Carrier signal phase error estimation
View Patent ↗A phase error and/or amplitude error of a global positioning system carrier signal is estimated through employment of an optimal minimum variance of the global positioning system carrier signal.
1. A method, comprising the steps of:
estimating a phase error and/or amplitude error of a global positioning system (GPS) carrier signal through employment of an optimal minimum variance of the GPS carrier signal;
generating an optimal estimate of carrier error in the presence of binary data bits having unknown states, said generating step minimizing carrier error due to an incorrect estimate of a sign of a data bit; and
applying the optimal estimated carrier error of the GPS carrier signals to correct the corresponding phase and/or amplitude of the received GPS carrier signals.
2. The method of claim 1 , wherein the step of estimating the phase error and/or amplitude error of the GPS carrier signal through employment of the optimal minimum variance solution comprises the step of:
determining an optimal minimum variance of the GPS carrier signal through employment of a plurality of pairs of in-phase terms I i and quadrature terms Q i that are based on the GPS carrier signal; and
wherein the generating step minimizes carrier error due to the incorrect estimate of the sign of the data bit by modeling an expected probability of 50% of receiving a +1 data bit and an expected probability of 50% of receiving a −1 data bit.
3. The method of claim 2 , wherein the step of determining the optimal minimum variance of the GPS carrier signal through employment of the plurality of in-phase and quadrature terms that are based on the GPS carrier signal comprises the step of:
calculating a plurality of pair terms P i based on the plurality of pairs of in-phase terms I i and quadrature terms Q i :
P
i
=
ⅇ
-
1
2
σ
y
2
[
(
Q
i
+
A
sin
X
)
2
+
(
I
i
+
A
cos
X
)
2
]
+
ⅇ
-
1
2
σ
y
2
[
(
Q
i
-
A
sin
X
)
2
+
(
I
i
-
A
cos
X
)
2
]
calculating a phase error estimate {circumflex over (x)} and/or an amplitude error estimate â based on the plurality of pair terms P i .
4. The method of claim 3 , wherein the plurality of pairs of in-phase terms and quadrature terms comprises N terms, wherein the step of calculating the phase error estimate {circumflex over (x)} and/or the amplitude error estimate â based on the plurality of pair terms P i comprises the steps of:
calculating the phase error estimate:
x
^
=
∫
-
X
max
X
max
Xf
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
∫
-
X
max
X
max
f
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
;
and
calculating the amplitude error estimate:
a
^
=
∫
-
A
max
A
max
Af
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
∫
-
A
max
A
max
f
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
.
5. The method of claim 3 , wherein the plurality of pairs of in-phase terms and quadrature terms comprises N terms, wherein the step of calculating the phase error estimate {circumflex over (x)} and/or the amplitude error estimate â based on the plurality of pair terms P i comprises the steps of:
calculating the phase error estimate:
x
^
=
∫
-
X
max
X
max
Xf
x
(
X
)
[
∫
-
A
max
A
max
Af
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
]
ⅆ
X
∫
-
X
max
X
max
f
x
(
X
)
[
∫
-
A
max
A
max
f
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
]
ⅆ
X
;
and
calculating the amplitude error estimate:
a
^
=
∫
-
A
max
A
max
Af
a
(
A
)
[
∫
-
X
max
X
max
Xf
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
]
ⅆ
A
∫
-
A
max
A
max
f
a
(
A
)
[
∫
-
X
max
X
max
f
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
]
ⅆ
A
.
6. A method implemented in a global positioning system (GPS) receiver for optimizing the extraction of information from received GPS carrier signals comprising the steps of:
receiving GPS carrier signals that are subject to non-linear effects;
determining an optimal minimum variance of the GPS carrier signals using a Kalman filter based on a plurality of pairs of in-phase terms I i and quadrature terms Q i that represent the GPS carrier signals;
estimating a phase error and/or amplitude error of the GPS carrier signals based on the optimal minimum variance of the GPS carrier signals;
said estimating including generating an optimal estimate of carrier error in the presence of binary data bits having unknown states, said generating step minimizing carrier error due to an incorrect estimate of a sign of a data bit; and
applying the estimated phase and/or amplitude error of the GPS carrier signals to correct the corresponding phase and/or amplitude of the received GPS carrier signals.
