DE19508208A1 - Satellite navigation procedures - Google Patents

Abstract

The invention concerns a satellite navigation process, in particular for an automatic landing process for aircraft, according to the ICAO requirements under the CAT-II or CAT-III terms. The necessary degrees of accuracy are achieved by analytical phase evaluation of the carrier signals of at least seven satellites (GPS and/or GLONASS and/or reference stations).

Description

The invention relates to a satellite navigation method according to the preamble of claim 1.

The invention is particularly applicable to the Naviga tion of aircraft approaching the landing.

For navigation, especially the three-dimensional Na vigation, is the evaluation of suitable satellites signals possible. Such satellites are to the Navigati onssysstemen GPS ("Global Positioning System") and GLONASS ("Global Orbiting Navigation Satellite System") summarized. GPS and GLONASS form the global satellite lit navigation system GNSS (Global Navigation Satellite  System). The signals emitted by these satellites can in depending on the required accuracy can be evaluated in different ways. A kind of Satellite navigation uses the evaluation of the code or Carrier phase measurements of a GNSS user receiver, the On board a vehicle, e.g. B. an aircraft whose Position to be determined is installed. To increase the navigation accuracy becomes the differential work wise (DGNSS) used by GNSS. In addition to the User receiver a second receiver, the reference temp catcher is called in a known position puts. This determines using the known antennas position existing measurement errors and corrects the measurements of the user recipient.

For high-precision navigation, for example automatic Airplane landings are made for safety reasons Accuracies of meters or even decimeters are required. For example, the U.S. Aviation Authority, FAA (Federal Aviation Administration) from the microwave landing system (MLS) Accuracy requirements (95%) for navigation systems sensors for precision approaches with GNSS under CAT-I / II / III visibility conditions the International Civil Aviation Organization (ICAO) derived in Table 1 below are shown.

The standard foot (ft) is used in aviation and means it
DH: Decision Height
PFE: Path Following Error (low-frequency error component)
CMN: Control Motion Noise (high-frequency error component)
In the DGNSS method (or DGPS method for GPS), the correlated errors occurring in measurements with GNSS receivers, for example satellite clock errors, satellite orbit model errors, atmospheric errors and the influence of earth rotation, can be reduced by the differential mode of operation. However, other errors, for example noise, multipath influences and dynamic influences, are uncorrelated between measurements by user and reference receivers. These errors cannot be reduced by forming differences.

These disturbing influences of noise and dynamics Typi lie on the position determination in code measurements usually in the meter range. The disruptive reusable influences with code measurements can with strong multipath reflections even cause a navigation error greater than 100 m chen. The uncorrelated errors in the carrier phase measurement solutions, on the other hand, only move in the range of milli or Centimeters and are compared to the corresponding Errors in code measurements significantly lower. The bearers In contrast to code measurement, however, phase measurement points an initial ambiguity with the number of Wavelengths on the path of signal transmission from one  Satellite to a (user and / or reference) receiver related.

A well-known procedure that complements the behavior the code and phase measurement under the name "carrier smoothed code "combined, [Hatch, R, (1982): "The Synergism of GPS code and carrier measurements ", Proceedings: Third International Symposium on Satellite Doppler Positioning, Austin, Texas, April 28 - May 2, vol 2.), can influence the influence of code noise reduce the navigation error to the centimeter range gladly. The Emp catcher dynamics determined between two times and over the phase-smoothed code measurement the phase ambiguity approximately determined. This procedure is currently in progress Widely used for real-time GPS navigation applications tet. The disadvantage of the method is that it is relatively large Sensitivity to multipath and dyna mix influences due to the still existing code measurement share. The Ge achieved by this method Accuracies have so far not met those for landing approaches required vertical accuracy of 1.2 m with a true 95% probability (CAT III PFE requirement).

