  Online selection of optimal waveforms for target tracking with active sensors
has long been a problem of interest. Many conventional solutions utilize an
estimation-theoretic interpretation, in which a waveform-specific
Cram\'{e}r-Rao lower bound on measurement error is used to select the optimal
waveform for each tracking step. However, this approach is only valid in the
high SNR regime, and requires a rather restrictive set of assumptions regarding
the target motion and measurement models. Further, due to computational
concerns, many traditional approaches are limited to near-term, or myopic,
optimization, even though radar scenes exhibit strong temporal correlation.
More recently, reinforcement learning has been proposed for waveform selection,
in which the problem is framed as a Markov decision process (MDP), allowing for
long-term planning. However, a major limitation of reinforcement learning is
that the memory length of the underlying Markov process is often unknown for
realistic target and channel dynamics, and a more general framework is
desirable. This work develops a universal sequential waveform selection scheme
which asymptotically achieves Bellman optimality in any radar scene which can
be modeled as a $U^{\text{th}}$ order Markov process for a finite, but unknown,
integer $U$. Our approach is based on well-established tools from the field of
universal source coding, where a stationary source is parsed into variable
length phrases in order to build a context-tree, which is used as a
probabalistic model for the scene's behavior. We show that an algorithm based
on a multi-alphabet version of the Context-Tree Weighting (CTW) method can be
used to optimally solve a broad class of waveform-agile tracking problems while
making minimal assumptions about the environment's behavior.
