# US 10,871,374 B2 · Estimating the speed and the heading of an aircraft, independently of a magnetic measurement

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- Number: US 10,871,374 B2
- Document ID: US10871374B2
- Status: Granted
- Kind: B2
- Application number: 15/794,021
- Filed: 2017-10-26
- Published: 2018-05-03
- Granted: 2020-12-22
- Earliest claimed: 2016-10-27
- Assignees: Airbus Helicopters
- Applicants: Airbus Helicopters
- Inventors: Jean Paul Petillon; Julien Florens
- Web page: https://patentgrep.com/patent/US10871374B2

## CPC

- G01C 21/165: {combined with non-inertial navigation instruments}
- G01C 23/005: {Flight directors (indicating arrangements specially adapted for rotary gyroscopes G01C19/32)}
- G01S 19/49: whereby the further system is an inertial position system, e.g. loosely-coupled
- G05D 1/0825: {using mathematical models}
- B64D 43/02: for indicating aircraft speed or stalling conditions
- G01C: MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY (measuring liquid level G01F; radio navigation, determining distance or velocity by use of propagation effects, e.g. Doppler effects, propagation time, of radio waves, analogous arrangements using other waves G01S)
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G05D: SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- B64D: EQUIPMENT FOR FITTING IN OR TO AIRCRAFT; FLIGHT SUITS; PARACHUTES; ARRANGEMENT OR MOUNTING OF POWER PLANTS OR PROPULSION TRANSMISSIONS IN AIRCRAFT

## Abstract

A device for estimating an aircraft's speed relative to the ground and heading, while making no use of the rotation of the Earth or of the Earth's magnetic field. The device comprises in particular a first linear estimator that hybridizes a measurement of the speed of the aircraft relative to the ground as provided by a global navigation satellite system (GNSS) receiver with measurements of the acceleration and the attitudes of the aircraft coming from an attitude and heading reference system (AHRS) device without a gyrocompass and without a magnetometer. The first estimator is made linear by replacing the single “heading error estimate Δψ” state of prior art embodiments with two states, namely estimates of the sine and of the cosine of the heading error.

## Claims

### Claim 1

A device for estimating ground speed and heading of an aircraft, the aircraft having three axes forming a fuselage reference frame rigidly associated with a structure of the aircraft, the device comprising:
a global navigation satellite system (GNSS) receiver receiving signals from a plurality of satellites and configured to provide a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, the geographical reference frame including a horizontal plane;
an attitude and heading reference system (AHRS) device providing a measurement of an acceleration vector of the aircraft in the fuselage reference frame together with estimates of the attitude angles, and a directional estimate of the heading of the aircraft; and
a first estimator connected to the GNSS receiver and to the AHRS;
wherein the first estimator is linear and configured to prepare an estimate of an unbounded error affecting the directional estimate of the heading determined by the AHRS device by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector, independently of any magnetic measurement.

### Claim 2 (depends on 1)

The device according to claim 1, wherein the first estimator is a linear estimator having at least four states, which are estimated values for horizontal components of the speed vector relative to the ground of the aircraft in the geographical reference frame, and estimated values for the values of cosine and of sine of the estimate of the unbounded error affecting the directional estimate of the heading.

### Claim 3 (depends on 2)

The device according to claim 2, wherein the first estimator performs trigonomic calculations to determine the estimate of the unbounded error from the estimated values and for the cosine and for the sine, and performs a difference operation to subtract the estimate of the unbounded error from the directional estimate of the heading determined by the AHRS device in order to generate an estimated value for a geographical heading of the aircraft that is unaffected by potential magnetic disturbances of the environment of the aircraft.

### Claim 4 (depends on 2)

The device according to claim 2, wherein the device includes two outputs constituted by the estimated values for the horizontal components of the speed vector relative to the ground, which values take account of the estimate of the unbounded error.

### Claim 5 (depends on 2)

The device according to claim 2, wherein the first estimator applies the equations of a Kalman filter based on a model of a process, in continuous time, such that:
d
dt
⁢
x
⁡
(
t
)
=
F
⁡
(
t
)
·
x
⁡
(
t
)
+
w
c
⁡
(
t
)
,
and
⁢
⁢
⁢
z
⁡
(
t
)
=
H
⁡
(
t
)
·
x
⁡
(
t
)
+
w
m
⁡
(
t
)
;
with:
x
⁡
(
t
)
=
(
C
⁢
⁢
Δψ
S
⁢
⁢
Δψ
v
x
N
v
y
N
…
)
being a state vector comprising at least the four states, namely the estimated values for the cosine and for the sine of the estimate of the unbounded error and the estimated values for the horizontal components of the speed vector relative to the ground of the aircraft in the geographical reference frame;
wc(t) being a control noise vector;
wm(t) being a measurement noise vector;
z
⁡
(
t
)
=
(
v
x
N
v
y
N
…
)
being an estimation vector of the measurement comprising at least the two estimated values for the horizontal components of the speed vector relative to the ground of the aircraft in the geographical reference frame;
F
⁡
(
t
)
=
(
-
1
τ
0
0
0
…
0
-
1
τ
0
0
…
γ
x
N
*
-
γ
y
N
*
0
0
…
γ
y
N
*
γ
x
N
*
0
0
…
…
…
…
…
…
)
being a sub-matrix of a matrix relating the derivative of the state vector to the state vector; and
H
⁡
(
t
)
=
(
0
0
1
0
…
0
0
0
1
…
…
…
…
…
…
)
being a sub-matrix of a measurement matrix relating the estimation vector of the measurement to the state vector.

