Aerospace and Electronic Systems Magazine August 2017 - 38

Feature Article:

DOI. No. 10.1109/MAES.2017.160174

Control Theoretic Approach to Gyro-Free Inertial
Navigation Systems
Uriel Nusbaum, Israel Institute of Technology, Haifa, Israel
Itzik Klein, Rafael Advanced Defense Systems Ltd., Haifa, Israel

INTRODUCTION
In general, an inertial navigation system (INS) consists of a navigation computer and an inertial measurement unit (IMU). Given
initial conditions and IMU measurements, the INS provides the
position, velocity, and orientation of its carrying platform. The inertial sensors, namely, the accelerometers and gyroscopes (gyros),
are part of the IMU. A classical IMU architecture has three accelerometers (to measure specific force) and three gyros (to measure
angular velocity) arranged in orthogonal triads.
Experimental INS were first developed in the 1920s; however,
the sensor and computation technology of the time was not good
enough for practical applications. The first application of inertial
navigation technology was in the German V2 rockets during World
War II [3], and in February 1953, Draper's team demonstrated an
INS flight on a Boeing B-29 in which the INS system weighted
1,225 kg [26]. This opened the era of the INS for military usages until the 1960s, when INS was adopted by civil aviation for
long-range navigation. Strapdown INS technology was developed
during the 1970s. Later, microelectromechanical system (MEMS)
revolution [14] enabled a dramatic reduction in INS size, weight,
and power consumption, allowing the usage of INS technology in
new applications and instruments such as wildlife and livestock
tracking, smartphones, and medical instruments [22]. Most effort
during those years was made in improving sensor performance and
reducing its size. Yet the architecture of three orthogonal accelerometers and three orthogonal gyros survived from the beginning
of the modern INS era and is still the only architecture available.
Several years after the classical INS architecture gained its
popularity, several authors proposed a new IMU architecture based
only on accelerometers, known as all-accelerometer INS or gyrofree (GF) INS [18], [24]. In GF-INS architecture, six or more
distributed accelerometers are used to form a system capable of
obtaining three accelerations and three angular accelerations and
Authors' current addresses: U. Nusbaum, Autonomous
Systems and Robotics Program, Technion-Israel Institute of
Technology, Sderot David Rose, Haifa 32000, Israel, E-mail:
(urieln@campus.technion.ac.il). I. Klein, Rafael Advanced
Defense Systems Ltd., Haifa 31021, Israel.
Manuscript received August 14, 2016, revised January 4, 2017,
and ready for publication February 19, 2017.
Review handled by A. Dempster.
0885/8985/17/$26.00 © 2017 IEEE
38

thereby capable of functioning as a classical IMU. To that end,
all accelerometers measurements are used to calculate the specific
force and angular acceleration vectors at the origin of some coordinate frame. The angular acceleration vector is integrated to obtain
the angular velocity vector. Thus, the GF-IMU can provide the specific force and angular velocity vectors as if a classical IMU were
located at the same point. However, when the GF-INS concept was
first suggested, the appropriate technology was not available and
the idea was abandon except for several publications. Only in the
mid-1990s, with the advent in MEMS accelerometers technology,
was research on GF-INS restarted.
The motivation and contributions behind this article are threefold. First, we present a state-of-the-art literature review of GFINS and argue about its architecture relative to the classical INS
architecture. We then provide a summary of recent GF theory, a
unified approach regardless of the number of accelerometers in
the configuration. Finally, inspired by the work of Bar-Itzhack
and Berman [2], we offer a control theoretic point of view for the
GF-INS architecture analysis using concepts from systems theory
such as stability and observability during stationary fine alignment
(FA).

GF-INS LITERATURE REVIEW AND DISCUSSION
As mentioned in the introduction, research on GF-INS was restarted only in the mid-1990s. From that point, most literature on
GF-INS was focused on two aspects of GF-INS as a standalone
system:
1. The number of accelerometers to use in the GF configurations
2. How to determine the accelerometers geometry
Less attention was given to deriving appropriate state-space
models, analytical error assessment, and fusion of GF-INS with
additional sensors or data.
The question of how many accelerometers to use in a GF-IMU
configuration is still an open issue in the literature, because the
number of accelerometers can imply how to determine the type
of output from the GF-IMU. Will the GF-IMU output includes
both the angular velocity vector (as in a classical IMU) and the
angular acceleration vector (which requires at least nine accelerometers and additional algorithms to determine the angular velocity sign)? Or will the output include only the angular acceleration

IEEE A&E SYSTEMS MAGAZINE

AUGUST 2017

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