IEEE Aerospace and Electronic Systems Magazine - December 2020 - 16

Feature Article:

DOI. No. 10.1109/MAES.2020.3002001

State Estimation Methods in Navigation:
Overview and Application
Jindrich Dunık, University of West Bohemia
Sanat K. Biswas, Indian Institute of Technology Delhi
Andrew G. Dempster, UNSW Sydney
€ nchen
€t der Bundeswehr Mu
Thomas Pany, Universita
Pau Closas, Northeastern University

INTRODUCTION TO BAYESIAN STATE ESTIMATION
The state of a system is a variable, which fully characterizes the status of the system at a given time. Knowledge
of the state is, thus, essential for control or prediction of
the system's future behavior. Unfortunately, the state of
the system is typically not directly measurable, i.e., it is
not known. Instead, the state is indirectly observed via
measurement only which is somehow related to the state.
The measurements are, moreover, affected by the noise.
State estimation of stochastic dynamic systems deals
with the estimation of the time-varying state from noisy
measurements. State estimation has been a subject of considerable research interest for more than five decades.1
Although its development was motivated by the needs of
tracking and navigation applications, state estimation
these days plays an indispensable role also in many other
technical and nontechnical fields such as automatic

State estimation is a part of a general estimation theory of which
development can be dated back to the beginning of 19th century.
The development started with a design of the least-squares method
by C. F. Gauss and A.-M. Legendre and it was motivated by
modeling planetary motion [1].

Authors' current addresses: J. Dunık, University of
West Bohemia, Pilsen 30100, Czech Republic (e-mail:
dunikj@kky.zcu.cz). S. K. Biswas, Indian Institute of
Technology Delhi, Delhi 110016, India. A. G. Dempster, UNSW Sydney, Sydney, NSW 2052, Australia. T.
Pany, Universit€at der Bundeswehr M€
unchen, 85579
Neubiberg, Germany. P. Closas, Northeastern University, Boston, MA 02115, USA.
Manuscript received December 2, 2019, revised April 15,
2020, May 20, 2020, and ready for publication June 10,
2020.
Review handled by Peter Willett.
0885-8985/20/$26.00 ß 2020 IEEE
16

control, speech and image processing, biology, economy,
weather forecasting, etc., [1], [2].
The goal of this article is to introduce selected methods of the state estimation, which are used in navigation
applications. In particular, the article is focused on navigation applications, which belong into the area of expertise
of the IEEE AESS Navigation Systems Panel2 (NSP), of
which the authors are members.
The article is organized as follows. In the rest of this
section, state-space modeling and Bayesian state estimation are briefly reviewed. In the sections " State Estimation
Methods: An Overview " and " State Estimation Methods:
Additional Topics, " an overview of state estimation methods, related terminology, and algorithms is given with
stress on topics relevant to NSP technologies. Selected
state-of-the-art applications falling within the scope of the
NSP are then described and discussed with emphasis on
sensor error sources in " Estimation in Navigation Systems. " Finally, concluding remarks are given.

SYSTEM STATE-SPACE MODEL
State estimation methods provide the state estimate on the
basis of the available measurements and a known state-space
model. In this article, the following discrete-time nonlinear
stochastic dynamic state-space model with additive noises
xkþ1 ¼ fk ðxk ; uk Þ þ wk

(1)

zk ¼ hk ðxk Þ þ vk

(2)

is considered, where the vector xk 2 Rnx represents the
unknown state of the system at time instant k, the vectors
uk 2 Rnu and zk 2 Rnz represent the known input and
measurement at time instant k, the functions fk : Rnx Â
Rnu ! Rnx and hk : Rnx ! Rnz are known state and
2

The NSP webpage is http://ieee-aess.org/tech-ops/navigation-systems-panel

IEEE A&E SYSTEMS MAGAZINE

DECEMBER 2020

http://www.ieee-aess.org/tech-ops/navigation-systems-panel http://www.ieee-aess.org/tech-ops/navigation-systems-panel

IEEE Aerospace and Electronic Systems Magazine - December 2020

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