Method for using three GPS frequencies to resolve whole-cycle carrier-phase ambiguities
View Patent ↗A new three-frequency technique for obtaining geometry free, refraction-corrected, ambiguity-resolved, carrier-phase measurements has been described. First, the ambiguities on at least two wide-lane carrier-phase measurement differences are obtained by averaging the corresponding frequency weighted code measurements. These two ambiguity-resolved measurements are then combined into a composite refraction-corrected measurement. The resulting composite measurement is quite noisy due to the amplification of the multipath noise in the original carrier-phase measurements. But this noisy refraction-corrected carrier-phase measurement can be smoothed with another minimum-noise, refraction-corrected carrier-phase composite measurement. The minimum-noise, refraction-corrected composite measurement is constructed from the primary carrier-phase measurements prior to resolving their whole-cycle ambiguities. By smoothing the difference in the two refraction-corrected measurements, the noise can be reduced and the bias in the low-noise measurement (due to incorrect ambiguities) can be estimated and subsequently corrected.
1. A method for generating an ambiguity-resolved, refraction-corrected, and minimum-noise carrier-phase measurement, comprising:
forming a first composite carrier-phase measurement using primary carrier-phase measurements on three carrier frequencies, wherein the first composite carrier-phase measurement is a wide-lane ambiguity-resolved, refraction-corrected composite carrier-phase measurement;
forming a second composite carrier-phase measurement using the primary carrier-phase measurements on the three carrier frequencies, wherein the second composite carrier-phase measurement is a minimum-noise, refraction-corrected composite carrier-phase measurement, and wherein the second composite carrier-phase measurement includes an unresolved whole-cycle ambiguity; and
smoothing the first composite carrier-phase measurement with the second composite carrier-phase measurement;
wherein the unresolved whole-cycle ambiguity is resolved by:
estimating a refraction-corrected wavelength for the second composite carrier-phase measurement;
determining a smoothed offset value between the first and second composite carrier-phase measurements;
dividing the smoothed offset value by the refraction-corrected wavelength; and
rounding the dividing result to a nearest integer to produce a resolved value of the whole-cycle ambiguity of the second composite carrier-phase measurement.
2. The method of claim 1 , wherein the first composite carrier-phase measurement is a linear combination of only the primary carrier-phase measurements on the three carrier frequencies.
3. The method of claim 1 , wherein the first composite carrier-phase measurement is a linear combination of two distinct ambiguity-resolved, wide-lane carrier-phase measurements, each wide-lane carrier-phase measurement being formed by differencing two of the three primary carrier-phase measurements.
4. The method of claim 3 , wherein each wide-lane carrier-phase measurement has a whole-cycle ambiguity based on a frequency-weighted average of corresponding code measurements and a difference in raw measurement between the two respective primary carrier-phase measurements.
5. The method of claim 1 , wherein the second composite carrier-phase measurement is a linear combination of the three primary carrier-phase measurements, each weighted by a respective coefficient, and the three coefficients satisfy one or more predefined conditions so as to minimize noise in the second composite carrier-phase measurement.
6. The method of claim 5 , wherein the predefined conditions include that the sum of the three coefficients equals to a constant.
7. The method of claim 5 , wherein the predefined conditions include that the sum of the three coefficients, each divided by a square of an associated carrier frequency, equal to zero.
8. The method of claim 5 , wherein the predefined conditions include that the three coefficients have values such that the sum of the square of each of the three values is minimized assuming equal phase-noise in each of the three primary carrier-phase measurements.
9. The method of claim 1 , wherein the ambiguity-resolved, refraction-corrected, and minimum-noise composite measurement is achieved by summing the second composite carrier-phase measurement and a result of multiplying the refraction-corrected wavelength and the resolved value of the whole-cycle ambiguity of the second composite carrier-phase measurement.
10. The method of claim 1 , wherein the smoothing operation further comprises:
generating an offset by differencing the first and second composite carrier-phase measurements at each of a plurality of measurement epochs;
smoothing the offset using an expanding average filter over the plurality of measurement epochs; and
adding the smoothed offset to the second composite carrier-phase measurement to obtain the ambiguity-resolved, refraction-corrected, and minimum-noise carrier-phase measurement.
