on a computer readable medium, the software being adapted to run at a computer or other processing means characterized in that when said computer executable software is loaded and read by said computer or other processing means, said computer or other processing means is able to perform the steps of the method according to any of claims 1-11.

Brief Description of the Drawings

The previous and other advantages and features will be more fully understood from the following detailed description of embodiments, with reference to the attached, which must be considered in an illustrative and non-limiting manner, in which:

Figure 1 is a block diagram of the present invention general architecture.

Description of Preferred Embodiments

Fig. 1 shows the elements of the system of the present invention using a Global

Navigation Satellite Systems (GNSS). The system mainly includes a computing device 25 such as a Smartphone, among any other computing device, that has installed therein a GNSS (such as GPS and/or GLONASS) receiver or chipset 26, a remote server or Central Computational Facility (CPF, which is able to access to the GNSS navigation messages, for instance through Internet) 20 and the GNSS satellites 100, 101, 10η. For simplicity in the figure, the base stations providing communication to the computing device 25 or any other implicit stationary infrastructure, i.e. serving mobile location center, etc. have not been illustrated.

The GNSS receiver 26 that runs in the computing device 25 of the user to whom the ionospheric errors have to be corrected receives from the GNSS satellites 100, 101, 10η in view a time mark on dual-frequency L-band electromagnetic carriers. With that information, the GNSS receiver 26 is able to measure an apparent or pseudo distance (affected by effects changing the velocity of signals) to each GNSS satellite 100, 101, 10η. Then, this measured pseudorange or pseudo-distance, combined with the knowledge of the satellite position thanks to the information provided by the control segment for each of the GNSS satellites 100, 101, 10η to the computing device 25 of the user, through a navigation message broadcast within a subcarrier, provides the equation of a pseudo-sphere containing the user, which can be resolved, as explained before, to determine a position of said user, i.e. x' , and a corresponding time in which said position has been determined.

Preferably, according to an embodiment, x' is done by Least Mean Squares (LMS) in the following known way, where ε=(ει,..., 8m) represents the vector of the predominant delay error (for instance the ionospheric one, 30-50% of the total ionospheric effect) for all the GNSS satellites 100, 101, 10η in view:

ΔΧ' = (A'WA) A'W^»(AY-½) (Eq.3) where W is the weighting matrix (typically a diagonal matrix with a weight higher for higher elevation observations), and consequently:

Χ'=Χ₀+ΔΧ'= Χ₀+(Α'λνΑ) Α'λν·(ΔΥ+ε) (Eq.4) The invention, to overcome said lack of access to the raw GNSS data, characteristically takes profit of the knowledge of the set of GNSS satellites 100, 101, 10η in view, of the solution given by X'(Eq. 4), and of a standard SPS model, for instance GPS ICD 2000 [3] and computes by means of using a remote server 20 the positioning corrections i.e. δχ', to be applied directly to the coordinates computed by the GNSS receiver 26, and without the need of knowing the raw pseudorange measurements, due to the ionospheric correction error ε.

The remote server 20 to compute the positioning corrections δχ' to be done can receive the measures previously computed by the GNSS receiver 26 either automatically from the GNSS receiver 26, for instance periodically every certain period of time, or from the user whenever (s)he desires to correct their position. Preferably, the transmitted measures to the remote server 20 will indicate the less accurate geographical location X' that can include only coordinates x and y, perpendicular to each other, or can also include a z coordinate perpendicular to both of said x and y coordinates.

Alternatively, the transmitted measures that need to be corrected or improved by the remote server 20 do not need to be totally accurate but could have a certain radius, i.e. up to 10 kilometers, e.g. 1 to 10 Km.

In addition, in order to improve the corrections, a user clock error dt of the GNSS receiver 26, or improved clock and orbital errors for each GNSS satellite 100, 101, 10η may also be computed by the remote server 20.

The positioning corrections δχ', and also said user clock error, is done approximating them by the broadcast values minus the more accurate correction values (e.g. ionospheric) for each pseudorange, and taking them as pseudo observations:

δΧ'= (A'WA) A'W · ε (Eq.5)

Then, the determined position and user clock error can be properly corrected, subtracting this correction directly computed in a 4D positioning and clock error space:

X'- δΧ'= Χ₀+(Α'λνΑ) Α'λν·(ΔΥ+ε)- (A'WA) A'W · ε = X₀+(A'WA) A'W^»AY = X (Eq.6) therefore obtaining the user positioning and clock error without knowing the raw GNSS data.

The functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or encoded as one or more instructions or code on a computer-readable medium. Computer-readable media includes computer storage media. Storage media may be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. Any processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal.

As used herein, computer program products comprising computer-readable media including all forms of computer-readable medium except, to the extent that such media is deemed to be non-statutory, transitory propagating signals.

The scope of the present invention is defined in the following set of claims.