7. The method of claim 6 further comprising the step of pre-filtering the in-phase and quadrature terms by consolidating a plurality of measurements of the in-phase and quadrature terms taken at a first sample rate into a single corresponding measurement of the in-phase and quadrature terms, the determining of the optimal minimum variance of the GPS carrier signals using a Kalman filter based on the single corresponding measurement of the in-phase and quadrature terms to reduce computational load on a processing unit of the GPS receiver.
8. The method of claim 6 wherein the step of estimating a phase error and/or amplitude error of the GPS carrier signals based on the optimal minimum variance of the GPS carrier signals generates phase and/or amplitude error estimates that provide more accurate estimates of the corresponding errors than error estimates made by using an arctan method.
9. The method of claim 8 wherein the accuracy of the phase and/or amplitude error estimates made by said estimating step as compared with the error estimates made using the arctan method increases as signal-to-noise of the received GPS carrier signals decreases.
10. The method of claim 6 further comprising the step of providing the Kalman filter with complete access to pairs of in-phase terms I i and quadrature terms Q i .
11. The method of claim 6 wherein the generating step minimizes carrier error due to the incorrect estimate of the sign of the data bit by modeling an expected probability of 50% of receiving a +1 data bit and an expected probability of 50% of receiving a −1 data bit.
12. The method of claim 10 further comprising the steps of:
generating injection signals with digitally controlled oscillators that are combined with the received GPS carrier signals as part of recovery of GPS information from the GPS carrier signals; and
controlling the digitally controlled oscillators directly by the optimal minimum variance of the GPS carrier signals as determined by the Kalman filter.
13. The method of claim 6 wherein said step of determining comprises the step of:
calculating a plurality of pair terms P i based on the plurality of pairs of in-phase terms I i and quadrature terms Q i :
P
i
=
ⅇ
-
1
2
σ
y
2
[
(
Q
i
+
A
sin
X
)
2
+
(
I
i
+
A
cos
X
)
2
]
+
ⅇ
-
1
2
σ
y
2
[
(
Q
i
-
A
sin
X
)
2
+
(
I
i
-
A
cos
X
)
2
]
calculating a phase error estimate {circumflex over (x)} and/or an amplitude error estimate â based on the plurality of pair terms P i .
14. The method of claim 13 , wherein the plurality of pairs of in-phase terms and quadrature terms comprises N terms, wherein the step of calculating the phase error estimate {circumflex over (x)} and/or the amplitude error estimate â based on the plurality of pair terms P i comprises the steps of:
calculating the phase error estimate:
x
^
=
∫
-
X
max
X
max
Xf
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
∫
-
X
max
X
max
f
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
;
and
calculating the amplitude error estimate:
a
^
=
∫
-
A
max
A
max
Af
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
∫
-
A
max
A
max
f
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
.
15. The method of claim 13 wherein the plurality of pairs of in-phase terms and quadrature terms comprises N terms, wherein the step of calculating the phase error estimate {circumflex over (x)} and/or the amplitude error estimate â based on the plurality of pair terms P i comprises the steps of:
calculating the phase error estimate:
x
^
=
∫
-
X
max
X
max
Xf
x
(
X
)
[
∫
-
A
max
A
max
Af
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
]
ⅆ
X
∫
-
X
max
X
max
f
x
(
X
)
[
∫
-
A
max
A
max
f
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
]
ⅆ
X
;
and
calculating the amplitude error estimate:
a
^
=
∫
-
A
max
A
max
Af
a
(
A
)
[
∫
-
χ
max
χ
max
Xf
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
]
ⅆ
A
∫
-
A
max
A
max
f
a
(
A
)
[
∫
-
χ
max
χ
max
f
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
]
ⅆ
A
.
16. A global positioning system (GPS) receiver for optimizing the extraction of information from received GPS carrier signals comprising:
means for receiving GPS carrier signals that are subject to non-linear effects;
means, coupled to the receiving means, for determining an optimal minimum variance of the received GPS carrier signals using a Kalman filter based on a plurality of pairs of in-phase terms I i and quadrature terms Q i that represent the GPS carrier signals;
means, coupled to the determining means, for estimating a phase error and/or amplitude error of the GPS carrier signals based on the optimal minimum variance of the GPS carrier signals, said estimating means generating an optimal estimate of carrier error in the presence of binary data bits having unknown states to minimize carrier error due to an incorrect estimate of a sign of a data bit; and
means, coupled to the estimating means, for applying the estimated phase and/or amplitude error of the GPS carrier signals to correct the corresponding phase and/or amplitude of the received GPS carrier signals.
