Aerospace and Electronic Systems Magazine May 2017 - 26

The Tracker Component Library
the most implemented functions. For example, GaussianD.PDFSGradHessVechS will
find the gradient of a multivariate Gaussian
distribution, with respect to the elements of a
lower-triangular Cholesky decomposition of
the covariance matrix.
Some functions in the Mathematical
Functions folder are redundant with respect to
functions built into MATLAB. However, they
are usually there because they are superior
to MATLAB's built-in functions or they are
useful if one wishes to overload operations
in MATLAB. For example, though MATLAB has the chol command for performing
a Cholesky decomposition, the library contains cholSemiDef, which will not fail if the
matrix given is positive semidefinite. Similarly, though matrix multiplication is built
into MATLAB, the matMultiply function is
present and is actually used in the Interval
class (in the Container Classes folder, not the
Mathematical Functions folder) to implement
Figure 5.
matrix multiplication in Interval arithmetic.
A plot of the deviation of the compass direction from true north using the World Magnetic Model,
Of interest when considering data associaas generated by using the Tracker Component Library.
tion is the Combinatorics subfolder. Therein,
one can find a great many functions for genMANY MATHEMATICAL ROUTINES
erating combinations, permutations, partitions, compositions, and
other combinatoric sequences. Functions related to combinatorics,
The Mathematical Functions folder contains the most functions of
such as perm for computing matrix permanents (useful for evaluatthe entire library. Many functions are essential in a great many
ing exact target measurement association probabilities), as well as
aspects of target tracking and span a wide variety of fields. For
functions for generating random compositions and partitions, are
example, the Polynomials subfolder includes methods relating to
also provided.
using various types of polynomials, such as Chebyshev, Laguerre,
Many additional functions are also present in the Mathematical
and Legendre polynomials, as well as functions for simultaneous
Functions folder of the library, and it is generally useful to look
multivariate polynomial integration, differentiation, and evaluathrough the folders to see what is available. From a tensor singulartion. The function taylorSeriesPoly might also be of particular invalue decomposition in HOSVD to a discrete cosine transform in
terest for some, as it produces the multivariate polynomial associdiscCosTrans, the functions are used in a wide variety of applicaated with an arbitrary-order multivariate Taylor series expansion,
tions.
when given all multivariate moments up to a particular order.
Much of the work in target tracking is stochastic. Thus, the
Statistics subfolder provides a number of basic routines that might
be of interest to those doing tracking. For those interested in data
OTHER PARTS OF THE LIBRARY
fusion, the functions covarianceIntersect, covarianceIntersectSCI,
The library contains a number of other routines that can be useand ellipsoidIntersect provide ways of fusing Gaussian measureful for those designing target-tracking algorithms. For example,
ments having unknown correlations.6
routines for decoding automatic identification system messages
Of particular interest might be the Statistics/Distributions foldbroadcast by ships to use as "truth" data when assessing algoer, as it contains many functions related to probability distriburithms, as well as algorithms related to determining navigation
tions. To reduce clutter and make the correct functions easier to
courses and handling terrain models. Much information can be
find, multiple functions are placed in classes. The classes do not
gained by browsing through the code.
contain any data; they are just used to group functions. One can
use the command ChiSquareD.mean to find the mean of a noncentral chi-squared distribution or similarly LaplaceD.mean to find
CONCLUSION
the mean of a multivariate Laplace distribution. Some distributions
Version 2.0 of the Tracker Component Library, available online at
contain more functions than others. The Gaussian distribution has
[28], provides free, open-source, copyleft-free code for MATLAB
6
that can be used by all who are interested in the design of targetTraditional covariance intersection is overly conservative in its
tracking algorithms. The library contains a great many routines
covariance estimates [2, Ch. 9.3.7]. Thus, the sampling covarifor filtering, data association, coordinate systems, and many other
ance intersections version [23] is also provided.
26

IEEE A&E SYSTEMS MAGAZINE

MAY 2017

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine May 2017