DECOUPLED CLOCK MODEL WITH AMBIGUITY DATUM FIXING

• US 20100188285A1
• Filed: 01/23/2009
• Published: 07/29/2010
• Est. Priority Date: 01/23/2009
• Status: Active Grant

• Current Assignee: Her Majesty The Queen In Right Of Canada (Government of Canada)
• Original Assignee: Her Majesty The Queen In Right Of Canada (Government of Canada)
• Inventors: Collins, John Paul
• Granted Patent: US 8,018,377 B2
• Time in Patent Office: Days
• US Class Current: 342/357.310
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

The present invention relates to a method of processing Global Positioning System (GPS) carrier phase and pseudorange information. Dual-frequency carrier phase and pseudorange measurements from GPS receivers are processed by specifying separate oscillator parameters for the carrier phase and pseudorange measurements. Carrier phase estimates of errors of the oscillator are arbitrarily biased with respect to the pseudorange estimates, and ambiguity parameters are constrained to be integer-valued. Isolating the ambiguities as integer valued parameters provides extra information that can be exploited to maximize the use of GPS and other Global Navigation Satellite Systems.

Claims

1. A method of processing undifferenced GPS carrier phase and pseudorange measurements, made at two frequencies, by one or more receivers, from a plurality of satellite transmitters, comprising the steps of:

defining separate clock parameters for the carrier phase and pseudorange measurements;

arbitrarily biasing carrier phase estimates of oscillator errors with respect to the pseudorange estimates; and

constraining the ambiguity parameters to be integer-valued.

2. The method of claim 1 being based on the following relationship:

P₁=ρ

+T+I+c(dt_P1^r−

dt_P1^s)+ε

_P1

P₂=ρ

+T+q²I+c(dt_P2^r−

dt_P2^s)+ε

_P2

L₁=ρ

+T−

I+c(dt_L1^r−

dt_L1^s)−

λ

₁N₁ε

_L1

L₂=ρ

+T−

q²I+c(dt_L2^r−

dt_L2^s)−

λ

₂N₂ε

_L2

wherein;

P_i is a pseudorange measurement made at frequency i,

L_i is an ambiguous carrier phase measurement made at frequency i,

N_i is the integer ambiguity at frequency i,

λ

_i is the wavelength of the carrier phase measurements at frequency i,

ρ

is the geometric range between transmitter and receiver antennas,

T is the range delay caused by signal propagation through the lower atmosphere (predominantly the Troposphere),

I is the range delay and apparent phase advance on the first frequency caused by signal propagation through the upper atmosphere (predominantly the Ionosphere),

the factor q is the ratio of the first frequency to the second,

the factor c is the vacuum speed of light,

dt_k^j is the combined oscillator and hardware time delay bias (clock error) on measurement k for receiver or transmitter j,

ε

_k represents unmodelled random or quasi-random errors on measurement k.

3. The method of claim 1 further comprising the step of fixing to arbitrary value a subset of ambiguity parameters, whereby a minimum constraint least-squares solution can be computed.

4. The method of claim 1 wherein the steps thereof are applied to the processing of measurements from a plurality of GPS receivers, whereby satellite clock corrections therefor are computed.

5. The method of claim 4 comprising the formation of a least squares solution based on the following relationship:

P₃=ρ

+T+c(dt_P3^r−

dt_P3^s)+ε

_P3

L₃=ρ

+T+c(dt_L3^r−

dt_L3^s)−

λ

₃N₃+ε

_L3

wherein;

P₃ is a combined pseudorange measurement free of the ionospheric effect to first-order,

L₃ is a combined ambiguous carrier phase measurement free of the ionospheric effect to first-order,

N₃ is the resulting integer ambiguity,

λ

₃ is the ionosphere-free wavelength of the carrier phase measurements,

ρ

is the geometric range between transmitter and receiver antennas,

T is the range delay caused by signal propagation through the lower atmosphere (predominantly the Troposphere),

the factor c is the vacuum speed of light,

dt_k^j is the combined ionosphere-free oscillator and hardware time delay bias (clock error) on measurement k for receiver or transmitter j,

ε

_k represents unmodelled random or quasi-random errors on measurement k, as well as second- and higher-order ionospheric effects.

6. The method of claim 4 further comprising the step of fixing one carrier phase clock parameter as a network datum.

7. The method of claim 4 further comprising the step of fixing one pseudorange clock parameter as a network datum.

8. The method of claim 4 further comprising the step of fixing one ambiguity parameter associated with each estimated carrier phase clock parameter, to an arbitrary integer value.

9. The method of claim 4 further comprising, for certain ionosphere-free combinations, an estimation of a widelane combination of ambiguities, whereby the ionosphere-free wavelength is numerically amplified to that of the narrowlane, such that the use of standard integer fixing techniques is made feasible.

