Aerospace and Electronic Systems Magazine May 2017 - 25

Crouse

Figure 3.

The Tracker Component Library provides celestial ephemeris data,
as well as standard refraction models. Here, the rising Sun near Hilo,
Hawaii, on June 1, 2013 at 15:42 Coordinated Universal Time is shown.
The blue circle is the outline of the Sun in the absence of atmospheric
refraction; the red ellipse is the outline of the Sun with standard atmospheric refraction.

folder. For example, as shown in real weather-radar data in [13],
the Sun can cause interference in a particular direction, making
low detection probability targets harder to detect. The Sun might
also blind optical sensors. The solarBodyVec function in the Astronomical Code folder can tell a user the location of a celestial
body with regard to his location on or near the Earth, and with the
addAstroRefrac function in Atmospheric Models, one can find
the apparent refraction-corrupted location of the body. For example, the outline of the Sun with and without standard atmospheric
refraction at sunrise in Hilo, Hawaii, is shown in Figure 3. In
SampleCode/Celestial Models, the demoSunLocation function
reproduces the figure.
Additional astronomical functions tend to relate to the use
of star catalogs, orbital ephemerides, and rudimentary orbital
estimation. Other atmospheric code implements bistatic refraction-corrupted measurement conversions by using a simple
exponential refraction model. Unbiased measurement conversion with consistent covariance matrices, as described in [6],
[7], is provided by the functions Cart2RuvStdRefracCubature
and ruv2CartStdRefracCubature with sample code included in
the comments to those functions. The Atmospheric Code folder
also includes additional atmospheric models and routines for
converting types of humidity, computing the speed of sound in
air, given atmospheric constituents, and the conversion between
pressure altitude and orthometric altitude. A standard conversion between pressure altitude and orthometric altitude, as in the
function presTemp4OrthoAlt, is useful for tracking algorithms
that might make use of aircraft transponder returns that report
such information.
MAY 2017

Figure 4.

An exaggerated plot of the geoid by using the EGM2008 model, as
generated with the Tracker Component Library.

When simulating ballistic targets, one might want to make
use of Earth and Moon gravitation models. Thus, such models
can be loaded by using the functions in the Gravity folder. In
SampleCode/Celestial Models, the functions DemoGravCodeMoonModel, DemoGravCode, and DemoGravCodeNoCompile
demonstrate the use of the gravitational models. The gravitational models can also produce the height of the geoid above the
reference ellipsoid. The geoid is a theoretical surface of constant
gravitational potential that coincides with a definition of mean
sea level. The geoid as can be produced by using the function
DemoGravCode, as shown in Figure 4. Such geoid heights are
useful when using certain air pressure models. However, they are
also useful when using terrain models, as some terrain models
only report the elevation of the surface above the geoid, not the
reference ellipsoid, which makes conversion of points into Cartesian coordinates difficult.
Terrain models are useful in ballistic simulations for determining whether a missile will go over a mountain or crash into a mountain. Extremely high-fidelity terrain models tend to be extremely
large and are not included in the library. However, routines for
handling a few simple terrain models that are saved as spherical
harmonic coefficients are in the Terrain folder along with an algorithm for handling solid Earth tides.
The final set of physical functions provided by the library relates to magnetic fields. Numerous functions for handling standard
magnetic models are provided, with examples in the SampleCode/
Magnetic Models folder. For example, the deviation of magnetic
North from true North, as generated by using the demoMagneticCode function in the Sample Code/Magnetic Models folder is
shown in Figure 5. Numerous routines for conversions to magnetic
coordinate systems that parameterize ionospheric models are also
provided.

IEEE A&E SYSTEMS MAGAZINE

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