To achieve accuracy with a standard deviation in the centimeter or lower decimeter range a pure carrier phase evaluation is used. Here must phase ambiguities under dynamic conditions be resolved. There are search procedures for determining determination of the phase ambiguities under kinematic conditions gungen (moving recipient) known, for. B. from the litera door positions

Hatch, R., (1990): "Instantaneous Ambiguity Resolution", in: Schwarz KP, Lachapelle G (eds): Kinematic systems in geodesy, surveying and remote sensing. Springer, New York Berlin Heidelberg London Paris Tokyo Hong Kong, 299-308.
Landau, H .; Euler, HJ, (1991): "The Key to Decimeter-Level Differential GPS Navigation: Carrier Phase Ambiguity Determination," Proceedings of the First International Symposium for Real Time Differential Applications of the Global Positioning System, Braunschweig, Sept. 1991, vol 1 .
Abidin, HZ / Wells, DE / Kleusberg, A. (1991): "Multi-Monitor Station" On The Fly "Ambiguity Resolution. Pro ceedings: First International Symposium for Real Time Differential Applications of the Global Positioning System, Braunschweig, Sept ., vol 1.
Remondi, BW (1991): "Kinematic GPS Results without Static Initialization", NOAA Technical Memorandum, NOS NGS-55, Rockville, MD.

Such search methods have the particular disadvantage that that a search space specification is required. Becomes this large chosen to certainly find the solution in search Having space means a high computing time requirement. At for example you can use for a spherical search space a radius of three meters for carrier phase measurements using four satellites, even without considering Noise, a maximum of 32768 potential solutions exist. Such a search process requires a large one technical effort and complicates its real time  sentence. To avoid this disadvantage, only one given a small search space, there is disadvantageously the possibility that the solution sought outside the Search space and therefore cannot be determined.

Furthermore, ne in the search space disadvantageously ben a searched global main minimum several subsidiary minimum be present. It is then possible to that a search process locks onto such a secondary minimum and thus provides a wrong solution.

The invention has for its object a genus to specify a procedure that is reliable, genuine timely and highly accurate positioning of a allows moving recipient, especially with one Approach of an airplane.

This problem is solved by the in the characteristic Part of claim 1 specified features. Advantage sticky refinements and / or further training are the Removable subclaims.

A first advantage of the invention is that the Navigation accuracy through evaluation of pure carriers phases of the satellite signals the lower decimeter range achieve and thus the accuracy requirements of the pre precision approaches up to CAT III requirements.

A second advantage is that navigation use an analytical carrier phase evaluation det and thus a clear, reliable navigation solution solution at all times.  

A third advantage is that the navigation ver drive due to the pure carrier phase evaluation the movement, e.g. B. shuttered during a landing approach and then after a short start-up time enables high-precision navigation.

A fourth advantage is that the technical wall and the computing effort for the navigation solution are small that the navigation procedure during a flight witness navigation is real-time capable and that a related spatially small, mechanically compact and reliable casual device can be produced.

A fifth advantage is that the evaluation process also the future satellite constellation of GNSS (operational constellation of GPS and GLONASS) inspects.

Further advantages result from the following Be spelling.

The invention is based on the carrier phase measurements of GPS and / or GLONASS and / or pseudo satellites out sent signals. Pseudo satellites, e.g. B. several Bodensta tion, send out GNSS signals and have a known one Position. When navigating a plane with high precision, especially during a landing approach, in addition to a GNSS On-board receiver at least one GNSS receiver in one place fixed reference station for carrier phase measurement required Lich as well as a data connection (data link), e.g. Legs Radio connection with which he in the reference station  averaged carrier phase corrections to the GNSS board be transmitted to the recipient.

In the invention, an evaluation of the carrier phases measurements of the GNSS satellite signals according to the following For mel uses:

Φ _E ^S = (1 / λ) · (R _E ^S + ΔR ^S + ΔR _E + ε _E ^S + N _E ^S (1)

With
Φ _E ^S measured carrier phase;
λ wavelength of the transmitted GNSS carrier signal;
R _E ^S Geometric distance from the satellite to the receiver;
ΔR ^S errors correlated between satellites, e.g. B. Receiver error;
ΔR _E errors correlated between receivers, e.g. B. Errors in ephemeris parameters and satellite clocks as well as in the ionos and troposphere;
ε _E ^S errors such as multipath influences, dynamic influences and noise;
N _E ^S phase ambiguity at an initial point in time t₀.

The (subscript) E denotes the dependent of the recipient and the (superscript) superscript S the dependence on a satellite.

