Device and method for three-dimensional positioning
A device and method for three-dimensional positioning are provided. The three-dimensional positioning of a common reference point is determined by fusion of supplied measurements, taking into account a lever arm compensation between the reference point, a global navigation satellite system (GNSS) receiver antenna, at least one radar antenna, and an inertial measuring unit.
1. A device ( 10 ) for three-dimensional positioning, comprising:
a secondary radar base station with at least one radar antenna, the secondary radar base station arranged to perform range measurement for transponders;
a global navigation satellite system (GNSS) receiver with a GNSS receiver antenna, the GNSS receiver arranged to measure GNSS signals;
an inertial measuring unit, which is arranged to determine a location of the GNSS receiver antenna and of the at least one radar antenna in a shared coordinate system in relation to a reference point; and
an integration processor, which is arranged to be supplied with pseudorange measurements of the GNSS receiver, radar range measurements, and motions of the device about an axes of the shared coordinate system measured by the inertial measuring unit, and which is arranged to determine a three-dimensional position of a common reference point by fusion of the pseudorange measurements, radar range measurements and motions of the device, wherein a lever arm compensation is carried out that accounts for the measured motions.
2. The device according to claim 1 , wherein the secondary base station operates in a C-band frequency band and uses frequency modulated continuous wave (FMCW) radar signals for the range measurement for the transponders.
3. The device according to claim 1 , wherein an inertial navigation system contains the inertial measuring unit, and
wherein the integration processor is arranged to determine, outside an operational area of the secondary radar base station, a three-dimensional position using a first coupled navigation based on the pseudorange measurements of the GNSS receiver and inertial navigation measurements of the inertial navigation system, and the integration processor is further arranged to determine, inside the operational area of the secondary radar base station, a three-dimensional position using a second coupled navigation based on the radar range measurements, the pseudorange measurements of the GNSS receiver, and the inertial navigation measurements of the inertial navigation system.
4. The device according to claim 1 , wherein the integration processor has a nonlinear filter arranged to process the pseudorange measurements of the GNSS receiver, inertial measurement unit data, and the radar range measurements.
5. The device according to claim 4 , wherein the nonlinear filter is arranged to determine inertial navigation system navigation solution correction data based on the pseudorange measurements of the GNSS receiver and the radar range measurements, and
the integration processor is arranged to execute a strapdown algorithm which, based on the correction data and the motions of the device about the axes of the shared coordinate system measured by the inertial measuring unit, determines the three-dimensional position.
6. The device according to claim 4 , wherein the nonlinear filter is arranged to determine the three-dimensional position based on the pseudorange measurements of the GNSS receiver, the radar range measurements, and the inertial navigation system navigation solution, and
for calibration purposes, the determined three-dimensional position is coupled back to the inertial navigation system of the device.
7. The device according to claim 4 , wherein the nonlinear filter is arranged to approximate a slant range r between the at least one radar antenna and one of the transponders using the following nonlinear function:
r
~
(
x
_
U
,
k
)
=
r
(
x
_
U
,
k
-
)
+
(
x
_
U
,
k
-
x
_
U
,
k
-
)
T
∇
r
(
x
_
U
,
k
-
)
+
1
2
(
x
_
U
,
k
-
x
_
U
,
k
-
)
T
H
(
x
_
U
,
k
-
)
(
x
_
U
,
k
-
x
_
U
,
k
-
)
where x U,k is a three-dimensional position vector between a transponder TP and the device U at time k, x U,k − is a current approximation point, ∇r( x U,k − ) is the vector of the partial derivative of r at point x U,k − , and H( x U,k − ) is the matrix of the second partial derivative of r at point x U,k − .
8. The device according to claim 7 , wherein the nonlinear filter is arranged to use a sigma point Kalman filter or a second-order filter for nonlinear optimization.
9. The device according to claim 4 , wherein the nonlinear filter is arranged to implement a state model having linear or nonlinear state equations, depending on an application of the device.
10. A method for three-dimensional positioning, the method comprising the steps of:
receiving radar range measurements of a secondary radar base station, which is provided for range measurement for transponders and which has at least one radar antenna;
receiving pseudorange measurements of a global navigation satellite system (GNSS) receiver, which is provided for measuring GNSS signals and which has a GNSS receiver antenna;
receiving motion measurements of an inertial measuring unit, which is provided for determining the location of the GNSS receiver antenna and of the at least one radar antenna in a shared coordinate system in relation to a reference point; and
determining, by an integration processor, a three-dimensional position of a common reference point by fusing the pseudorange measurements of the GNSS receiver, the radar range measurements, and the motion measurements of the inertial measuring unit, taking into account a lever arm compensation between the reference point, the GNSS receiver antenna, the at least one radar antenna, and the inertial measuring unit.
11. The method according to claim 10 , further comprising the steps of:
nonlinear filtering to determine inertial navigation system navigation solution correction data based on the received pseudorange measurements and the received radar range measurements; and
executing a strapdown algorithm to determine the three-dimensional position based on the correction data and the received motion measurements, or
nonlinear filtering to determine the three-dimensional position based on the received pseudorange measurements, the received radar range measurements, and the received inertial navigation system navigation solution.
12. The method according to claim 11 , wherein the nonlinear filtering includes an approximation of a slant range between the at least one radar antenna and one of the transponders using the following nonlinear function:
r
~
(
x
_
U
,
k
)
=
r
(
x
_
U
,
k
-
)
+
(
x
_
U
,
k
-
x
_
U
,
k
-
)
T
∇
r
(
x
_
U
,
k
-
)
+
1
2
(
x
_
U
,
k
-
x
_
U
,
k
-
)
T
H
(
x
_
U
,
k
-
)
(
x
_
U
,
k
-
x
_
U
,
k
-
)
where x U,k is a three-dimensional position vector between a transponder TP and the device U at time k, x U,k − is a current approximation point, ∇r( x U,k − ) is the vector of the partial derivative of r at point x U,k − , and H( x U,k − ) is the matrix of the second partial derivative of r at point x U,k − .
13. The method according to claim 12 , wherein the nonlinear filtering uses a sigma point Kalman filter or a second-order filter for optimization.
14. A non-transitory computer program product containing a machine-readable program medium on which a computer program is stored, wherein the computer program, when executed by a processor, causes the processor to:
receive radar range measurements of a secondary radar base station, which is provided for range measurement for transponders and which has at least one radar antenna;
receive pseudorange measurements of a global navigation satellite system (GNSS) receiver, which is provided for measuring GNSS signals and which has a GNSS receiver antenna;
receive motion measurements of an inertial measuring unit, which is provided for determining the location of the GNSS receiver antenna and of the at least one radar antenna in a shared coordinate system in relation to a reference point; and
determine a three-dimensional position of a common reference point by fusing the pseudorange measurements of the GNSS receiver, the radar range measurements, and the motion measurements of the inertial measuring unit, taking into account a lever arm compensation between the reference point, the GNSS receiver antenna, the at least one radar antenna, and the inertial measuring unit.