Automatic decorrelation and parameter tuning real-time kinematic method and apparatus
View Patent ↗A method of and computer-readable medium containing instructions for high accuracy, reliable position determination. The ADAPT-RTK Technology (Automatic Decorrelation and Parameter Tuning Real-Time Kinematic technology) is described using an innovative decorrelation algorithm to decorrelate the correlation between L1 and L2 measurements through a functional model and a stochastic model reducing the impact on performance of distance dependent biases.
1. A method of determining a position estimate based on an updated Kalman filter, comprising:
receiving a first measurement L 1 based on a first signal with wavelength λ 1 and frequency f 1 ;
receiving a second measurement L 2 based on a second signal with wavelength λ 2 and frequency f 2 ;
selecting a model α of distance dependent and distance independent errors in the first and second measurements, wherein the model α is selected from α=λ 1 /λ 2 , α=λ 2 /λ 1 , and α=1;
based on the model α, calculating a double differenced variance matrix:
D
(
L
1
,
L
2
)
=
D
11
0
0
D
_
22
;
wherein
D
11
=
2
R
L2
2
W
1
+
W
ref
W
ref
…
W
ref
W
ref
W
ref
W
2
+
W
ref
…
W
ref
W
ref
⋮
⋮
⋰
⋮
⋮
W
ref
W
ref
…
W
n
-
2
+
W
ref
W
ref
W
ref
W
ref
…
W
ref
W
n
-
1
+
W
ref
;
wherein
D
_
22
=
(
R
L2
2
+
α
2
R
L1
2
-
2
α
R
L1
,
L2
)
W
1
+
W
ref
W
ref
…
W
ref
W
ref
W
ref
W
2
+
W
ref
…
W
ref
W
ref
⋮
⋮
⋰
⋮
⋮
W
ref
W
ref
…
W
n
-
2
+
W
ref
W
ref
W
ref
W
ref
…
W
ref
W
n
-
1
+
W
ref
;
wherein
R
L1
=
(
1
λ
1
2
[
R
non
-
dist
,
L1
2
+
(
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
B
2
]
)
1
2
;
wherein
R
L2
=
(
1
λ
2
2
[
R
non
-
dist
,
L2
2
+
(
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
B
2
]
)
1
2
;
wherein
R
L1
,
L2
=
1
λ
1
λ
2
(
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
(
f
1
4
f
2
4
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
B
2
;
wherein R non-dist,L1 is a non-distance dependant measurement error for the L 1 measurement;
wherein R non-dist,L2 is a non-distance dependant measurement error for the L 2 measurement;
wherein R ion is measurement error due to ionospheric delay;
wherein R trop is measurement error due to tropospheric delay;
wherein R orb is measurement error due to orbit bias;
wherein each W is: W n =1.0+7.5e −E/15 ;
wherein n is a satellite ordinal of a plurality of satellites;
wherein W ref corresponds to a reference satellite of the plurality of satellites;
wherein E is the elevation angle of each satellite of the plurality of satellites;
updating a Kalman filter with the calculated variance matrix; and
determining a present position estimate based on the updated Kalman filter.
2. The method of claim 1 , wherein the updated Kalman filter with the calculated variance matrix is K=D(L 1 ,L 2 ) new H 2 T {H 2 T D(L 1 ,L 2 ) new H 2 T +V 2 } −1 ;
wherein H 2 T is a transpose of a design matrix H 2 for the measurement L 2 ;
wherein V 2 is a residual measurement of measurement L 2 ;
wherein D(L 1 ,L 2 ) new =D(L 1 ,L 2 ) old −K old H 2 D(L 1 ,L 2 ) old ;
wherein D(L 1 ,L 2 ) new is the calculated variance matrix including the received measurements L 1 and L 2 ;
wherein D(L 1 ,L 2 ) old is a previous calculated variance matrix which was calculated before receiving both of the received measurements L 1 and L 2 ; and
wherein K old is a previous Kalman filter which was calculated before receiving both of the received measurements L 1 and L 2 .
3. A computer readable medium having computer-executable instructions, comprising:
receiving a first measurement L 1 based on a first signal with wavelength λ 1 and frequency f 1 ;
receiving a second measurement L 2 based on a second signal with wavelength λ 2 and frequency f 2 ;
selecting a model α of distance dependent and distance independent errors in the first and second measurements, wherein the model α is selected from α=λ1/λ2, α=λ2/λ1, and α=1;
based on the model α, calculating a double differenced variance matrix:
D
(
L
1
,
L
2
)
=
D
11
0
0
D
_
22
;
wherein
D
11
=
2
R
L2
2
W
1
+
W
ref
W
ref
…
W
ref
W
ref
W
ref
W
2
+
W
ref
…
W
ref
W
ref
⋮
⋮
⋰
⋮
⋮
W
ref
W
ref
…
W
n
-
2
+
W
ref
W
ref
W
ref
W
ref
…
W
ref
W
n
-
1
+
W
ref
;
wherein
D
_
2
=
(
R
L
2
2
+
α
2
R
L
1
2
-
2
αR
L
1
,
L
2
)
W
1
+
W
ref
W
ref
⋯
W
ref
W
ref
W
ref
W
2
⋯
W
ref
W
ref
⋮
⋮
⋰
⋮
⋮
W
ref
W
ref
⋯
W
n
-
2
+
W
ref
W
ref
W
ref
W
ref
⋯
W
ref
W
n
-
1
+
W
ref
;
wherein
R
L1
=
(
1
λ
1
2
[
R
non
-
dist
,
L1
2
+
(
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
B
2
]
)
1
2
;
wherein
R
L2
=
(
1
λ
2
2
[
R
non
-
dist
,
L2
2
+
(
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
B
2
]
)
1
2
;
wherein
R
L1
,
L2
=
1
λ
1
λ
2
(
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
(
f
1
4
f
2
4
R
ion
2
+
R
trop
2
+
R
orb
2
)
·
B
2
;
wherein R non-dist,L1 is a non-distance dependant measurement error for the L 1 measurement;
wherein R non-dist,L2 is a non-distance dependant measurement error for the L 2 measurement;
wherein R ion is measurement error due to ionospheric delay;
wherein R trop is measurement error due to tropospheric delay;
wherein R orb is measurement error due to orbit bias;
wherein each W is: W n =1.0 +7.5e −E/15 ;
wherein n is a satellite ordinal of a plurality of satellites;
wherein W ref corresponds to a reference satellite of the plurality of satellites;
wherein E is the elevation angle of each satellite of the plurality of satellites;
updating a Kalman filter with the calculated variance matrix; and
determining a present position estimate based on the updated Kalman filter.
4. The computer readable medium of claim 3 , wherein the updated Kalman filter with the calculated variance matrix is:
K=D ( L 1 ,L 2 ) new H 2 T {H 2 T D ( L 1 ,L 2 ) new H 2 T +V 2 } −1 ;
wherein H 2 T is a transpose of a design matrix H 2 for the measurement L 2 ;
wherein V 2 is a residual measurement of measurement L 2 ;
wherein D(L 1 ,L 2 ) new =D(L 1 ,L 2 ) old −K old H 2 D(L 1 ,L 2 ) old ;
wherein D(L 1 ,L 2 ) new is the calculated variance matrix including the received measurements L 1 and L 2 ;
wherein D(L 1 ,L 2 ) old is a previous calculated variance matrix which was calculated before receiving both of the received measurements L 1 and L 2 ; and
wherein K old is a previous Kalman filter which was calculated before receiving both of the received measurements L 1 and L 2 .