In the invention, which is also called the TD6U method (triple difference GPS with 6 unknowns), a so-called triple difference (triple difference) of the carrier phase measurements between two receivers F (aircraft), Ref (fixed reference station) is formed, two satellites S _i , S _j , where i, j are integers, and two time points t₀, t ( FIG. 1), where t is greater than t₀, according to the following formula:

δ∇∆Φ = {[Φ _F ⁱ (t) - Φ _R ⁱ (t)] - [Φ _F ^j (t) - Φ _R ^j (t)]} - {[Φ _F ⁱ (t₀) - Φ _{- R} ⁱ (t₀)] - [Φ _F ^j (t₀) - Φ _R ^j (t₀)]} (2)

This formula corresponds to the spelling used in the GPS literature is currently common. Here means

∆ the difference shown in square brackets,
Differenz the difference shown in curly brackets,
δ the difference between the braces,
Φ _R ⁱ (t) the carrier phase of the satellite S _i measured at the time t at the reference station Ref,
Φ _F ⁱ (t) the carrier phase of the satellite S _i measured at the time t on the aircraft F,
Φ _R ^j (t) is the carrier phase of the satellite S _j measured at the reference station Ref at time t,
Φ _F ^j (t) is the carrier phase of the satellite S _j measured on the aircraft F at time t,
Φ _R ⁱ (t₀) the carrier phase of the satellite S _i measured at the time t₀ at the reference station Ref,
Φ _F ⁱ (t₀) the carrier phase of the satellite S _i measured on the aircraft F at the time t₀,
Φ _R ^j (t₀) is the carrier phase of the satellite S _j measured at the time t Ref at the reference station Ref,
Φ _F ^j (t₀) is the carrier phase of the satellite S _j measured on the aircraft F at the time t₀.

The difference shown in square brackets [] becomes Called single difference; the difference in curly Parentheses {} means double difference and the difference between triple difference between the braces Called (triple difference).

It follows from formulas (1) and (2)

With

ε _E ^S (τ) (S = i, j E = R, Fτ = t, t₀)

as an error one of the satellite receiver and time dependent observation.

With the triple difference, the errors ΔR _E correlated between receivers, the errors ΔR ^S correlated between satellites and the time-independent phase ambiguities N _E ^S are advantageously eliminated. The only condition for eliminating the phase ambiguities is a continuous carrier phase measurement without phase jumps (cycle slips) between the two points in time t, t₀. The remaining uncorrelated errors, the terms in the square brackets of the formula ( 3 ), are the influences of aircraft dynamics, the multipath propagation influences and the noise during the carrier phase measurement. However, these remaining errors are in the millimeter or centimeter range after triple difference formation.

To reduce the data to be transferred from the Refe Reference station Ref to become the user receiver instead of the raw one Carrier phases of Ref the correction values of the carrier phases transmitted. A correction value for the carrier phase is determined by moving the measured integrated Doppler Exercise with the known reference position and the integrated double calculated from the satellite trajectory comparison compared according to the formula:

Φ _Corr (t) = [R _R ⁱ (t) - R _R ⁱ (t _Anf )] - λ [Φ _R ^j (t) - Φ _R ^j (t _Anf )] (4)

wherein t _Anf refers Renz station to an initial time at the Refe and i denotes a variable as a function with any received satellites. The difference in the first square bracket describes the expected Doppler shift and the difference in the second square bracket describes the measured integrated Doppler shift. If the time t₀ in the formula (3) is greater than t _Anf , the difference Φ _Korr (t) - Φ _Korr (t₀) matches the time difference of the reference values in the formula (3).

The unknowns to be resolved are on board distance measurements on the left side of formula (3) included

F (t, t₀, i, j) = R _F ⁱ (t) - R _F ^j (t) - R _F ⁱ (t₀) + R _F ^j (t₀).

The unknowns are the positions of the onboard receiver too the times t and t₀

(X _B (t), Y _B (t), Z _B (t), X _B (t₀), Y _B (t₀), Z _B (t₀)).

Formula (3) is non-linear and must be used to resolve the Unknowns first linearized around an estimation point become. With an estimation point

(X _F * (t), Y _F * (t), Z _F * (t), X _F * (t₀), Y _F * (t₀), Z _F * (t₀))

you get

and

where the superscripts i and j identify the sizes of the satellites S _i and S _j .