10. The method of claim 9 comprising the formation of a least squares solution based on the following relationship:

A₄=L₄−

P₆=b_A4^r−

b_A4^s−

λ

₄N₄+ε

_A4

wherein;

P₆ is the narrowlane combination of dual-frequency pseudoranges,

L₄ is the widelane combination of dual-frequency carrier phases,

λ

₄ is the widelane wavelength,

N₄ is the widelane ambiguity,

b_k^j is the combined carrier phase and pseudorange hardware time delay (clock-like error) on measurement k for receiver or transmitter j,

ε

_k represents unmodelled random or quasi-random errors on measurement k.

11. The method of claim 9 further comprising the step of fixing one widelane clock-like parameter as a network datum.

12. The method of claim 9 further comprising the step of fixing one ambiguity parameter associated with each estimated widelane clock-like parameter, to an arbitrary integer value.

13. The method of claim 4 comprising the simultaneous implementation of the method of claim 9, or the separate implementation of said claim and the subsequent insertion of the estimated integer ambiguities as fixed quantities into the relationship described in claim 5.

14. The method of claim 1 as applied to the processing of measurements from a single GPS receiver, whereby use is made of the satellite clock and clock-like parameters computed by the method of claim 4, such that a precise point positioning solution is realized.

15. The method of claim 14 comprising the formation of a least squares solution based on the following relationship:

P₃=ρ

+T+c(dt_P3^r−

dt_P3^s)+ε

_P3

L₃=ρ

+T+c(dt_L3^r−

dt_L3^s)−

λ

₃N₃ε

_L3

wherein;

P₃ is a combined pseudorange measurement free of the ionospheric effect to first-order,

L₃ is a combined ambiguous carrier phase measurement free of the ionospheric effect to first-order,

N₃ is the resulting integer ambiguity,

λ

₃ is the ionosphere-free wavelength of the carrier phase measurements,

ρ

is the geometric range between transmitter and receiver antennas,

T is the range delay caused by signal propagation through the lower atmosphere (predominantly the Troposphere),

the factor c is the vacuum speed of light,

dt_k^j is the combined ionosphere-free oscillator and hardware time delay bias (clock error) on measurement k for receiver or transmitter j,

ε

_k represents unmodelled random or quasi-random errors on measurement k, as well as second- and higher-order ionospheric effects.

16. The method of claim 14 further comprising the step of fixing of the satellite carrier phase clock parameters with values computed using the method of claim 4.

17. The method of claim 14 further comprising the step of fixing the satellite pseudorange clock parameters with values computed using the method of claim 4.

18. The method of claim 14 further comprising the step of fixing one ambiguity parameter to an arbitrary integer value.

19. The method of claim 14 further comprising, for certain ionosphere-free combinations, an estimation of a widelane combination of ambiguities, whereby the ionosphere-free wavelength is numerically amplified to that of the narrowlane, such that the use of standard integer fixing techniques is made feasible.

20. The method of claim 19 comprising the formation of a least squares solution based on the following relationship:

A₄=L₄−

P₆=b_A4^r−

b_A4^s−

λ

₄N₄+ε

_A4

wherein;

P₆ is the narrowlane combination of dual-frequency pseudoranges,

L₄ is the widelane combination of dual-frequency carrier phases,

λ

₄ is the widelane wavelength,

N₄ is the widelane ambiguity,

b_k^j is the combined carrier phase and pseudorange hardware time delay (clock-like) error on measurement k for receiver or transmitter j,

ε

_k represents unmodelled random or quasi-random errors on measurement k.

21. The method of claim 19 further comprising the step of fixing the satellite widelane clock-like parameters with values computed using the method of claim 9.

22. The method of claim 19 further comprising the step of fixing one ambiguity parameter to an arbitrary integer value.

23. The method of claim 14 comprising the simultaneous implementation of the method of claim 19, or the separate implementation of said claim and the subsequent insertion of the estimated integer ambiguities as fixed quantities into the relationship described in claim 15.

24. A method of determining GPS position information comprising the steps of:

receiving GPS signals at one or more GPS receivers from a plurality of GPS satellite transmitters;

obtaining from the GPS signals undifferenced GPS carrier phase and pseudorange measurements, made at two frequencies, at the one or more GPS receivers;

defining separate clock parameters for the carrier phase and pseudorange measurements;

arbitrarily biasing carrier phase estimates of oscillator errors with respect to pseudorange estimates;

constraining the ambiguity parameters to e integer-valued; and

determining the estimated position of the one or more GPS receivers based on the constraint of the estimated ambiguities.

25. A system for determining GPS position information comprising:

one or more GPS receivers for receiving GPS signals from a plurality of GPS satellite transmitters;

means for obtaining from the GPS signals undifferenced GPS carrier phase and pseudorange measurements, made at two frequencies, at the one or more GPS receivers;

means for defining separate clock parameters for the carrier phase and pseudorange measurements;

means for arbitrarily biasing carrier phase estimates of oscillator errors with respect to pseudorange estimates;

means for constraining the ambiguity parameters to e integer-valued; and

means for determining the estimated position of the one or more GPS receivers based on the constraint of the estimated ambiguities.