![](bg2.png)
with an accuracy of 0.25
◦
/baseline length [m] and an
absolute position with an accuracy of 1 m. Similar de-
velopments may be found within space vehicles, for
example in (Springmann and Cutler, 2014).
However, as stated in (Yun et al., 2008), many of
the presented methods such as the ones employing lo-
cal magnetic field vectors, are only valid for estimat-
ing the orientation of a static or slow-moving rigid
body. In the research described in this paper, two
measured quantities are used to obtain attitude infor-
mation for high dynamic vehicles: speed and grav-
ity vectors. They are obtained in two different refer-
ence frames using a GNSS sensor and a strap-down
accelerometer.
1.1 Contributions
The main contribution of this paper is the develop-
ment of a novel algorithm which aims at avoiding
the use of gyroscopes, and its implicit high costs if
high precision is required (Ismail et al., 2015), in
a long term and to require lower performance gy-
roscopes for attitude determination in the immediate
term. This is pretended to decrease costs in attitude
sensors and even to improve attitude determination by
applying filtering techniques, especially for artillery
device purposes, where high solicitation force condi-
tions increase the price of precise attitude determina-
tion devices such as gyroscopes.
Nonlinear simulations based on ballistic rocket
launches are performed to determine real attitude and
compare it to the estimated attitude obtained from the
algorithms. The applicability of the proposed solu-
tion for aircraft flight navigation, guidance and con-
trol, and for ballistic rocket terminal guidance, where
attack and side-slip aerodynamic angles are relatively
small, is also demonstrated.
This paper is organized as follows. Section II de-
scribes the problem in detail. Section III is devoted to
flight dynamics and sensor models. Section IV shows
simulations results. Finally, in Section V some con-
clusions and further work are drawn.
2 PROBLEM DESCRIPTION
Attitude determination is a fundamental field in
aerospace engineering, as maneuvers in order to
change vehicle trajectories are governed by aerody-
namic forces, which depend directly on ship orienta-
tion angles. Furthermore, attitude in artillery rockets
terminal phase is vital as it determines factors such
as penetrability of payload or countermeasures avoid-
ability. Therefore, developing algorithms to improve
attitude determination is a cornerstone in guidance,
navigation and control research.
One of the techniques to determine attitude is to
calculate it from the director cosine matrix (DCM)
which completely determines the rotation of a body.
Two reference frames are defined, one fixed to the
body and another one as a reference. In order to ob-
tain the DCM, a geometrical plane defined in both
reference triads must be obtained. Every geometrical
plane is defined by two vectors. Therefore, knowing
the same two vectors expressed in the two reference
frames, the DCM can be calculated.
2.1 Triad Definition
Two axes systems are defined in order to express
forces and moments: North-East-Down (NED) axes
and Body (B) axes. NED axes are defined by sub in-
dex NED. x
NED
pointing north, z
NED
perpendicular to
x
NED
and pointing nadir, and y
NED
forming a clock-
wise trihedron. Body axes are defined by sub index
B. x
B
pointing forward and contained in the plane
of symmetry of the aircraft, z
B
perpendicular to x
B
pointing down and contained in the plane of symme-
try of the aircraft, and y
B
forming a clockwise trihe-
dron. The origin of body axes is located at the center
of mass of the aircraft.
2.2 Involved Vectors Determination
If a GNSS sensor device is equipped on the aircraft,
velocity vector can be directly expressed from sen-
sor measurements in the NED triad. Expression for
velocity in NED is defined on equation (1), where
v
x
NED
,v
y
NED
and v
z
NED
are the components of this ve-
locity vector in NED axes.
−−→
v
NED
= [v
x
NED
,v
y
NED
,v
z
NED
]
T
(1)
The same velocity vector expressed in body triad
can be obtained from a set of accelerometers equipped
on the ship, one on each of the axes. This devices
are able to measure acceleration. After integration
of each of the components along the time, velocity
vector is obtained as it is expressed on equation (2),
where a
x
B
,a
y
B
and a
z
B
are the components of the ac-
celeration vector in body axes.
−→
v
B
=
Z
[a
x
B
,a
y
B
,a
z
B
]
T
dt (2)
Another vector expressed in the two reference
frames is required in order to define the rotation.
Gravity vector is easily determined in NED triad as
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
378