Formula (3) is linearized around the estimation point

in which

and analogous to (7a)

The position of the user receiver can be represented with n satellites (n <6) according to the formula:

in which  

From the formula (8) are the positions of the user receiver at times t and t₀ Can be determined using the least squares method:

 = (A ^T A)^-1 A ^T Z.      (9)

With
 = [ΔX_F(t), ΔY_F(t), ΔZ_F(t), ΔX_F(t₀), ΔY_F(t₀), ΔZ_F(t₀)]^T Vector with the Deviations from an estimation point [X_F* (t), Y_F* (t), Z_F* (t), X_F* (t₀), Y_F* (t₀), Z_F* (t₀)]^T

Z = λ [ DΦ _F (t) - DΦ _F (t₀)] - λ [ DΦ _R (t) - DΦ _R (t₀)] + [ DR _R (t) - -DR _R (t₀)] - [ DR _F * (t) - DR _F * (t₀)

FIG. 1 illustrates the formation of these triple differences using aircraft navigation as an example. The user receiver on board an aircraft F and the reference receiver in a fixed reference station Ref continuously received the signals from two satellites S _i and S _j . At a time t₀, the satellites S _i , S _j and the aircraft F are in the initial positions S _i (t₀), S _j (t₀) and X _F (t₀). The starting time t₀ can be any time, e.g. B. be a time shortly before landing. The positions of the satellites S _i and S _j at times t₀ and t are known, as is the position of the fixed reference station Ref. The carrier phase corrections determined at the reference station are determined by the data link, for. B. a data or voice radio channel to the aircraft F. The triple difference equations are formed on board the aircraft F from the carrier phases measured on board and the transmitted carrier phase corrections.

Instead of the phase ambiguities as unknowns as in to determine a search method, the TD6U-Ver only drive the positions of the on-board receiver to the two Times (six unknown coordinate sizes) in the Triple difference equations determined analytically. Because everyone Satellite pairing provides a triple difference equation, are used to determine the six unknowns at least seven satellite measurements needed.

Fig. 2 shows a schematically illustrated block diagram for determining the three coordinates which the current position X _F (t) of the aircraft F or navigation determine sizes. Here, the six unknowns (coordinates at the starting time t₀ and the current time t) with sufficient triple difference equations are determined by the least squares method, which is also referred to as the least square algorithm (LSQ). Of the six unknowns, only the coordinate sizes of the current position are used for navigation. The coordinate sizes of the starting position (at time t₀) are not used directly. The starting position in the position solutions is unknown but unchanged over time, so that this position can advantageously be statistically evaluated in the solutions. This property is used to reduce the noise component when determining the starting position by means of a filter, preferably a low-pass filter.

The low-pass filter smoothes the values of the starting position X _F (t₀) determined by the first LSQ solutions with six unknowns. In order to shorten the settling process in the filter, the filter only assumes the difference from an estimated starting position. The filtered starting position X _F (t₀) is used again in the triple difference equations to determine the unknown current position X _F (t). In the second LSQ solution, however, the three coordinate sizes of the low-pass filtered starting position are no longer considered unknown, but only the three coordinates of the current position.

The advantage of this method is that the geometric influence in the second LSQ solution with three unknowns is significantly smaller than in the first LSQ solution with six unknowns. The influence of the geometry in the first LSQ solution depends on the time interval between the starting time t₀ and the current time t and behaves like an e ^{-t / T} function with a time constant T that is in the range of a few minutes. With small time spans between t and t₀, the factor between the position error (1 Dd) and the distance error (1 δ), the so-called PDOP (Position Dilution of Precision), with the first LSQ solution with six unknowns, can be greater than 100, while the PDOP in the second LSQ solution, with three unknowns, is typically less than 3. Consequently, all residual errors of the triple difference equations in the second LSQ solution, apart from the estimation error of the starting position, have fewer influences on the positioning accuracy.

Another advantage of this filtering process arises from the clear separation between the starting position and the current position. Since the current position in the Navigation is unfiltered, affects the filtering of the Starting position not the dynamic behavior of the navigation system gation, that is, real-time navigation is possible Lich.

The TD6U method has at least six simultaneous ones Observation equations for the solution of six unknowns required. As already mentioned, this requires carriers phase measurements using at least seven satellites. Even the full GPS constellation with 24 satellites can just covering four satellites for almost 100% of them pass. Currently still missing for the precision approach Required availability (e.g. <98% for CAT-I) can, however, through the Russian satellite navigation system GLONASS or pseudo-satellites (ground stations that  Send GNSS signals). After the complete The system structure of the GLONASS is available to everyone at all times Place on earth with a combined GPS / GLONASS system At least eight satellites are visible, so their GNSS signals can be received. The required satellite lite availability can also be supported by three pseudo satellites, preferably near one Runway. In addition to the combination with This method can also be used without additional satellites additional satellites in combination with more than one Insert the ground station. Since the procedure with every Refe reference station due to the GPS satellite constellation at least at least four satellites or three triple difference equations gene, the procedure is by means of two reference stations which have at least six independent equations can only be used with GPS alone. In addition, the procedure may be due to its real nature temporality also currently on other kinematic real time applications are used where there is no continuous Availability of the satellites is required.

