Aerospace and Electronic Systems Magazine October 2017 - 29

Fertig, Baden, and Guerci
is represented by a brown rectangle, the true position of a vehicle
is denoted with a black diamond, and the drivable region is indicated with a white background. The airborne radar is located to
the southeast. The potential multipath returns associated with a
single detection are shown by the solid green, blue, and red lines,
which correspond to LOS, single-bounce, and double-bounce multipath returns. The black diamond falls on a red line, because the
detection chosen for this example corresponds to a double-bounce
return. Although an initial version of the MER processing architecture considered the immediate application of the ray tracer to the
inverse problem, more robust tracking results were obtained from
the approach in Figure 5, where various computations (described
below) are implemented in measurement space before conversion
to Cartesian space.
The proposed architecture necessitates that a ray tracer also
be used to solve the forward problem, which is the computation
of measurement-space quantities representing a set of multipath
modes that are expected to result from a given radar, vehicle, or
urban geometry. Typically, the solution to this problem yields a
small set (rarely more than three) of multipath modes. An illustration of the output of the ray tracer for the forward problem is provided in Figure 6b, where regions predicted with high probability
to support a double-bounce return are color-coded yellow. Regions
with marginal probability of generating this return are color-coded
green, regions that are drivable but not expected to support doublebounce returns are color-coded light blue, and regions that are not
drivable are color-coded dark blue.
The multiplicity of the solution to both forward and inverse
problems is a function of the number of permissible multipath
modes that are assumed. In general, this is determined by whether the multipath modes of interest will yield local maxima (after
range, Doppler, and spatial processing) with a sufficient signal-tonoise ratio (SNR) for reliable detection. This in turn is dependent
on radar parameters such as transmit power and scenario parameters such as standoff range. For the geometry and radar selected in
the blind data test, it was estimated that paths involving more than
two reflections with buildings would generally not be detectable.

Transition between Measurement and Cartesian Space
Figure 6.

Sample ray tracer output obtained during MER Phase II. (a) Example
of an inverse solution. (b) Example of a forward solution for doublebounce returns in Area 1.

the forward problem of mapping predicted vehicle position and
velocity into measurement-space quantities.

Ray Tracing for Multipath Prediction
The inverse problem is the computation of state vectors representing a feasible set of vehicle positions and velocities that are consistent with the given detection and city model. Due to uncertainty
with respect to which road a vehicle is traversing and which buildings contribute multipath, it is not uncommon for nine or more
possible vehicle locations to result from a single detection. An illustration of the output of the ray tracer for the inverse problem
is provided in the overhead view in Figure 6a, where a building
OCTOBER 2017

At the output of the block labeled radar signal processing, detections are compared to extrapolations of existing tracks, which can
consist of tracks still in measurement space or tracks that have
been promoted to Cartesian space. In certain situations discussed
below, initiation directly into Cartesian space with a simple form
of the ray tracer is conducted. Detections still unassociated are
considered for use in the initiation of new measurement-space
tracks. Depending on the radar, vehicle, or building geometry,
the measurement-space tracks may be immediately and uniquely
mapped to Cartesian space via the ray tracer. When a unique mapping cannot be accomplished, a geometric ambiguity is present and
the decision is delayed. In a similar fashion, Cartesian tracks may
be demoted to measurement-space tracks if a geometric ambiguity
is encountered. Additional algorithmic features, such as coasting of
measurement and Cartesian tracks, gating, initiation and association of measurement-space tracks, and feedback of track information to STAP training, are employed but not shown in Figure 5.

IEEE A&E SYSTEMS MAGAZINE

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