Method for determining the half-cycle ambiguity of a GNSS carrier phase
Signals L 1CA , L 1P , L 2P and L 2C transmitted by a GPS satellite are received and the carrier phases φ LCA and φ L2C are estimated from L 1CA and L 2C . The cross-correlation P between the downconverted signals L 1P and L 2P is determined, taking into account the delay between signals. The sign of P is used to enable direct determination of the half-cycle ambiguity A L1CA of the L 1CA signal. In some examples, this is done by downconverting the L 2P signal by a replica having a phase derived from φ L2C , instead of determining the phase of the L 2P replica by a tracking loop, enabling determination of A L1CA directly from the sign of P. In some examples, the phase φ L2P of the L 2P replica is determined by a tracking loop, and the half-cycle ambiguity A L1CA is determined based on the sign of P and on the difference between the carrier phases φ L2P and φ L2C .
1 . A method for resolving the half-cycle ambiguity of a Global Positioning System (GPS) carrier phase, the method comprising:
receiving a plurality of signals from a GPS satellite, the plurality of signals including:
a first signal L 1CA transmitted on a first carrier frequency f L1 ,
a second signal L 1P transmitted on the first carrier frequency f L1 , the second signal having a known phase offset δφ L1P,CA with respect to the first signal,
a third signal L 2C transmitted on a second carrier frequency f L2 , and
a fourth signal L 2P transmitted on the second carrier frequency f L2 , the fourth signal having a known phase offset δ φL2P,C with respect to the third signal;
tracking the first signal and the third signal and determining thereby respective estimations of carrier phases φ L1CA and φ L2C of said first and third signals, wherein said estimation of the carrier phase φ L1CA of the first signal comprises the term A L1CA ·π, wherein A L1CA is equal to 0 or 1, A L1CA being referred to hereafter as a half-cycle ambiguity of the L 1CA carrier phase; and
downconverting the second and fourth signals L 1P and L 2P to baseband by multiplication with a carrier replica of said second and fourth signals, determining a delay between the downconverted second and fourth signals, and determining a cross-correlation P between the downconverted second and fourth signals by integrating a product of the downconverted second and fourth signals over an integration time T, taking into account said delay;
wherein a positive or negative sign of the cross-correlation P and the known phase offsets δ φL2P,C and δ φL1P,CA are used for determining the half-cycle ambiguity A L1CA to generate a resolved half-cycle ambiguity; and
based on the resolved half-cycle ambiguity, improving a downstream application utilizing the signals from the GPS satellite.
2 . The method according to claim 1 , wherein the half-cycle ambiguity A L1CA of the first signal L 1CA is determined by:
executing said step of downconverting the fourth signal L 2P by multiplication of the fourth signal L 2P with a carrier replica having the phase ω L2 t+φ L2C +δφ L2P,C , with ω L2 =2πf L2
determining the half-cycle ambiguity A L1CA of the L 1CA signal directly from the sign of the cross-correlation P, according to the following verification steps:
if P is positive, A L1CA =0,
if P is negative, A L1CA =1.
3 . The method according to claim 2 , wherein the delay between the downconverted second and fourth signals is determined by a delay lock loop (DLL) circuit ( 15 ) tracking the delay between L 1P and L 2P .
4 . The method according to claim 2 , wherein the step of tracking the first signal and the third signal includes determining respective estimations R L1CA and R L2C of the satellite range, and wherein the delay between the downconverted second and fourth signals is a difference between the respective estimations of the satellite range obtained from the third and first signals L 2C and L 1CA , divided by the speed of light, i.e. (PR L2C −PR L1CA )/C.
5 . The method according to claim 1 , wherein the half-cycle ambiguity A L1CA of the first signal L 1CA is determined by:
tracking the carrier phase L2P of the fourth signal by a tracking loop that maximizes an amplitude of the cross-correlation P, and executing said step of downconverting the fourth signal by multiplication of the fourth signal with a carrier replica having the phase ω L2 t+φ L2P ; and
from the sign of the cross-correlation P, and from the difference between φ L2P and φ L2C , determining the half-cycle ambiguity A L1CA of the first signal L 1CA according to the following steps:
determining a parameter D,
with
D
=
1
π
(
φ
L
2
P
-
φ
L
2
C
-
δφ
L
2
P
,
C
)
,
if the integer closest to D is even: A L1CA =0 if P>0 or A L1CA =1 if P<0,
if the integer closest to D is odd: A L1CA =1 if P>0 or A L1CA =0 if P<0.