Through experimental tests with independent reference systems, the inventive TD6U method was used checks. The evaluations of the recorded measurement data were for security reasons under a pseudo real time condition performed, d. that is, the measured TD6U data were at an interface from a data store (File) fed into an evaluation unit. At the end only those available up to the input were evaluated Data used.  

The first test was based on a DGPS level measurement carried out two measurement points. The antennas from two GPS receivers were on the two survey points set up, with the first GPS receiver for reference station and the second as a "mobile station" (user receiver ger) were taken.

Fig. 3 shows the evaluation results with the TD6U method. During the evaluation, the "mobile station" is considered to be unknown and mobile. From the time t₀, the signals from eight satellites with elevation angles greater than 7 degrees are received by the reference and "mobile" receivers, so that sufficient satellite measurements are available for the TD6U solution. The time t₀ is referred to as the start time for the TD6U solution. Since the geometry or PDOP of the triple difference equations with six unknowns is unfavorable for a short period of time, only the measured values are registered at the start time t₀ and only started two minutes later at the time t _min . In the interval from t₀ to t _min , the evaluation is carried out with the "carrier smoothed code" mentioned. The maximum deviation of the measured position of the "mobile" receiver from the actual, highly precisely determined position during this phase is approximately 1.5 m. From time t _Min , the method according to the invention (TD6U solution) is started from an initial position ( X _F * (t₀) in FIG. 2) estimated by the carrier-smoothed code. The accuracy of this estimate is generally in the range of meters. A big estimation error, e.g. B. of 100 m, the settling process, but not affect the stability and the final value be. With a filter time constant of 15 seconds, the values of the starting position (see FIG. 2) determined by the first LSQ solutions with six unknowns are low-pass filtered. The estimation error is thus reduced by approx. 80% after the first 30 seconds. After this brief settling process, the error components of the filtered starting position fall below an error value of 25 cm in all directions. Due to the time behavior of the PDOP change (like an e ^{-t / T} function with a time constant T of approximately 3 minutes), the courses (settling processes) of the position deviations took about 10 minutes ( 3 T) until the position accuracy became one Errors less than five centimeters converged. Long-term residual errors of the carrier phase differences, such as low-frequency multipath influences, can, as already mentioned, adversely affect the TD6U accuracies. The errors in the carrier phase measurements caused by the multipath propagation are in the millimeter or centimeter range. Although the measuring environment cannot be called favorable here, the influence of the long-wave residual errors on the position, even with the unfavorable geometry at the beginning, remains below an error value of 25 cm. The accuracy is significantly increased compared to the current state of the art, the carrier smoothed code.

The second test was carried out by a flight test with a so-called laser tracker (laser range finder) as an absolute reference. The three-dimensional position of a laser specular reflector can be determined with the laser tracker. Fig. 4 shows the locations of the GPS reference station and the laser tracker, which have already been measured very precisely in the coordinate system WGS84 before the flight test. On a test plane, e.g. B. a twin-engine propeller aircraft, a laser mirror reflector of the laser tracker and the GPS antenna, as illustrated in Fig. 5, were attached. The laser tracker can emit a laser signal to the reflector attached to the aircraft. By receiving the reflected laser signal, the bearing angle and the distance (corresponding to the duration of the laser signal) between the laser tracker and the specular reflector are determined. The measuring accuracy of the laser tracker used is shown in the following table 2:

Before the flight test, the laser tracker was calibrated (calibrated) using a (calibration) mirror reflector attached to the so-called tower of the airport ( FIG. 4). However, due to the measurement accuracies shown in Table 2, this calibration can have an offset within the accuracy tolerance. There is z. For example, if a calibration error of 0.01 ° in the elevation angle, this error causes a vertical error of approximately 0.22 m at the runway threshold R27 (distance between the runway threshold and the laser tracker: approximately 1250 m).

