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Online selection of optimal waveforms for target tracking with active sensorshas long been a problem of interest. Many conventional solutions utilize anestimation-theoretic interpretation, in which a waveform-specificCram\'{e}r-Rao lower bound on measurement error is used to select the optimalwaveform for each tracking step. However, this approach is only valid in thehigh SNR regime, and requires a rather restrictive set of assumptions regardingthe target motion and measurement models. Further, due to computationalconcerns, 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 forlong-term planning. However, a major limitation of reinforcement learning isthat the memory length of the underlying Markov process is often unknown forrealistic target and channel dynamics, and a more general framework isdesirable. This work develops a universal sequential waveform selection schemewhich asymptotically achieves Bellman optimality in any radar scene which canbe 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 ofuniversal source coding, where a stationary source is parsed into variablelength phrases in order to build a context-tree, which is used as aprobabalistic model for the scene's behavior. We show that an algorithm basedon a multi-alphabet version of the Context-Tree Weighting (CTW) method can beused to optimally solve a broad class of waveform-agile tracking problems whilemaking minimal assumptions about the environment's behavior.

Universal Learning Waveform Selection Strategies for Adaptive Target Tracking