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Position/Velocity Aided Leveling Loop: Continuous-Discrete Time State
Multiplicative-Noise Filter Case
Irina Avital
1
, Isaac Yaesh
1
and Adrian-Mihail Stoica
2 a
1
Elbit Systems, Land and IMI Division, Ramat Ha Sharon, Israel
2
University POLITEHNICA of Bucharest, Romania
Keywords:
Leveling Loop, Kalman Filtering, Multiplicative Noise, Systems With Finite Jumps.
Abstract:
The problem of leveling using a low cost Inertial Measurement Unit (IMU) is considered, where the IMU mea-
surements are corrupted with white noise. In such a case the state equations are subject to state-multiplicative
noise. To cope with this noise, a state-Multiplicative Kalman Filter (MKF) is applied. The state compo-
nents for the Kalman filter implementation include the Body Position Vector (BPV), the Body Velocity Vector
(BVV), which is just the Ground Velocities Vector (GVV), projected onto the body axes and the three direction
cosines related to the roll and pitch angles. The BVB is assumed to be measured using a Doppler Velocity
Log (DVL) device which consists of four antennas measuring the Doppler effect. Similarly, it is assumed that
the corresponding BPV can be measured, for instance, using the received signal power at those four antennas.
The paper includes numerical simulations and implementation aspects related to the sampled data nature of
the estimation problem.
1 INTRODUCTION
Strap Down Inertial Navigation Systems (SDINS) re-
quire initialization of position, velocity and attitude.
When the platform on which the SDINS is station-
ary, the roll and pitch of the SDINS may be measured
directly from the accelerometers readings. When the
platform moves and no transfer alignment is possi-
ble (e.g. no accurate reference INS is available), one
may resort to the leveling loop approach providing
so called coarse alignment, where the roll and pitch
angles are estimated utilizing velocity measurements
(see e.g. (Xu, 2017) and (Tal, 2017)) and accelerom-
eters and rate sensors provided by an Inertial Mea-
surement Unit (IMU). The present paper deals with
the case where the IMU is a low cost one, provid-
ing measurements corrupted with white noise. In
such a case (see also (Yaesh, 2013)) the state equa-
tions are subject to state-multiplicative noise, mak-
ing related estimation problems readily tractable, us-
ing a state-multiplicative Kalman Filter (MKF), see
(Stoica, 2009). The state vector components for the
Kalman filter implementation include the Body Posi-
tion Vector (BPV), the Body Velocity Vector (BVV),
which is just the Ground Velocities Vector (GVV),
a
https://orcid.org/0000-0001-5369-8615
projected onto the body axes and the three direction
cosines related to the roll and pitch angles. In the
present paper, the BVB is assumed to be measured us-
ing say a Doppler Velocity Log (DVL) device which
consists of four antennas measuring the Doppler ef-
fect. Similarly, the BPV is measured from the four
corresponding range (i.e. received power) measure-
ments. We deal with the special case of a low range
navigation mission, allowing a simple Cartesian for-
mulation of equations of motion, where both Earth
rotation and curvature are neglected. The resulting
equations of motion are then linear equations of the
states, simplifying both dealing with real time calcu-
lation of the transition matrix and exact modeling of
the above mentioned multiplicative noise effect. It is
well known in the inertial navigation community that
navigation initialization with ’large’ attitude-errors
usually results in error divergence. In contrast, since
in our case the states include the directions cosines
and not just errors of the attitude angles (i.e. the rota-
tion from true to calculated Local Level Local North),
the leveling loop we consider, can deal with large ini-
tialization errors for both roll and pitch angles. In the
present paper it is shown that when the IMU measure-
ment noises are taken into account, a stochastic model
with state-dependent noisy terms for the equations of
motion is naturally obtained. Two specific Kalman fil-
Avital, I., Yaesh, I. and Stoica, A.
Position/Velocity Aided Leveling Loop: Continuous-Discrete Time State Multiplicative-Noise Filter Case.
DOI: 10.5220/0012208200003543
In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2023) - Volume 1, pages 485-488
ISBN: 978-989-758-670-5; ISSN: 2184-2809
Copyright © 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
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