Bayesian Echo Detection Applied to IMAGE Radio Plasma Imager Data

To be presented at the 2000 Fall Meeting of the AGU.

M. L. Rilee
S. A. Boardsen
J. L. Green
B. W. Reinisch
S. F. Fung

Bayesian echo detection uses probability to model ones' uncertainty
about the characteristics of an echo signal within a given context.  A
likelihood function encodes the understanding or knowledge we wish to
bring to the analysis and is a probability density defined on
observations, models, and defining parameters. By likelihood we mean
the probability that a specific observation obtains for a specific
context; these become densities when the observations and context can
take on continuous values.  The observations hopefully contain
evidence of echoes, while the models and their parameters define the
context of the questions we ask of the observations.

We have constructed a likelihood function for a simple echo model with
additive noise for the Radio Plasma Imager (RPI) on IMAGE.  RPI is a
low power radar that is currently obtaining remote sensing data about
the density distribution of magnetospheric plasmas.  RPI's chief
product is the plasmagram which shows received signal strength as a
function of echo delay (range) and radio frequency of the radar
pulses.  Strong radar echoes from important magnetospheric structures
such as the magnetopause and the plasmaspause should show up as traces
or ridges on the plasmagrams.  However, various natural and artificial
radio emissions will interfere and obscure echoes in the RPI data.

Our simple echo models attempt to recreate aspects of the echo traces,
ridges, and noise, especially correlations in received echo strength
that should occur across a number of sounding frequencies.  We use the
statistical properties of the noise observed by RPI as the basis of
our likelihood function.  This analysis combines information obtained
at a number of pulse frequencies so that echoes with low
signal-to-noise ratios may be detected.  Furthermore, by restricting
our likelihood model and parameter domain, we are able to construct
readily interpretable plasmagram-like maps that summarize the odds
that an echo has been observed by RPI.  This restriction amounts to
quantitatively biasing our analysis towards features that "look
right".  However this bias is admitted in a controlled manner, and
therefore can be tested so that the significance of the conclusions
can be assessed.

In practice, this analysis resembles the mapping of model residuals
that occurs in least-squares model fitting, to which our approach
reduces in the limit of normal probability densities.