Phase Ambiguity Resolution Method for a Satellite Based Positioning System

• US 20080204312A1
• Filed: 05/16/2006
• Published: 08/28/2008
• Est. Priority Date: 05/18/2005
• Status: Active Grant

• Current Assignee: Leica Geosystems AG (Hexagon AB)
• Original Assignee: Leica Geosystems AG (Hexagon AB)
• Inventors: Euler, Hans-Jürgen
• Granted Patent: US 7,728,767 B2
• Time in Patent Office: Days
• US Class Current: 342/357.04
• CPC Class Codes: G01S 19/32 Multimode operation in a single same satellite system, e.g. GPS L1/L2
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

The invention relates to a satellite-based positioning system in which a transmitter (2) emits electromagnetic radiation at least at N≧3 carrier frequencies (3, 4, 5). In order to resolve the phase ambiguity for said satellite-based positioning system, the electromagnetic radiation is received by a receiver (1), and K pseudo paths (3a, 4a, 5a, 6a) and L carrier phases (3b, 4b, 5b, 6b), especially at least two pseudo paths (3a, 5a) and at least two carrier phases (3b, 4b), are derived from the received radiation as M pieces of distance data, wherein M=K+L. In order to determine the position, the integer phase ambiguity is derived from the linear combination of a maximum of M≦2N−1 pieces of distance data.

Claims

1-11. -11. (canceled)

12. A phase ambiguity resolution method for a satellite-based positioning system, the method comprising the following acts:

transmitting electromagnetic radiation by a transmitting unit, the electromagnetic radiation having N carrier frequencies with at least one first carrier frequency, one second carrier frequency, and one third carrier frequency, where N≧

3;

receiving the electromagnetic radiation by a receiving unit;

deriving K pseudo-paths and L carrier phases as M distance data, where M=K+L, from the received radiation; and

determining an integral phase ambiguity from a linear combination of the carrier phases and the pseudo-paths for the position determination, wherein not more than M≦

2N−

1 distance data are used for the derivation.

13. A phase ambiguity resolution method according to claim 12, wherein:

at least two pseudo-paths and at least two carrier phases are used as distance data, the first and second carrier phases coordinated with the first carrier frequency and the second carrier frequency and the third pseudo-path coordinated with the third carrier frequency being linearly combined.

14. A phase ambiguity resolution method according to claim 12, wherein the derivation act comprises solving the following set of equations:

${\mathrm{\phi <br><br>}}_1=\mathrm{\rho <br><br>}-\frac{I}{f_1^2}+N_1<br><br>{\mathrm{\lambda <br><br>}}_1+{\mathrm{\varepsilon <br><br>}}_{{\mathrm{\phi <br><br>}}_1}$ ${\mathrm{\phi <br><br>}}_2=\mathrm{\rho <br><br>}-\frac{I}{f_2^2}+N_2<br><br>{\mathrm{\lambda <br><br>}}_2+{\mathrm{\varepsilon <br><br>}}_{{\mathrm{\phi <br><br>}}_2},<br><br>R_1=\mathrm{\rho <br><br>}+\frac{I}{f_1^2}+{\mathrm{\varepsilon <br><br>}}_{R_1},<br><br>R_3=\mathrm{\rho <br><br>}+\frac{I}{f_3^2}+{\mathrm{\varepsilon <br><br>}}_{R_3},$

where, with i=1, 2, 3,

φ

_i designates a phase path coordinated with a i th carrier phase as a measured variable;

R_i designates the i th pseudo-path as a measured variable;

ρ

designates a geometrical path between the transmitting unit and the receiving unit including clock errors and non-dispersive error terms;

I/f_i² designates an ionospheric influence for the specified i th carrier frequency;

N_i designates a phase ambiguity for the wavelength λ

_i coordinated with the i th carrier frequency;

ε

<sub>φ

i</sub> designates a noise term for the phase path coordinated with the i th carrier frequency; and

ε

_Ri designates a noise term for the i th pseudo-path, the solution comprising a determination of the phase ambiguities N_i.