6 . The method according to claim 5 , further comprising:
determining whether the absolute value of the difference between D and the closest integer is larger or smaller than a pre-defined threshold value D th ;
wherein the step of determining the half-cycle ambiguity A L1CA of the L 1CA signal is executed only if the absolute value of the difference between D and the closest integer is smaller than the pre-defined threshold value D th .
7 . The method according to claim 1 , further comprising:
determining whether the absolute value of P is larger than a pre-defined threshold value P th ;
wherein the step of determining the half-cycle ambiguity A L1CA of the L 1CA signal is executed only if |P|>P th .
8 . The method according to claim 1 , wherein said method is performed repeatedly so as to enable an essentially continuous monitoring of the half cycle ambiguity A L1CA .
9 . The method according to claim 8 , wherein the half-cycle ambiguity A L1CA is determined only if the same result is obtained a given number of times.
10 . The method according to claim 1 , wherein said method is performed repeatedly and wherein said method is performed in parallel with a method for determining the half-cycle ambiguity A L1CA on the basis of a preamble transmitted in the first signal and wherein the time between two consecutive determinations of the half-cycle ambiguity is smaller than the time between two consecutive preambles.
11 . The method according to claim 1 , wherein the time between two consecutive determinations of the half-cycle ambiguity is smaller than 6 s.
12 . A method for processing Global Positioning System (GPS) signals, the method comprising:
acquiring a plurality of signals from a GPS satellite, the plurality of signals including:
a first signal L 1CA transmitted on a first carrier frequency f L1 ,
a second signal L 1P transmitted on the first carrier frequency f L1 , the second signal having a known phase offset Δφ L1P,CA with respect to the first signal,
a third signal L 2C transmitted on a second carrier frequency f L2 , and
a fourth signal L 2P transmitted on the second carrier frequency f L2 , the fourth signal having a known phase offset δ φL2P,C with respect to the third signal;
tracking the first signal and the third signal and determining thereby respective estimations of carrier phases φ L1CA and φ L2C of said first and third signals, wherein said estimation of the carrier phase φ L1CA of the first signal comprises the term A L1CA ·π, wherein A L1CA is equal to 0 or 1, A L1CA being referred to hereafter as a half-cycle ambiguity of the L 1CA carrier phase; and
downconverting the second and fourth signals L 1P and L 2P to baseband by multiplication with a carrier replica of said second and fourth signals, determining a delay between the downconverted second and fourth signals, and determining a cross-correlation P between the downconverted second and fourth signals by integrating a product of the downconverted second and fourth signals over an integration time T, taking into account said delay;
determining the half-cycle ambiguity A L1CA using a positive or negative sign of the cross-correlation P and the known phase offsets δ φL2P,C and δ φL1P,CA thereby generating a resolved half-cycle ambiguity; and
based on the resolved half-cycle ambiguity, detecting half-cycle slips during acquisition and processing of the GPS signals.
13 . A GPS receiver comprising one or more receiver channels, each channel being configured to track the following four signals from a GPS satellite:
a first signal L 1CA transmitted on a first carrier frequency f L1 ,
a second signal L 1P transmitted on the first carrier frequency f L1 , the second signal having a known phase offset δφ L1P,CA with respect to the first signal,
a third signal L 2C transmitted on a second carrier frequency f L2 ,
a fourth signal L 2P transmitted on the second carrier frequency f L2 , the fourth signal having a known phase offset δφ L2P,C with respect to the third signal;
wherein at least one of said channels comprises a half-cycle ambiguity calculation unit ( 20 ) configured to calculate the half-cycle ambiguity A L1CA of the L 1CA signal in accordance with the method of claim 1 .
14 . The method of claim 1 , wherein improving the downstream application comprises recovering positioning accuracy with respect to the GPS satellite after an interruption of the plurality of signals.
15 . The method of claim 1 , wherein improving the downstream application comprises faster restoration of integer-ambiguity carrier phase after a signal slip.