Claims

1. A method for correcting errors in satellite positioning systems, comprising:

a) computing, by a GNSS receiver (26) running in a computing device (25) of a user, a pseudo-distance of the GNSS receiver (26) to each GNSS satellite (100, 101, ..., 10η) in view thereof, said computing being performed by means of the receiving of a time mark from each GNSS satellite (100, 101, ..., 10η) and/or by means of an integrated Doppler effect;

b) receiving, by said GNSS receiver (26), from a control segment of each GNSS satellite (100, 101... 10η), a broadcast navigation message within a subcarrier; and

c) determining, by said GNSS receiver (26), a position of said user and a corresponding time by using said computed pseudo-distances and said received broadcast navigation message of steps a) and b),

the method being characterized by correcting said determined position of the user by further performing following steps:

d) receiving, by a remote server (20) to which said user connects at a given time, the determined position x' and corresponding time of step c); and

e) computing, by said remote server (20), at least positioning corrections δχ' to be applied to said determined position taking into account at least a delay error ε due to the ionospheric effects or any other predominant error of each of the GNSS satellites (100, 101... 10η).

2. The method of claim 1, wherein the remote server (20) further comprises transmitting the determined position correction δχ'οί the user to the GNSS receiver (26), the latter using said transmitted determined position correction that has been computed thanks to the prediction of the state of the ionosphere for a determined time ahead.

3. The method of claim 1, wherein user positioning and clock corrections δΧ' are further computed by approximating them by a broadcast navigation message ionospheric, or any other predominant error, values minus a more accurate value of the predominant error for each pseudorange of each GNSS satellite (100, 101... 10η) and taking them as pseudo observations, so that:

δΧ' = (δχ', 6dt)' = (A'WA^A'W · ε

where:

(A)i_j = (5fi/5X_j)₀ , i=l,...,m, j=l,..,n, is the Jacobean Matrix evaluated at the position guess, corresponding to a linearized model of the GNSS observations or Y:

Y=f(x)_¾f(x_o)+(af/ax)_o (x-x₀)=Y₀ + A ΔΧ

and W is a weighting matrix.

4. The method of claim 3, wherein said determined position x' and clock error dt of the GNSS receiver (26) are properly corrected, subtracting this correction directly computed in the 4D positioning and clock error space or in a n-D general space when additional unknowns are also solved for in a more general model:

X'- δΧ'= Χ₀+(Α'λνΑ) Α'λν·(ΔΥ+ε)- (A'WA^A'W · ε = Χ₀+(Α'λνΑ) Α'λν·ΔΥ = X so that the user can directly correct the unknowns X' including position (and velocity in some models) from the effect of the remaining range error ε (for instance of ionospheric origin) thanks as well to the use of the projector P= (A'WA^A'W corresponding to a same modelling and set of GNSS satellites (100, 101... 10η) in view.

5. The method of claim 1, wherein said given time of connection in said step d) is performed automatically from the GNSS receiver (26), manually by said user or by a set of programs inside the user computing device (25) itself.

6. The method of claim 1, wherein said determined position comprises a geographical location including at least coordinates x and y which are perpendicular to each other.

7. The method of claim 6, further comprising including a z coordinate perpendicular to both of said x and y coordinates.

8. The method of claim 1, wherein said determined position comprises a geographical area, said geographical area being of a certain radius including said user.

9. The method of claim 8, wherein said certain radius at least comprises a distance between 1 to 10 Km.

10. The method of claim 1, wherein said GNSS receiver (26) works in a single frequency.

11. The method of claim 1 , wherein said position is determined by using a Least Mean Square strategy.

12. A system for correcting errors in satellite positioning systems, said system including:

a set of GNSS satellites (100, 101... 10η); and

a GNSS receiver (26) running in a computing device (25) of a user and being configured to:

- compute a pseudo-distance of the GNSS receiver (26) to each one of said GNSS satellite (100, 101... 10η) in view thereof, said computing being performed by means of the receiving of a time mark from each GNSS satellite

(100, 101...10n) and/or by means of an integrated Doppler effect;

- receive from a control segment of each GNSS satellite (100, 101... 10η), a broadcast navigation message within a subcarrier; and

- determine a position of said user and a corresponding time by using said computed pseudo-distance and said received broadcasted navigation message, the system being characterized in that it further comprises:

a remote server (20) to which said user connects at a given time being configured to:

- receive from the GNSS receiver (26) said determined position x' and corresponding time thereof; and

- compute at least positioning corrections δ ' to be applied to said determined position taking into account at least a delay error ε due to the ionospheric effects or any other predominant error of each of the GNSS satellites (100, 101, 10η).

13. The system of claim 12, wherein said system is adapted to implement a method according to any of the previous claims.

14. A computer program product comprising computer executable software stored on a computer readable medium, the software being adapted to run at a computer or other processing means characterized in that when said computer executable software is loaded and read by said computer or other processing means, said computer or other processing means is able to perform the steps of the method according to any of claims 1-11.