Two GPS receivers with 10 reception channels were used in the flight test. The antenna of the ground receiver (reference receiver) was on the reference point shown in FIG. 4. Six approaches were carried out with different intercept angles. Fig. 6 shows, the trajectories of the six square round in the horizontal and the vertical plane.

The six approaches are evaluated both with the GPS measurement data using the TD6U method and with the measurement data of the laser tracker. The two results are compared to each other during the landing phases. Fig. 7 shows the PFE and CMN errors from the comparison of the TD6U results with the laser tracker results in the final phases of the landings. For five out of six approaches, evaluations with the TD6U method are only possible at a time of 4 to 6 minutes before landing due to the shadowing of some satellite signals during each turn (number of received satellite signals less than 7). Although the geometry conditions are unfavorable due to the short time spans and the error of the laser tracker measurement must also be taken into account, the comparison results of all six approaches meet the requirements of the precision approaches. The requirements of the CAT I to CAT III conditions are also entered to assess the location accuracy. The following table 3 summarizes the PFE errors of all approaches at altitudes above the runway threshold (HAT) of 50 ft and 100 ft (decision height for CAT III and II) by specifying the mean value and the scatter.

Mean
HAT: (Height Above Threshold), the height above the runway threshold (decision height) in foot (ft)
Y: the cross direction to the runway
H: the vertical direction.

To create a reference, the three-dimensional position of the runway was measured with high precision using the laser tracker. By using the low-pass filter for the initial position and the subsequent LSQ solution with three unknowns ( Fig. 2), the high-frequency error parts of the initial position are reduced to the centimeter range.

The CMN errors shown in FIG. 7 essentially contain the high-frequency errors of the laser tracker.

The measured runway was used for the third test used. To the TD6U location accuracy among the dynami The height profile also provides a means of checking conditions the runway is an absolute reference. The height profile of the Landing strip was by a roll test with the same measurement equipment between the points of the runway sleepers L09 and R27 measured. The measurement accuracy included an error less than 10 cm.

In Fig. 8a) the height trajectories of all six flights are entered in the runway area. The touchdown point aimed for by the pilot is in the range of approximately 150 to 180 m behind the runway threshold R27. The GPS antenna was attached above the fuselage ( Fig. 5) and is 2.21 m from the ground when the aircraft is standing. Fig. 8 b) also shows a section of the roll phase, in which the deviations from the target profile can be seen more clearly. Due to the better accuracy of the reference system compared to the laser tracker, the deviations determined here are smaller than the comparison results with the laser tracker. The mean value of the height differences compared to the measured runway profile is 0.35 m and the scatter 0.13 m. The mean value consists of a TD6U offset (TD6U offset), a measurement error on the runway and an operational error in the antenna setup of the reference station. Compared to the mean value of the vertical PFE error (0.61 m to 0.62 m) in Table 3, the mean value is smaller here and the difference between the two results corresponds to the accuracy of the laser tracker. In contrast to the comparison results with the laser tracker, the scatter here is the pure scatter of the TD6U error, since the runway as the reference remains constant in all measurements. The difference in scatter compared to the result in Table 3 corresponds to the measurement scatter of the laser tracker.

With the described method it is possible to get one on navigation system based on the procedure at the prezi turn on approaches. This has after an An a measurement error in the un lower decimeter range for the navigation of the aircraft. The accuracy requirements are up to CAT-III for an automatic landing.

The invention is not based on the embodiment described example limited, but analogously to other high  to transmit exact kinematic applications such as B. Photogrammetry, air gravimetry, loading and unloading in one port area, etc.

Claims (9)

1. Satellite navigation method with a moving User receiver and a reference station, their position is known, being in the user receiver and the Refe renzstation the Si emitted by several satellites gnale are received and evaluated and from that the Position of the user recipient is determined,characterized

