GPS carrier phase measurement representation and method of use
View Patent ↗Sequential GPS Doppler carrier phase count measurements are used for precision sequential determination of position and velocity of a GPS receiver, such as for orbit determination and geolocation, with minimum throughput time. Real-time orbit determination and geolocation performance is enabled with an optimal sequential filter, and near-real-time performance is enabled with an optimal fixed-lag smoother. Many problems associated with prior art orbit determination are eliminated by addressing the “cycle slip” problem, the unknown initial range problem with RANGE CP measurement representations, the problem of serial correlation in the measurements due to reprocessing of overlapping thermal noise. Also, the present invention significantly attenuates the carrier signal phase variation due to rotation of receiver antenna relative to transmitter antenna because the sequential phase count time intervals are sufficiently short.
1. A method of refining state estimates of a Global Positioning System (GPS) receiver based upon sequential GPS carrier phase measurements, comprising:
the GPS receiver periodically receiving, at a defined phase count interval Δt, Doppler-shifted carrier signals transmitted at two L-BAND frequencies f n NV from a Navigation System with Timing And Ranging (NAVSTAR) spacecraft, where NV indicates NAVSTAR and n is an integer of either 1 or 2 denoting one of the L-BAND frequencies, and wherein the periodically received carrier signals are Doppler shifted with multiplicative Doppler shift β ij , for each NAVSTAR link i at a time-tag t j , and are contaminated by random additive ionospheric effects δf n ION and wherein the GPS receiver approximates the nominal frequency {overscore (f)} n NV , at which the NAVSTAR spacecraft transmits, using the GPS receiver's internal clock;
the GPS receiver approximating f n U of the periodically received carrier signals using its internal clock;
determining a frequency difference at the GPS receiver to define instantaneous Doppler frequency f n D in units of cycles per second as:
f n D =f n NV (1−β ij )+δf n U −δf n ION ;
counting positive zero crossings of f n D , inclusive of a partial cycle, across the phase count interval Δt to measure a rational Doppler carrier phase count number N j ni wherein
N
j
ni
=
∫
t
j
-
Δ
t
t
j
f
n
D
ⅆ
t
+
δ
N
j
ni
in units of cycles;
calculating an estimated representation of Doppler carrier phase count number N j ni using the formula:
N j ni ={overscore (f)} n NV (ζ ij +I j nNi )+{overscore (f)} n U I j nU +AΔN TEC /└c{overscore (f)} n NV ┘+δN j ni
where:
ζ
ij
=
∫
j
-
Δ
t
j
(
1
-
β
)
ⅆ
t
=
Δ
ρ
ij
/
c
-
ϰ
ij
ϰ
ij
=
∫
j
-
Δ
t
j
{
μ
c
2
[
1
r
j
-
1
R
i
]
+
1
2
c
2
[
s
.
j
2
-
S
.
i
2
]
}
ⅆ
t
Δ
ρ
ij
=
∫
j
-
Δ
t
j
ρ
.
ij
ⅆ
t
=
ρ
ij
(
t
j
)
-
ρ
ij
(
t
j
-
Δ
t
)
Δ N TEC =N TEC ( t j )− N TEC ( t j −Δt )
A=40.30816 (m 3 Hz 2 /electron)
β
ij
=
1
-
1
c
ρ
.
ij
+
μ
c
2
[
1
r
j
-
1
R
i
]
+
1
2
c
2
[
s
.
j
2
-
S
.
i
2
]
I
j
nNi
=
∫
j
-
Δ
t
j
[
δ
f
n
N
f
_
n
N
]
(
1
-
β
ij
)
ⅆ
t
I
j
nU
=
∫
j
-
Δt
j
[
δ
f
n
U
f
_
n
U
]
ⅆ
t
where:
δN j ni is receiver thermal noise, independent for each NAVSTAR i,
c is speed of light in a vacuum,
μ is the geocentric two-body gravitational constant,
r j and {dot over (s)} j are magnitudes of GPS receiver position and velocity vectors at time t j ,
R i and {dot over (S)} i are magnitudes of NAVSTAR spacecraft position and velocity vectors at time t i ,
{dot over (ρ)} ij is the range-rate {dot over (ρ)} ij =dp ij /dt at time t=t j ,
ρ ij is the range between NAVSTAR spacecraft at time t i and GPS receiver at time t j ,
ζ ij is a signal term with X ij being a relativistic contribution, and
I represent clock phase perturbations;
differencing the measured and estimated representations of Doppler carrier phase count number N j ni to obtain measurement residuals;
mapping the measurement residuals to state estimate corrections; and
applying the state estimate corrections to a priori state estimates.
2. The method of claim 1 , wherein the state estimates comprise a state estimate structure that contains GPS receiver position, GPS receiver velocity, and GPS receiver clock parameters.
3. The method of claim 1 , further comprising calculating each Doppler carrier phase count measurement as a delta-range (Δρ ij ) representation using:
Δρ ij =λ n ( N j ni −δN j ni )+ c ( x ij −[I j nNi +I j nU ])− AΔN TEC /({overscore (f)} n NV ) 2 .
4. The method of claim 1 , further comprising removing ionospheric effects by defining N j Ei as:
N
j
Ei
=
f
_
1
NV
N
j
1
i
-
f
_
2
NV
N
j
2
i
f
_
1
NV
-
f
_
2
NV
=
γ
N
j
1
i
-
N
j
2
i
γ
-
1
where γ={overscore (f)} 1 NV /{overscore (f)} 2 NV .
5. The method of claim 4 , further comprising eliminating GPS receiver clock perturbations by taking a first difference of N j Ei as ΔN j E =N j Ep −N j Eq where p and q refer to distinct NAVSTARS.
6. The method of claim 1 , further comprising eliminating cycle slip by autonomous identification and rejection of any sequential carrier phase measurement that suffers loss of phase lock.
7. The method of claim 6 , further comprising continuing processing with a next acceptable sequential carrier phase measurement.
8. The method of claim 7 , wherein the autonomous identification and rejection of any sequential carrier phase measurement that suffers loss of phase lock further comprises:
using sequential carrier phase measurement y k at time t k to correct a propagated a priori state estimate X k|k−1 at time t k to calculate an improved state estimate X k|k at time t k ;
propagating the state estimate X k|k and its realistic error covariance matrix P k|k to time t k+1 to get X k+1|k and P k+1|k;
using X k+1|k to calculate a measurement representation y(X k+t|k );
forming the measurement residual Δy k+1 =y k+1−y (X k+1|k );
comparing the absolute value |Δy k+1 to a threshold T k+1 derived from P k+1|k and from a measurement residual variance matrix R k+1, such that:
if |Δy k+1 |<T k+1, then measurement y k+1 is accepted for processing; and
if |Δy k+1 |≧T k+1, the measurement y k+1 is autonomously rejected in real time.
9. The method of claim 1 , wherein serial correlation due to thermal noise δN j ni in overlapping measurements is eliminated by processing sequential Doppler carrier phase count measurements.
10. The method of claim 1 , further comprising processing the state estimates in a sequential filter or a sequential smoother.