11. A method for obtaining an ambiguity-resolved, refraction-corrected, and minimum-noise composite carrier-phase measurement, comprising:
obtaining primary carrier-phase measurements on three carrier frequencies at a particular measurement epoch;
forming a composite carrier-phase measurement from a linear combination of the primary carrier-phase measurements on the three carrier frequencies, the composite carrier-phase measurement including two wide-lane ambiguities and one primary ambiguity;
updating the two wide-lane ambiguities and the one primary ambiguity using the primary carrier-phase measurements;
repeating said obtaining, forming and updating operations for a plurality of measurement epochs until the wide-lane ambiguities and primary ambiguity are resolved; and
computing the ambiguity-resolved, refraction-corrected, and minimum-noise composite carrier-phase measurement using the resolved wide-lane ambiguities and primary ambiguity.
12. The method of claim 11 , wherein the wide-lane ambiguities and primary ambiguity are resolved when they do not change between two measurement epochs after being rounded to nearest integers.
13. A positioning or navigation system, comprising:
a receiver configured to obtain code and carrier-phase measurements based on signals from a plurality of satellites in view of the receiver, the signals being transmitted in three different carrier frequencies;
a computer coupled to the receiver, the computer including a processor and a memory coupled to the processor, the memory storing therein program instructions which, when executed by the processor, generate an ambiguity-resolved, refraction-corrected, and minimum-noise composite carrier-phase measurement, the program instructions comprising:
instructions for forming a first composite carrier-phase measurement using primary carrier-phase measurements on three carrier frequencies, wherein the first composite carrier-phase measurement is a wide-lane ambiguity-resolved, refraction-corrected composite carrier-phase measurement;
instructions for forming a second composite carrier-phase measurement using the primary carrier-phase measurements on the three carrier frequencies, wherein the second composite carrier-phase measurement is a minimum-noise, refraction-corrected composite carrier-phase measurement; and
instructions for smoothing the first composite carrier-phase measurement with the second composite carrier-phase measurement;
wherein the instructions for forming the second composite carrier-phase measurement includes instructions for solving a whole-cycle ambiguity of the second composite carrier-phase measurement; and
wherein the instructions for solving the whole-cycle ambiguity include:
instructions for estimating a refraction-corrected wavelength for the second composite carrier-phase measurement;
instructions for determining a smoothed offset value between the first and second composite carrier-phase measurements;
instructions for dividing the smoothed offset value by the refraction-corrected wavelength; and
instructions for rounding the dividing result to a nearest integer to produce a resolved value of the whole-cycle ambiguity of the second composite carrier-phase measurement.
14. The positioning system of claim 13 , wherein the ambiguity-resolved, refraction-corrected, and minimum-phase composite measurement is achieved by summing the second composite carrier-phase measurement and a result of multiplying the refraction-corrected wavelength and the resolved value of the whole-cycle ambiguity of the second composite carrier-phase measurement.
15. The positioning system of claim 13 , wherein the second composite carrier-phase measurement is a linear combination of the three primary carrier-phase measurements, each weighted by a respective coefficient, and the three coefficients satisfy one or more predefined conditions so as to minimize noise in the second composite carrier-phase measurement.
16. The positioning system of claim 13 , wherein the smoothing instructions further include:
instructions for generating an offset by differencing the first and second composite carrier-phase measurements at each of a plurality of measurement epochs;
instructions for smoothing the offset using an expanding average filter over the plurality of measurement epochs; and
instructions for adding the smoothed offset to the second composite carrier-phase measurement to obtain the ambiguity-resolved, refraction-corrected, and minimum-noise carrier-phase measurement.
17. The method of claim 11 , wherein updating the two wide-lane ambiguities and the one primary ambiguity using the primary carrier-phase measurements includes:
receiving a new set of code measurements and carrier-phase measurements;
computing changes in the two wide-lane ambiguities using the new set of code measurements and carrier-phase measurements;
determining whether values of the two wide-lane ambiguities have changed from prior values of the two wide-lane ambiguities; and
in response to determining that the values of the two wide-lane ambiguities have changed from the prior values of the two wide-lane ambiguities,
updating an offset value using the changes in the two wide-lane ambiguities; and
computing a change to the one primary ambiguity using the updated offset value.
18. The method of claim 17 , wherein after computing the change to the one primary ambiguity using the updated offset value, the method further comprises:
rounding the change to the one primary ambiguity to the nearest integer to produce a rounded version of the change to the one primary ambiguity;
determining whether the rounded version of the change to the one primary ambiguity is equal to zero; and
in response to determining that the rounded version of the change to the one primary ambiguity is not equal to zero, updating the one primary ambiguity and a smoothed offset value using the change to the one primary ambiguity.
19. The method of claim 11 , wherein the wide-lane ambiguities and primary ambiguity are resolved when they do not change over a predetermined number of measurement epochs after being rounded to nearest integers.