• - That in the user-receiver and the reference station (Ref) the signals received by several satellites (S _i , S _j ) and / or equivalent pseudo-satellites are evaluated by means of a carrier phase measurement according to the formula Φ _E ^S = (1 / λ) · (R _E ^S + ΔR ^S + ΔR _E + ε _E ^S + N _E ^S with
  Φ _E ^S measured carrier phase;
  λ wavelength of the transmitted GNSS carrier signal;
  R _E ^S Geometric distance from the satellite to the receiver;
  ΔR ^S errors correlated between satellites;
  ΔR _E errors correlated between receivers;
  ε _E ^S errors such as multipath influences, dynamic influences and noise;
  N _E ^S phase ambiguity at an initial point in time t₀,
• - That a triple difference is formed from the carrier phases determined at the start time (t₀) and a current time (t with t <t₀) according to the formula δ∇∆Φ = {[Φ _F ⁱ (t) - Φ _R ⁱ ( t)] - [Φ _F ^j (t) - Φ _R ^j (t)]} - {[Φ _F ⁱ (t₀) - Φ _-R ⁱ (t₀)] - [Φ _F ^j (t₀) - Φ _R ^j (t₀)]} with
  Φ carrier phase,
  ∆ the difference shown in square brackets,
  ∇ the difference shown in curly brackets,
  δ the difference between the braces,
  t the current time,
  t₀ the start time,
  Φ _R ⁱ (t) the carrier phase of the satellite S _i measured at the time t at the reference station Ref,
  Φ _F ⁱ (t) is the carrier phase of the satellite S _i measured at the user receiver F at time t,
  Φ _R ^j (t) is the carrier phase of the satellite S _j measured at the reference station Ref at time t,
  Φ _F ^j (t) is the carrier phase of the satellite S _j measured at the user receiver F at time t,
  Φ _R ⁱ (t₀) is the carrier phase of the satellite S _i measured at the initial point in time t der at the reference station Ref,
  Φ _F ⁱ (t₀) is the carrier phase of the satellite S _i measured at the initial receiver t F at the user receiver F,
  Φ _R ^j (t₀) is the carrier phase of the satellite S _j measured at the reference time Ref at the reference station Ref,
  Φ _F ^j (t₀) is the carrier phase of the satellite S _j measured at the initial receiver t F at the user receiver F, and
• - That from the triple difference, the position of the groove is determined analytically according to the Vector formula  = (A ^T A)^-1 A ^T Z.With
   Position vector of the user receiver,
  A a geometry matrix,
  A ^T the transpose tooA,
  Z. a measurement vector.

2. Satellite navigation method according to claim 1, characterized in that

• - That in the reference station (Ref) a phase correction value Φ _Corr (t) is determined according to the formula Φ _Corr (t) = [R _R ⁱ (t) - R _R ⁱ (t _Anf )] - λ [Φ _R ^j ( t) - Φ _R ^j (t _Anf )] with
  t _Anf initial instant at the reference station,
  λ wavelength of the transmitted GNSS signal,
  R _R ⁱ (t) geometric distance from the satellite S _i to the reference station at time t,
  R _R ⁱ (t _Anf ) geometric distance from the satellite L _i to the reference station at time t _Anf ,
  Φ _R ⁱ (t) at the time t at the reference station Ref measured carrier phase of the satellite S _i ,
  Φ _R ⁱ (t _Anf ) at the time t _Anf the carrier phase of the satellite S _i measured at the reference station Ref,
• that the phase correction value is transmitted to the user receiver by means of a data transmission link,
• - That the carrier phase determined there is corrected in the user receiver as a function of the phase correction value and
• - That the position of the user receiver is determined from the corrected carrier phase.

3. Satellite navigation method according to claim 1 or Claim 2, characterized in that the position of the  User receiver at an initial time (t₀) due their characteristic, unchanged over time, statistically is evaluated. 4. Satellite navigation method according to one of the previously going claims, characterized in that the sta statistically evaluated position of the user recipient on the Starting time (t₀) as known position in the observ equations of respect is used and that then to a determinable current time (t) only the current elle position of the user recipient is determined. 5. Satellite navigation method according to one of the previously going claims, characterized in that the to determined position belonging to an initial point in time (t₀) of the user receiver smoothed by low-pass filtering becomes. 6. Satellite navigation method according to one of the previously going claims, characterized in that for the Determining the starting position of the user recipient Estimate is used. 7. Satellite navigation method according to one of the previously outgoing claims, characterized in that the groove zer receiver is attached to an aircraft. 8. Satellite navigation method according to one of the previously going claims, characterized in that as lands help for planes near a runway at least a fixed reference station (Ref) with known Posi tion is set up.   9. Satellite navigation method according to one of the previously outgoing claims, characterized in that in addition to the reference station (Ref) near the runway at least one pseudo satellite station set up becomes.