North-finding using inertial navigation system
View Patent ↗A true north heading is determined by using gyroscopes of differing accuracy and orienting a gyroscope of a higher accuracy to a direction that is more sensitive to azimuth change (e.g., an east/west direction). A gyroscope with a lower accuracy is placed perpendicular to the gyroscope with a higher accuracy and can be oriented towards a north or south direction. The gyroscopes may be placed on a rotatable platform to properly orient the gyroscopes. The higher-accuracy gyroscope may be implemented by using multiple gyroscopes oriented in the same direction.
1. An apparatus for finding true north, comprising:
a first gyroscope having a first accuracy, and configured to measure a first angular velocity of a vehicle about a first axis;
a second gyroscope having a second accuracy higher than the first accuracy, and configured to measure a second angular velocity of the vehicle about a second axis that is orthogonal to the first axis; and
a rotary stage securing the first and the second gyroscopes, the rotary stage configured to align the second gyroscope in an East/West direction; and
a processor programmed to
(a) calculate a first true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position; and
(b) estimate a first East/West direction using the calculated azimuth and turn the rotary stage so that the second gyroscope is aligned in the estimated first East/West direction; and
(c) determine a second true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the second true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated first East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position;
(d) estimate a second East/West direction using the second true north heading and turn the rotary stage so that the second gyroscope is aligned in the estimated second East/West direction; and
(e) determine a third true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the third true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated second East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position.
2. The apparatus of claim 1 , wherein the second gyroscope includes a plurality of gyroscopes aligned in a same direction, each of the plurality of gyroscopes having an accuracy lower than the second accuracy.
3. The apparatus of claim 2 , wherein the plurality of gyroscopes includes a plurality of microelectromechanical (MEMS) gyroscopes.
4. The apparatus of claim 2 , further comprising a processor for calculating an error rate for the second gyroscope, the error rate calculated according to
σ
N
=
σ
i
n
where σ N is an error rate of the plurality, σ i is an error rate of a single gyroscope of the plurality, and n is the number of gyroscopes of the plurality.
5. The apparatus of claim 1 , wherein the first gyroscope is a first type of gyroscope and the second gyroscope is a second type of gyroscope.
6. The apparatus of claim 5 , wherein the second type of gyroscope is a microelectromechanical (MEMS) gyroscopes.
7. The apparatus of claim 1 , further comprising a processor in communication with the second gyroscope, the processor configured to estimate a true north direction by processing a signal from the second gyroscope.
8. The apparatus of claim 7 , wherein the processor is further configured to correct an Earth Rotation Vector measurement signal by calculating a measurement error of the second gyroscope and removing the measurement error from the Earth Rotation Vector measurement signal.
9. The apparatus of claim 1 , wherein the angular velocity is calculated according to
Ω
_
B
=
A
NED
Body
Ω
_
=
Ω
(
cos
φ
α
_
1
-
sin
φ
α
_
3
)
where Ω B is an Earth Rotation Vector in a frame of reference defined by a body of the vehicle, Ω is the angular velocity of the vehicle and α 1 and α 3 are vectors of a Direction Cosine Matrix, and φ is a latitude of the vehicle.
10. The apparatus of claim 1 , wherein the processor calculates the horizontal component of the earth rotation vector measured by the second gyroscope according to
r hy =r e cos(φ)sin(azimuth)+ε y
where r hy is the horizontal component of an earth rotation vector measured by the second gyroscope, ε y is the error measurement of the second gyroscope, r e is the earth rotation rate, φ is the latitude, and azimuth is the true north heading.
11. An apparatus for finding true north, comprising:
a gyroscope configured to measure an angular velocity of a vehicle about an axis, the gyroscope having a measurement axis;
an alignment system configured to determine the orientation of the measurement axis of the gyroscope with respect to true north; and
a rotary stage configured to align the second gyroscope within a range of approximately 0° to approximately 30° of true north; and
a processor programmed to
(a) calculate a first true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position; and
(b) estimate a first East/West direction using the calculated azimuth and turn the rotary stage so that the second gyroscope is aligned in the estimated first East/West direction; and
(c) determine a second true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the second true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated first East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position;
(d) estimate a second East/West direction using the second true north heading and turn the rotary stage so that the second gyroscope is aligned in the estimated second East/West direction; and
(e) determine a third true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the third true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated second East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position.
12. A vehicle, comprising:
a vehicle body;
a propulsion system connected to the vehicle body and configured to physically move the vehicle body; and
an inertial north-finding system secured to the vehicle body, the system comprising:
a first gyroscope having a first accuracy, and configured to measure a first angular velocity of a vehicle about a first axis;
a second gyroscope having a second accuracy higher than the first accuracy, and configured to measure a second angular velocity of the vehicle about a second axis that is orthogonal to the first axis; and
a rotary stage securing the first and the second gyroscopes, the rotary stage configured to align the second gyroscope in an East/West direction; and
a processor programmed to
(a) calculate a first true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position; and
(b) estimate a first East/West direction using the calculated azimuth and turn the rotary stage so that the second gyroscope is aligned in the estimated first East/West direction; and
(c) determine a second true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the second true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated first East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position;
(d) estimate a second East/West direction using the second true north heading and turn the rotary stage so that the second gyroscope is aligned in the estimated second East/West direction; and
(e) determine a third true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the third true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated second East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position.
13. A method for finding true north, comprising:
measuring a first angular velocity of a vehicle about a first axis using a first gyroscope having a first accuracy;
measuring a second angular velocity of the vehicle about a second axis that is orthogonal to the first axis using a second gyroscope having a second accuracy; and
rotating a rotary stage securing the first and the second gyroscopes to align the second gyroscope in an East/West direction; and
calculating a first true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position; and
estimating a first East/West direction using the calculated azimuth and turn the rotary stage so that the second gyroscope is aligned in the estimated first East/West direction; and
determining a second true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the second true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated first East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position;
estimating a second East/West direction using the second true north heading and turn the rotary stage so that the second gyroscope is aligned in the estimated second East/West direction; and
determining a third true north heading according to
azimuth
=
arc
sin
(
r
hy
-
ɛ
y
r
e
cos
(
φ
)
)
where the azimuth is the third true north heading, r hy is a horizontal component of an earth rotation vector measured by the second gyroscope aligned in the estimated second East/West direction, ε y is an error measurement of the second gyroscope, r e is an earth rotation rate, and φ is the latitude of the vehicle position.
14. The method of claim 13 , wherein the second accuracy is higher than the first accuracy.
15. The method of claim 14 , further comprising processing signals from two or more gyroscopes to obtain a measurement of the second angular velocity.
16. The method of claim 13 , further comprising:
calculating a measurement error of the second gyroscope; and
removing the measurement error from the second angular velocity measurement.
17. The method of claim 13 , further comprising determining an east or west direction of the vehicle by using the first angular velocity and the second angular velocity of the vehicle.