15. A phase ambiguity resolution method according to claim 12 wherein:

the electromagnetic radiation has a fourth carrier frequency; and

the first and the second carrier phases and the third pseudo-path and the fourth pseudo-path coordinated with the fourth carrier frequency are linearly combined.

16. A phase ambiguity resolution method according to claim 15, wherein the first and the second carrier phases and the third pseudo-path and the fourth pseudo-path coordinated with the fourth carrier frequency are linearly combined with solution of the following set of equations:

${\mathrm{\phi <br><br>}}_1=\mathrm{\rho <br><br>}-\frac{I}{f_1^2}+N_1<br><br>{\mathrm{\lambda <br><br>}}_1+{\mathrm{\varepsilon <br><br>}}_{{\mathrm{\phi <br><br>}}_1},<br><br>{\mathrm{\phi <br><br>}}_2=\mathrm{\rho <br><br>}-\frac{I}{f_2^2}+N_2<br><br>{\mathrm{\lambda <br><br>}}_2+{\mathrm{\varepsilon <br><br>}}_{{\mathrm{\phi <br><br>}}_2},<br><br>R_3=\mathrm{\rho <br><br>}+\frac{I}{f_3^2}+{\mathrm{\varepsilon <br><br>}}_{R_3},<br><br>R_4=\mathrm{\rho <br><br>}+\frac{I}{f_4^2}+{\mathrm{\varepsilon <br><br>}}_{R_4},$

where, with i=1, 2 and j=3, 4,

φ

_i designates a phase path coordinated with the i th carrier frequency as a measured variable;

R_j designates the j th pseudo-path as a measured variable;

ρ

designates a geometrical path between a transmitting unit and a receiving unit, including clock errors and non-dispersive error terms;

I/f_i² designates an ionospheric influence for the specified i th carrier frequency;

I/f_j² designates an ionospheric influence for the specified j th carrier frequency;

N_i designates a phase ambiguity for the wavelength λ

_i coordinated with the i th carrier frequency;

ε

<sub>φ

i</sub> designates a noise term for the phase path coordinated with the i th carrier frequency; and

ε

_Rj designates a noise term for the j th pseudo-path, the solution comprising a determination of the phase ambiguities N_i.

17. A phase ambiguity resolution method according to claim 16, further comprising smoothing at least one of the third and fourth pseudo-paths.

18. A phase ambiguity resolution method according to claim 17, wherein smoothing of at least one of the third and fourth pseudo-paths is accomplished by calculation of the mean value of differences of the third and/or fourth pseudo-path and a phase path coordinated with the first or second carrier phase.

19. A phase ambiguity resolution method according to claim 16, characterized in that a linear combination φ

* of the pseudo-paths is formed from the first and second carrier phases so that a positive sign results for ionospheric terms, so that the changes in the phase paths correspond to the changes in the pseudo-paths.

20. Phase ambiguity resolution method according to claim 19, wherein the linear combination φ

* is effected according to the following relationship;

${\mathrm{\phi <br><br>}}^{*}=F<br><br>\left({\mathrm{\phi <br><br>}}_1,{\mathrm{\phi <br><br>}}_2\right)=\mathrm{\rho <br><br>}+\frac{I}{f_k^2}+G<br><br>\left(N_1,N_2\right)+{\mathrm{\varepsilon <br><br>}}_{\mathrm{\phi <br><br>}}^{*}$

in which,

φ

₁ designates a phase path coordinated with the first carrier frequency;

φ

₂ designates a phase path coordinated with the second carrier frequency;

F(φ

₁,φ

₂) designates a linear combination;

