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 computer implemented method of providing improved real time kinematics determination, comprising:
determining, via a computing device, a first position estimate;
performing an ambiguity resolution function having an output that provides an ambiguity resolution of the first position estimate by decorrelating first and second measurements, wherein the first and second measurements are inputs to the ambiguity resolution function;
selecting a model of distance dependent and distance independent errors in the first and second measurements; and
deriving a second position estimate as an output from a filter by inputting into the filter the output of the ambiguity resolution function and the distance dependent and distance independent errors.
2. The method as claimed in claim 1 , wherein the filter is a Kalman filter, the method further comprising:
based on the model, calculating a double differenced variance matrix; and
updating the Kalman filter with the calculated variance matrix.
3. The method as claimed in claim 1 , wherein the first and second measurements are decorrelated using the function:
{tilde over (V)} 2 ={tilde over (H)} 2 X+{tilde over (L)} 2 ,
wherein
{tilde over (L)} 2 =L 2 −αL 1 ;
{tilde over (H)} 2 =H 2 −αH 1 ;
D
~
2
=
(
R
L
2
2
+
α
2
R
L
1
2
-
2
α
R
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
]
;
α
=
{
1
λ
1
/
λ
2
λ
2
/
λ
1
0
R
L
1
,
L
2
/
R
L
1
2
;
and
wherein
L 1 represents a first measurement of a first signal with wavelength λ 1 ;
L 2 represents a second measurement of a second signal with wavelength λ 2 ;
α represents the model, the model α selected from α=λ 1 /λ 2 for a geometry-free combination,
α=λ 2 /λ 1 for an ionosphere-free combination, α=1 for a widelane combination, α=0 for an L 2 independent measurement, and α=R L1,L2 /R L1 2 for the correlation approach;
V 2 represents the post-fit residual vector of L 2 ;
H 1 represents a design matrix of L 1 ;
H 2 represents a design matrix of L 2 ;
X represents a Kalman filter state vector;
D 2 represents a variance-covariance matrix of L 2 ;
{tilde over (V)} 2 , {tilde over (H)} 2 , {tilde over (L)} 2 , and {tilde over (D)} 2 represent orthogonalized versions of V 2 , H 2 , L 2 , and D 2 , respectively;
R L1 2 represents zenith variance for single differenced L 1 measurements;
R L2 2 represents zenith variance for single differenced L 2 measurements;
each W is: W n =1.0+7.5e −E/15 wherein E represents the elevation angle of a satellite n in a plurality of satellites, wherein n represents a satellite ordinal in the plurality of satellites;
W ref represents a reference satellite of the plurality of satellites; and
wherein after the new values of {tilde over (V)} 2 , {tilde over (H)} 2 , {tilde over (L)} 2 , and {tilde over (D)} 2 are formed, L 1 and L 2 are updated independently, thereby decorrelating L 1 and L 2 .
4. The method as claimed in claim 1 , wherein at least one of a ratio smoothing function and an ambiguity stability function are used if a baseline is 10 kilometers or greater.
5. The method as claimed in claim 4 , wherein the ratio smoothing function is:
{tilde over (R)}atio=Ratio+{tilde over (R)}atio *(N−1)/N where N is the width of the moving window.
6. The method as claimed in claim 4 , wherein the ambiguity stability function includes:
incrementing a counter for each epoch in which double differenced ambiguities remain the same; and
if the double differenced ambiguities are not zero and less than 50 epochs are counted, resetting the counter.
7. A computer readable medium comprising:
at least one sequence of machine executable instructions in machine form, wherein
execution of the instructions by a tangible processor perform a method comprising:
determining a first position estimate;
performing an ambiguity resolution function having an output that provides an ambiguity resolution of the first position estimate by decorrelating first and second measurements, wherein the first and second measurements are inputs to the ambiguity resolution function;
selecting a model of distance dependent and distance independent errors in the first and second measurements; and
deriving a second position estimate as an output from a filter by inputting into the filter the output of the ambiguity resolution function and the distance dependent and distance independent errors.
8. The method as claimed in claim 7 , wherein the filter is a Kalman filter, the method further comprising:
based on the model, calculating a double differenced variance matrix; and
updating the Kalman filter with the calculated variance matrix.
