Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 69

IEEE AES Tutorials

GEOMETRY OF COMPLEX DATA

TUTORIAL X

K. JAMES SANGSTON
Georgia Tech Research Institute
Atlanta, GA USA

OVERVIEW OF RADAR WAVEFORM DIVERSITY

Geometric algebra has been called a "unified language for mathematics and physics." Sometimes known as Clifford algebra, it is
based on the notion of an invertible product of vectors that captures
the geometric relationship between two vectors, i.e., their relative
magnitudes and the angle between them. This seemingly simple
concept leads to a rich system of algebra and calculus that encompasses the diverse areas of complex numbers, quaternions, vectors,
tensors, spinors, and differential forms. This tutorial provides a
basic introduction to geometric algebra and presents formulations
of known electrical engineering and signal processing concepts to
illustrate some inherent advantages of geometric algebra for formulating and solving problems involving vectors. Being introductory, the goal of the tutorial is to introduce this emerging area that,
although old as a mathematics discipline, has only recently started
to garner significant attention in engineering communities. Geometric algebra should give another potentially powerful tool for
pursuing research in any area that uses vectors.

RECURSIVE BAYESIAN FILTERING IN CIRCULAR STATE
SPACES

Waveform Diversity (WD) is an exciting technology that has sparked
intense interest from the research community in recent years because
of advances in high-fidelity electronic components and high-performance computing. WD is expected to have a profound impact on
radar spectrum management, particularly in light of increasing competition for spectrum usage, as well as to facilitate enhanced radar
sensitivity and discrimination and perhaps even to enable new sensing modes. The definition of WD is clearly broad, but such is to be
expected for a topic that continues to evolve. The purpose of this
tutorial is to provide the reader with the context in which WD has
arisen, a sense of the tremendous breadth of the subject, and a sufficient starting point from which to explore WD further.

COHERENT RADAR DETECTION IN COMPOUND-GAUSSIAN
CLUTTER: CLAIRVOYANT DETECTORS

GERHARD KURZ
Karlsruhe Institute of Technology
Karlsruhe, Germany
IGOR GILITSCHENSKI
Swiss Federal Institute of Technology
Zurich, Switzerland
UWE D. HANEBECK
Karlsruhe Institute of Technology
Karlsruhe, Germany

K. JAMES SANGSTON
Sensors and Electromagnetic Applications Laboratory
Georgia Tech Research Institute
Smyrna, GA, USA
ALFONSO FARINA
Independent Consultant
Rome, Italy

To facilitate recursive state estimation in the circular domain
based on circular statistics, we introduce a general framework
for estimation of a circular state based on different circular
distributions. Specifically, we consider the wrapped normal
(WN) distribution and the von Mises distribution. We propose
an estimation method for circular systems with nonlinear system and measurement functions. This is achieved by relying
on efficient deterministic sampling techniques. Furthermore,
we show how the calculations can be simplified in a variety of
important special cases, such as systems with additive noise,
as well as identity system or measurement functions, which
are illustrated using an example from aeronautics. We introduce several novel key components, particularly a distribution-free prediction algorithm, a new and superior formula
for the multiplication of WN densities, and the ability to deal
with nonadditive system noise. All proposed methods are thoroughly evaluated and compared with several state-of-the-art
approaches.

JULY 2017, Part II of II

SHANNON D. BLUNT
University of Kansa
Lawrence, KS, USA
ERIC L. MOKOLE
Private Consultant
Burke, VA, USA

This paper provides a historical and tutorial overview of coherent radar target detection in compound-Gaussian clutter and offers
some new perspectives and avenues of research in this challenging
area. It begins with a brief introduction that motivates the need
to develop statistical models of non-Gaussian clutter and then reviews some of the physical ideas that led to modeling multivariate
radar clutter statistics by the compound-Gaussian model. With this
starting point, the paper then reviews a series of ideas that have
been developed to describe clairvoyant detectors in such clutter.
The term "clairvoyant" refers to the assumption that the properties
of the clutter are assumed to be known. In a practical scenario, this
assumption does not hold and adaptive techniques are needed to
estimate clutter properties and implement the detector. Such techniques are guided however by the appropriate clairvoyant detector
structures and hence it is proper to start by studying these detectors. As part of this review, the paper offers new ways of looking
at this problem that suggest new research topics. This review is
limited to the problem of clairvoyant detection in which the relevant properties of the clutter are assumed to be known. Adaptive
detection in compound-Gaussian clutter will be the topic of a subsequent tutorial that the authors are preparing.

IEEE A&E SYSTEMS MAGAZINE

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine July 2017 Tutorial XI