### Claim 6 (depends on 1)

The device according to claim 1, wherein the device includes a second estimator operating with a model that is linearized by the “small angles” assumption, the first estimator operating during an initial convergence stage and subsequently being replaced by the second estimator for continuing to prepare the estimate of the unbounded error affecting the directional estimate of the heading, and consequently to refine the estimated values and for the horizontal components of the vector of the speed relative to the ground and for a geographical heading of the aircraft.

### Claim 7 (depends on 6)

The device according to claim 6, wherein the second estimator replaces the first estimator from the instant at which the covariance associated with the estimate of the unbounded error becomes less than a first predetermined threshold.

### Claim 8 (depends on 6)

The device according to claim 6, wherein the second estimator replaces the first estimator from the instant at which the modulus of the vector formed by the estimated values for sine and cosine of the estimate of the unbounded error become close to unity, to within a margin, such that:
|1−√{square root over ((SΔψ)2+(CΔψ)2)}|<margin.

### Claim 9 (depends on 6)

The device according to claim 6, wherein the second estimator replaces the first estimator from the instant at which the covariance associated with the estimate of the unbounded error becomes less than a first predetermined threshold, or else from the instant at which the modulus of the vector formed by the estimated values for sine and cosine of the unbounded error become close to unity, to within a margin, such that:
|1−√{square root over ((SΔψ)2+(CΔψ)2)}|<margin.

### Claim 10 (depends on 1)

The device according to claim 1, wherein the first estimator:
performs a first projection operation for projecting the fuselage reference frame onto a local horizontal reference frame, the local horizontal reference frame being formed firstly by a projection onto a horizontal plane of the direction of the fuselage reference frame, and secondly by a direction perpendicular to the projection and situated in the horizontal plane;
performs a second projection operation for projecting the local horizontal reference frame onto a horizontal pseudo-geographical reference frame, the horizontal pseudo-geographical reference frame being defined from the local horizontal reference frame and from the directional estimate of the heading, the directions of the horizontal pseudo-geographical reference frame each forming an angle equal to the directional estimate of the heading with a respective one of the directions of the local horizontal reference frame; and
performs a linear transformation operation for transforming the horizontal pseudo-geographical reference frame into an estimate of the horizontal plane, with the angle between the estimate of the horizontal plane and the horizontal pseudo-geographical reference frame being the estimate of the unbounded error affecting the directional estimate of the heading; and
the first estimator comprising a feedback loop having its gains calculated using the equations of a Kalman filter.

### Claim 11 (depends on 1)

The device according to claim 1, wherein the horizontal plane of the geographical reference frame is substantially perpendicular to the Earth's gravity direction.

### Claim 12

A method of estimating speed relative to the ground and heading of an aircraft, wherein the method comprises:
providing a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, by receiving signals from a plurality of satellites, the geographical reference frame including a horizontal plane;
providing a measurement of an acceleration vector of the aircraft in a fuselage reference frame rigidly associated with the aircraft, together with estimates of attitude angles and a directional estimate of the heading of the aircraft; and
preparing an estimate of an unbounded error affecting the directional estimate of the heading, which preparation is performed in a manner that is linear by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector.

### Claim 13 (depends on 12)

The method according to claim 12, wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading comprises the following sub-steps:
projecting the measurement of the acceleration vector onto a local horizontal reference frame while using the estimates of the attitude angles in order to obtain an estimate of a horizontal component of the acceleration vector, the local horizontal reference frame being formed firstly by a projection of the direction of the fuselage reference frame onto a horizontal plane, and secondly by a direction perpendicular to the projection and situated in the horizontal plane;
projecting the estimate of the horizontal component of the acceleration vector onto a horizontal pseudo-geographical reference frame in order to obtain a pseudo-geographical estimate of a horizontal component of the acceleration vector, the horizontal pseudo-geographical reference frame being defined from the local horizontal reference frame and from the directional estimate of the heading, the directions of the horizontal pseudo-geographical reference frame each forming an angle equal to the directional estimate of the heading with a respective one of the directions of the local horizontal reference frame;
linearly transforming the pseudo-geographical estimate of the horizontal component in the pseudo-geographical reference frame of the acceleration vector into an estimate of a horizontal component in a geographical reference frame of the acceleration vector, the estimate being corrected with the estimate of the unbounded error affecting the directional estimate of the heading, by means of the estimated values;
integrating the estimate of the horizontal component of the acceleration vector in the pseudo-geographical reference frame in order to obtain an estimate of the speed vector relative to the ground in the horizontal geographical reference frame, taking account of the estimate of the unbounded error affecting the directional estimate of the heading;
comparing the estimate of the speed vector relative to the ground in the horizontal geographical reference frame with the measurement of the speed vector relative to the ground; and
preparing corrections acting on the estimate of the unbounded error and on the estimate of the speed vector relative to the ground.

