Comparison of INS Transfer Alignments
through Observability Analysis
Wei Gao Zhilan Xiong, Yanling Hao and Feng Sun
School of Electrical Engineering and Automation College of Automation
Harbin Institute of Technology Harbin Engineering University
Harbin, Heilongjiang Province 150001 China Harbin, Heilongjiang Province 150001 China
Abstract-Transfer alignment provides a rapid and effective
way how to align and calibrate an inertial navigation system (INS)
using the accurate information of other INS. However, in the
previous literatures, it is found that not every transfer alignment
algorithm is efficient in any environments. In this paper, the
conventional velocity matching algorithm and the rapid velocity
and attitude matching algorithm are compared in several typical
environments by observability analysis. It is explained in theory,
in this paper, why the velocity matching algorithm could estimate
azimuth misalignment under constant velocity maneuver, but the
velocity and attitude matching algorithm could not. At the same
time, this paper analyzes the influence of sway and acceleration
maneuvers to improve the observability of the two transfer
alignment algorithms. Since GPS can provide the velocity and
attitude information of vehicle, the accurate information used in
transfer alignment can be replaced by the corresponding
information from GPS in order to reduce the cost. However, the
errors of velocity and attitude provided by GPS are larger than
by accurate INS. So the estimation errors caused by external
sensor errors must be considered if using GPS as the external
sensor. At the end of this paper, the estimation errors of azimuth
angle of the two algorithms due to the unobservable states and
the errors of external sensor are deduced using the control-
theoretic approach and proved by simulation, respectively.
I. INTRODUCTION
Transfer alignment is an effective method to use the
accurate information of the external sensor to align the inertial
navigation system (INS). The external sensor is another more
accurate INS usually. However, the accurate INS is very
expensive. With the development of GPS technology, people
more and more prefer GPS to it in order to reduce the cost.
There are a lot of transfer alignment methods in the past. The
velocity matching alignment algorithm and the velocity and
attitude matching alignment algorithm are two of the most
typical methods. Early research workers [1]-[12] proved that
the INS alignment system was not completely observable on
stationary base or special maneuver. The observability of INS
alignment at rest is discussed in [1]-[5]. It was shown that
three states were unobservable. The error estimation was
discussed through observability analysis on stationary base in
[2]. The observability on stationary base can be enhanced by
introducing attitude changes, which is named multiposition
alignment. The observability of INS in-motion alignment was
analyzed in [6]-[9]. The research on the observability of in-
motion alignment was mainly concerned with the effect of the
translatory motions such as changed in acceleration. The
familiar path in in-motion alignment is s-turns or circular
maneuvers, which generate changing lateral accelerations.
Another considered maneuver is straight motion with axial
accelerations. The alignment performances with the above
maneuvers were compared by investigating the error
covariance history in [6]. The control-theoretic approach was
first introduced to the observability analysis of INS in-motion
alignment in [8], which regarded INS as a piece-wise constant
system. The observability of GPS/INS during maneuvers is
analyzed in [9] and [10]. Ref. [10] proved all the errors could
be observable by maneuvering. The velocity and attitude
matching alignment algorithm is one of the rapidest alignment
methods. Ref. [11] analyzed the observability of this method
using the control theory of Ref. [9] and proved that the
alignment process will be instantaneous observable by simple
and appropriate maneuver if using it.
In this paper, the velocity matching algorithm and the
velocity and attitude matching algorithm are compared
through the observability analysis with four different common
motions. They are level constant velocity motion, sway and
level constant velocity motion, axial acceleration motion and
lateral acceleration motion. Then, the estimation error of the
azimuth misalignment angle caused by the unobservable states
is deduced. Since GPS can provide the velocity and attitude
information of the vehicle, the accurate information used in
the transfer alignment can be replaced by the corresponding
information from GPS in order to reduce the cost. However,
the errors of the velocity and attitude provided by GPS are
larger than by accurate INS. So the estimation errors caused
by the external sensor errors must be considered if using GPS
as the external sensor. At the end of this paper, the influence
of the measurement bias from the external sensor on the
estimation of the azimuth misalignment is analyzed by
simulation.
The outline of the remainder of the paper is as follows.
Section II and section III introduce two typical INS transfer
alignment models and the control-theoretic approach of the
observability analysis, respectively. Then, section IV
compares the two alignment models through observability
analysis. The deduction of the estimation error of the azimuth
misalignment caused by the unobservable states and the
influence of external sensor error are put on section V. At last,
in section VI, the main results of the investigation are
presented.