9. The method as claimed in claim 7 , wherein the first and second measurements are decorrelated using the function:
{tilde over (V)} 2 ={tilde over (H)} 2 X+{tilde over (L)} 2 ,
wherein
{tilde over (L)} 2 =L 2 −αL 1 ;
{tilde over (H)} 2 =H 2 −αH 1 ;
D
~
2
=
(
R
L
2
2
+
α
2
R
L
1
2
-
2
α
R
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
]
;
α
=
{
1
λ
1
/
λ
2
λ
2
/
λ
1
0
R
L
1
,
L
2
/
R
L
1
2
;
and
wherein
L 1 represents a first measurement of a first signal with wavelength λ 1 ;
L 2 represents a second measurement of a second signal with wavelength λ 2 ;
α represents the model, the model α selected from α=λ 1 /λ 2 for a geometry-free combination,
α=λ 2 /λ 1 for an ionosphere-free combination, α=1 for a widelane combination, α=0 for an L 2 independent measurement, and α=R L1,L2 /R L1 2 for the correlation approach;
V 2 represents the post-fit residual vector of L 2 ;
H 1 represents a design matrix of L 1 ;
H 2 represents a design matrix of L 2 ;
X represents a Kalman filter state vector;
D 2 represents a variance-covariance matrix of L 2 ;
{tilde over (V)} 2 , {tilde over (H)} 2 , {tilde over (L)} 2 , and {tilde over (D)} 2 represent orthogonalized versions of V 2 , H 2 , L 2 , and D 2 , respectively;
R L1 2 represents zenith variance for single differenced L 1 measurements;
R L2 2 represents zenith variance for single differenced L 2 measurements;
each W is: W n =1.0+7.5e −E/15 wherein E represents the elevation angle of a satellite n in a plurality of satellites, wherein n represents a satellite ordinal in the plurality of satellites;
W ref represents a reference satellite of the plurality of satellites; and
wherein after the new values of {tilde over (V)} 2 , {tilde over (H)} 2 , {tilde over (L)} 2 , and {tilde over (D)} 2 are formed, L 1 and L 2 are updated independently, thereby decorrelating L 1 and L 2 .
10. The method as claimed in claim 7 , wherein at least one of a ratio smoothing function and an ambiguity stability function are used if a baseline is 10 kilometers or greater.
11. The method as claimed in claim 7 , wherein the ratio smoothing function is:
{tilde over (R)}atio=Ratio+{tilde over (R)}atio *(N−1)/N where N is the width of the moving window.
12. The method as claimed in claim 10 , wherein the ambiguity stability function includes:
incrementing a counter for each epoch in which double differenced ambiguities remain the same; and
if the double differenced ambiguities are not zero and less than 50 epochs are counted, resetting the counter.
13. A system for providing improved real time kinematics determination comprising:
means for determining a first position estimate;
means for performing an ambiguity resolution function having an output that provides an ambiguity resolution of the first position estimate by decorrelating first and second measurements, wherein the first and second measurements are inputs to the ambiguity resolution function;
means for selecting a model of distance dependent and distance independent errors in the first and second measurements; and
means for deriving a second position estimate as an output from a filter by inputting into the filter the output of the ambiguity resolution function and the distance dependent and distance independent errors.
14. The system of claim 13 , wherein the filter is a Kalman filter, the system further comprising:
means for, based on the model, calculating a double differenced variance matrix; and
means for updating the filter with the calculated variance matrix.
15. The system of claim 13 , wherein the first and second measurements are decorrelated using the function:
{tilde over (V)} 2 ={tilde over (H)} 2 X+{tilde over (L)} 2 ,
wherein
{tilde over (L)} 2 =L 2 −αL 1 ;
{tilde over (H)} 2 =H 2 −αH 1 ;
D
~
2
=
(
R
L
2
2
+
α
2
R
L
1
2
-
2
α
R
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
]
;
α
=
{
1
λ
1
/
λ
2
λ
2
/
λ
1
0
R
L
1
,
L
2
/
R
L
1
2
;
and
wherein
L 1 represents a first measurement of a first signal with wavelength λ 1 ;
L 2 represents a second measurement of a second signal with wavelength λ 2 ;
α represents the model, the model α selected from α=λ 1 /λ 2 for a geometry-free combination,
α=λ 2 /λ 1 for an ionosphere-free combination, α=1 for a widelane combination, α=0 for an
L 2 independent measurement, and α=R L1,L2 /R L1 2 for the correlation approach;
V 2 represents the post-fit residual vector of L 2 ;
H 1 represents a design matrix of L 1 ;
H 2 represents a design matrix of L 2 ;
X represents a Kalman filter state vector;
D 2 represents a variance-covariance matrix of L 2 ;
{tilde over (V)} 2 , {tilde over (H)} 2 , {tilde over (L)} 2 , and {tilde over (D)} 2 represent orthogonalized versions of V 2 , H 2 , L 2 , and D 2 , respectively;
R L1 2 represents zenith variance for single differenced L 1 measurements;
R L2 2 represents zenith variance for single differenced L 2 measurements;
each W is: W n =1.0+7.5e −E/15 wherein E represents the elevation angle of a satellite n in a plurality of satellites, wherein n represents a satellite ordinal in the plurality of satellites;
W ref represents a reference satellite of the plurality of satellites; and
wherein after the new values of {tilde over (V)} 2 , {tilde over (H)} 2 , {tilde over (L)} 2 , and {tilde over (D)} 2 are formed, L 1 and L 2 are updated independently, thereby decorrelating L 1 and L 2 .