$F<br><br>\left({\mathrm{\phi <br><br>}}_1<br><br>{\mathrm{\phi <br><br>}}_2\right)=B+\underset{i=1}{\overset{2}{\sum <br><br>}}<br><br><br><br>b_i<br><br>{\mathrm{\phi <br><br>}}_i$

of the phase paths with coefficients bi and a term B independent of the phase paths;

ρ

designates a geometrical path between the transmitting unit and the receiving unit including clock errors and non-dispersive error terms;

I/f_k² designates an ionospheric influence for the carrier frequency to be smoothed, where kε

{1,2,3,4};

N₁ designates a phase ambiguity for the specified wavelength λ

₁ coordinated with the first carrier frequency;

N₂ designates a phase ambiguity for the specified wavelength λ

₂ coordinated with second carrier frequency;

G(N₁,N₂) designates a linear combination;

$G<br><br>\left(N_1,N_2\right)=A+\underset{i=1}{\overset{2}{\sum <br><br>}}<br><br><br><br>a_i<br><br>N_i$

with coefficients a_i and a part A independent of the phase ambiguities; and

ε

_φ

* designates a noise term for the linear combination, the resolution comprising a determination of the linear combination G(N₁,N₂) of the phase ambiguities N_i.

21. A phase ambiguity resolution method according to claim 20, wherein the linear combination φ

* is formed according to

${\mathrm{\phi <br><br>}}^{*}=-\frac{I}{f_k^2}+{\mathrm{\lambda <br><br>}}_1<br><br>N_1<br><br>\frac{f_2^2}{f_2^2-f_1^2}<br><br>\frac{f_1^2}{f_k^2}-{\mathrm{\lambda <br><br>}}_2<br><br>N_2<br><br>\frac{f_2^2}{f_2^2-f_1^2}<br><br>\frac{f_1^2}{f_k^2}$

in which f₁ and f₂ designate the first and second carrier frequencies and f_k designates the carrier frequency coordinated with the pseudo-path to be smoothed, where kε

{1,2,3,4}.

22. A phase ambiguity resolution method according to claim 21, further comprising calculating the difference between the linear combination φ

* and at least one of the third and fourth pseudo-paths.

23. A phase ambiguity resolution method according to claim 22, wherein the difference is calculated according to the following relationship:

$R_k-{\mathrm{\phi <br><br>}}^{*}=-G<br><br>\left(N_1,N_2\right)-{\mathrm{\varepsilon <br><br>}}_{{\mathrm{\phi <br><br>}}^{*}}+{\mathrm{\varepsilon <br><br>}}_{R_k}$ $R_k=\mathrm{\rho <br><br>}+\frac{I}{f_k^2}+{\mathrm{\varepsilon <br><br>}}_{R_k}$

where, with kε

{3,4},

R_k designates the pseudo-path of the specified k th carrier frequency;

ρ

designates a geometrical path between a transmitting unit and a receiving unit, including clock errors and non-dispersive error terms;

I/f_k² designates an ionospheric influence for the specified k th carrier frequency;

N₁ designates a phase ambiguity for the specified wavelength λ

₁ coordinated with the first carrier frequency;

N₂ designates a phase ambiguity for the specified wavelength λ

₂ coordinated with the second carrier frequency;

G(N₁,N₂) designates a linear combination;

$G<br><br>\left(N_1<br><br>N_2\right)=A+\underset{i=1}{\overset{2}{\sum <br><br>}}<br><br><br><br>a_i<br><br>N_i$

with coefficients a_i and a part A independent of the phase ambiguities;

ε

_φ

* designates a noise term for the linear combination; and

ε

_Rk designates a noise term for the pseudo-path of the k th carrier frequency, the resolution comprising a determination of the linear combination (G(N₁,N₂) of the phase ambiguities N_i.

24. A computer program product including program code stored on a machine-readable medium, the program code being configured to cause an electronic device to carry out the phase ambiguity resolution method according to claim 12.

25. A computer program product according to claim 24, wherein the electronic device is a computer.