### Claim 14 (depends on 13)

The method according to claim 13, wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading includes calculating the estimated value of the geographical heading.

### Claim 15 (depends on 13)

The method according to claim 13, wherein the preparing corrections acting on the estimate of the unbounded error and on the estimate of the speed vector relative to the ground applies a Kalman filter having at least four states, which are the estimated values for the horizontal component of the speed vector relative to the ground in the geographical reference frame, and also the estimated values and for cosine and sine of the estimate of the unbounded error affecting the directional estimate of the heading.

### Claim 16 (depends on 13)

The method according to claim 13, wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading applies a model that is linearized by the “small angles” assumption as from the instant at which the covariance associated with the estimate of the unbounded error becomes less than a first predetermined threshold, or else the modulus of the vector formed by the estimated values for sine and cosine of the estimate of the unbounded error come close to unity, to within a margin, such that:
|1−√{square root over ((SΔψ)2+(CΔψ)2)}|<margin.

### Claim 17 (depends on 12)

The method according to claim 12, wherein the horizontal plane of the geographical reference frame is substantially perpendicular to the Earth's gravity direction.

### Claim 18

A device for estimating ground speed and heading of an aircraft, the aircraft having three axes forming a fuselage reference frame rigidly associated with a structure of the aircraft, the device comprising:
a global navigation satellite system (GNSS) receiver receiving signals from a plurality of satellites and configured to provide a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, the geographical reference frame including a horizontal plane;
an attitude and heading reference system (AHRS) device providing a measurement of an acceleration vector of the aircraft in the fuselage reference frame together with estimates of the attitude angles, and a directional estimate of the heading of the aircraft; and
a first estimator connected to the GNSS receiver and to the AHRS;
wherein the first estimator is linear and configured to prepare an estimate of an unbounded error affecting the directional estimate of the heading determined by the AHRS device by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector, independently of any magnetic measurement; and
wherein the device includes a second estimator operating with a model that is linearized by the “small angles” assumption, the first estimator operating during an initial convergence stage and subsequently being replaced by the second estimator for continuing to prepare the estimate of the unbounded error affecting the directional estimate of the heading, and consequently to refine the estimated values and for the horizontal components of the vector of the speed relative to the ground and for a geographical heading of the aircraft.

### Claim 19 (depends on 18)

The device according to claim 18, wherein the horizontal plane of the geographical reference frame is substantially perpendicular to the Earth's gravity direction.

### Claim 20

A method of estimating speed relative to the ground and heading of an aircraft, wherein the method comprises:
providing a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, by receiving signals from a plurality of satellites, the geographical reference frame including a horizontal plane;
providing a measurement of an acceleration vector of the aircraft in a fuselage reference frame rigidly associated with the aircraft, together with estimates of attitude angles and a directional estimate of the heading of the aircraft; and
preparing an estimate of an unbounded error affecting the directional estimate of the heading, which preparation is performed in a manner that is linear by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector;
wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading comprises the following sub-steps:
projecting the measurement of the acceleration vector onto a local horizontal reference frame while using the estimates of the attitude angles in order to obtain an estimate of a horizontal component of the acceleration vector, the local horizontal reference frame being formed firstly by a projection of the direction of the fuselage reference frame onto a horizontal plane, and secondly by a direction perpendicular to the projection and situated in the horizontal plane;
projecting the estimate of the horizontal component of the acceleration vector onto a horizontal pseudo-geographical reference frame in order to obtain a pseudo-geographical estimate of a horizontal component of the acceleration vector, the horizontal pseudo-geographical reference frame being defined from the local horizontal reference frame and from the directional estimate of the heading, the directions of the horizontal pseudo-geographical reference frame each forming an angle equal to the directional estimate of the heading with a respective one of the directions of the local horizontal reference frame;
linearly transforming the pseudo-geographical estimate of the horizontal component in the pseudo-geographical reference frame of the acceleration vector into an estimate of a horizontal component in the geographical reference frame of the acceleration vector, the estimate being corrected with the estimate of the unbounded error affecting the directional estimate of the heading, by means of the estimated values;
integrating the estimate of the horizontal component of the acceleration vector in the pseudo-geographical reference frame in order to obtain an estimate of the speed vector relative to the ground in the horizontal geographical reference frame, taking account of the estimate of the unbounded error affecting the directional estimate of the heading;
comparing the estimate of the speed vector relative to the ground in the horizontal geographical reference frame with the measurement of the speed vector relative to the ground; and
preparing corrections acting on the estimate of the unbounded error and on the estimate of the speed vector relative to the ground; and
wherein, during certain stages, preparing the estimate of the unbounded error affecting the directional estimate of the heading applies a model that is linearized by the “small angles” assumption.