Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 67

IEEE AES Tutorials
as data with nonsensor context information. The feedback from
data processing to the data acquisition process is illustrated by a
sensor management example.

PARTICLE FILTER THEORY AND PRACTICE WITH
POSITIONING APPLICATIONS

TUTORIAL VII

FREDRIK GUSTAFSSON, Senior Member, IEEE
Linköping University
Sweden
The particle filter (PF) was introduced in 1993 as a numerical approximation to the nonlinear Bayesian filtering problem, and there
is today a rather mature theory as well as a number of successful
applications described in literature. This tutorial serves two purposes: to survey the part of the theory that is most important for
applications and to survey a number of illustrative positioning applications from which conclusions relevant for the theory can be
drawn.
The theory part first surveys the nonlinear filtering problem
and then describes the general PF algorithm in relation to classical
solutions based on the extended Kalman filter (EKF) and the point
mass filter (PMF). Tuning options, design alternatives, and user
guidelines are described, and potential computational bottlenecks
are identified and remedies suggested. Finally, the marginalized (or
Rao-Blackwellized) PF is overviewed as a general framework for
applying the PF to complex systems.
The application part is more or less a stand-alone tutorial without equations that does not require any background knowledge in
statistics or nonlinear filtering. It describes a number of related
positioning applications where geographical information systems
provide a nonlinear measurement and where it should be obvious
that classical approaches based on Kalman filters (KFs) would
have poor performance. All applications are based on real data and
several of them come from real-time implementations. This part
also provides complete code examples.

BASIC TRACKING USING NONLINEAR 3D MONOSTATIC AND
BISTATIC MEASUREMENTS
DAVID CROUSE
Naval Research Laboratory
Washington, DC USA
Monostatic and bistatic position and Doppler measurements
used in radar and sonar systems are nonlinear transformations
of a Cartesian state. These nonlinearities pose a challenge for
many target tracking algorithms, causing the so-called contact
lens problem, which describes the nonlinear appearance of the
measurement probability density function in Cartesian coordinates. This tutorial considers methods for measurement filtering
(tracking without considering data association) using a singleGaussian approximation when monostatic and bistatic position and Doppler measurements are available. The connection
between the cubature Kalman filter and numerous other filtering algorithms is shown, and the accuracy and consistency of
different algorithms are compared through simulation. An effort
is made to express the geometric relationships associated with
multistatic tracking in a simple vectorial manner. This tutorial
focuses on basic tracking, and the companion tutorials "Tracking Using 3D Monostatic and Bistatic Measurements in Refractive Environments" and "Basic Tracking Using Nonlinear
Continuous-Time Dynamic Models" extend the results to more
sophisticated physical models.

BASIC TRACKING USING NONLINEAR 3D MONOSTATIC AND
BISTATIC MEASUREMENTS IN REFRACTIVE ENVIRONMENTS

TUTORIAL VI
REVIEW OF RANGE-BASED POSITIONING ALGORITHMS
JUNLIN YAN
Intel Mobile Communications GmbH
CHRISTIAN C. J. M. TIBERIUS & GERARD J. M. JANSSEN
Delft University of Technology
PETER J. G. TEUNISSEN
Curtin University of Technology
GIOVANNI BELLUSCI
Xsens
This tutorial reviews algorithms which turn measured ranges into
position solutions. From their basic mathematical principles, we
relate and compare relevant aspects of these algorithms. Special
attention is given to the direct (non-iterative) algorithms, which are
frequently applied in indoor positioning. Most of them are shown
to be essentially the same, as they can be related through applying

JULY 2017, Part II of II

different weighting schemes. This tutorial is intended as a useful
guide to help researchers and system designers evaluate and select
appropriate range-based positioning algorithms for their applications at hand.

DAVID CROUSE
Naval Research Laboratory
Washington, DC USA
The deleterious effects of atmospheric refraction are often
overlooked in work on target tracking. This tutorial shows how
the effects of refraction can be directly incorporated into tracking algorithms, improving the performance of tracking algorithms that make use of monostatic and bistatic measurements.
Additionally, a technique for converting measurements from
the radar's refraction-corrupted local coordinate system (typically bistatic r - u - v coordinates) into Cartesian coordinates
is presented. The refraction-compensation algorithms can be
used with arbitrary refraction models for which ray tracing
techniques for solving boundary value problems and initial
value problems are available, though extensions to more complicated propagation scenarios are possible. The algorithms

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