and then we develop an inference algorithm using
approximate inference techniques proposed recently
in the AI and machine-learning communities.
Existing Models and the
Problem of Aliasing
How can one reconstruct the true direction and
speed of migrating birds from the partial information
contained in radial velocity data? Our interpretation
in figure 3 relied on the overall pattern of the radial
velocity image combined with an implicit assumption that targets (in this case, birds) behaved in a reasonably consistent way, and thus had similar velocities, throughout the region covered by the sweep.
This is a basic assumption made by radar-based wind
profiling algorithms, and it will also be the founda-
tion for our algorithms.
Our starting point is the uniform velocity model
from the weather community (Doviak and Zrnic
1993), which assumes that target velocity varies
only with elevation, so it is constant within a given
elevation range. Suppose the true unknown velocity components in the x and y directions of the horizontal plane are u and v. 1 Then, for a fixed elevation angle ρ, it is a simple exercise in trigonometry
to determine the radial velocity at a given antenna
angle in the horizontal plane. Figure 5 illustrates the
The radial velocity μ(ϕ) predicted by this model is
−200 − 100 0 100 200 −200 − 100 0 100
−200 − 100 0 100 200
Figure 2. Illustration of Three-Dimensional Nature of a Radar Sweep.
(a) The beam rises with distance from the radar station, and thus traces out an approximately conical two-dimensional surface; (b) a
conventional plan view (top down image) of the same sweep. Dark blue lines in (a) and (b) illustrate the distance-height relationship: at 100 kilometers, the beam center height is approximately 1. 5 kilometers; density of migrating birds drops off substantially
after this. (Color version of figure presented in electronic version of AI Magazine).