17. The receiver of claim 16 further comprising means for pre-filtering the in-phase and quadrature terms by consolidating a plurality of measurements of the in-phase and quadrature terms taken at a first sample rate into a single corresponding measurement of the in-phase and quadrature terms, the determining means determining of the optimal minimum variance of the GPS carrier signals using a Kalman filter based on the single corresponding measurement of the in-phase and quadrature terms to reduce computational load on a processing unit of the GPS receiver.
18. The receiver of claim 16 wherein the estimating means estimates a phase error and/or amplitude error of the GPS carrier signals based on the optimal minimum variance of the GPS carrier signals generates phase and/or amplitude error estimates that provide more accurate estimates of the corresponding errors than error estimates made by using an arctan method.
19. The receiver of claim 18 wherein the estimating means provides an accuracy of the phase and/or amplitude error estimates that increases as signal-to-noise of the received GPS carrier signals decreases as compared with an error estimate made using the arctan method.
20. The receiver of claim 16 wherein the determining means provides the Kalman filter with complete access to pairs of in-phase terms I i and quadrature terms Q i .
21. The receiver of claim 16 wherein the estimating means minimizes carrier error due to the incorrect estimate of the sign of the data bit by modeling an expected probability of 50% of receiving a +1 data bit and an expected probability of 50% of receiving a −1 data bit.
22. The receiver of claim 20 further comprising:
means for generating injection signals with digitally controlled oscillators that are combined with the received GPS carrier signals as part of recovery of GPS information from the GPS carrier signals; and
means for controlling the digitally controlled oscillators directly by the optimal minimum variance of the GPS carrier signals as determined by the Kalman filter.
23. The receiver of claim 16 wherein said determining means comprises:
means for calculating a plurality of pair terms P i based on the plurality of pairs of in-phase terms I i and quadrature terms Q i :
P
i
=
ⅇ
-
1
2
σ
y
2
[
(
Q
i
+
A
sin
X
)
2
+
(
I
i
+
A
cos
X
)
2
]
+
ⅇ
-
1
2
σ
y
2
[
(
Q
i
-
A
sin
x
)
2
+
(
I
i
-
A
cos
X
)
2
]
means for calculating a phase error estimate {circumflex over (x)} and/or an amplitude error estimate â based on the plurality of pair terms P i .
24. The receiver of claim 23 , wherein the plurality of pairs of in-phase terms and quadrature terms comprises N terms, wherein the calculating means calculates the phase error estimate {circumflex over (x)} and/or the amplitude error estimate â based on the plurality of pair terms P i comprises:
means for calculating the phase error estimate:
x
^
=
∫
-
X
max
X
max
Xf
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
∫
-
X
max
X
max
f
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
;
and
means for calculating the amplitude error estimate:
a
^
=
∫
-
A
max
A
max
Af
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
∫
-
A
max
A
max
f
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
.
25. The receiver of claim 23 wherein the plurality of pairs of in-phase terms and quadrature terms comprises N terms, wherein the calculating means calculates the phase error estimate {circumflex over (x)} and/or the amplitude error estimate â based on the plurality of pair terms P i comprises:
means for calculating the phase error estimate:
x
^
=
∫
-
X
max
X
max
Xf
x
(
X
)
[
∫
-
A
max
A
max
Af
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
]
ⅆ
X
∫
-
X
max
X
max
f
x
(
X
)
[
∫
-
A
max
A
max
f
a
(
A
)
∏
i
=
1
N
P
i
ⅆ
A
]
ⅆ
X
;
and
means for calculating the amplitude error estimate:
a
^
=
∫
-
A
max
A
max
Af
a
(
A
)
[
∫
-
χ
max
χ
max
Xf
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
]
ⅆ
A
∫
-
A
max
A
max
f
a
(
A
)
[
∫
-
χ
max
χ
max
f
x
(
X
)
∏
i
=
1
N
P
i
ⅆ
X
]
ⅆ
A
.