Universal Learning Waveform Selection Strategies for Adaptive Target Tracking

• URL: http://arxiv.org/abs/2202.05294v1
• Date: Thu, 10 Feb 2022 19:21:03 GMT
• Title: Universal Learning Waveform Selection Strategies for Adaptive Target Tracking
• Authors: Charles E. Thornton, R. Michael Buehrer, Harpreet S. Dhillon, Anthony F. Martone
• Abstract summary: This work develops a sequential waveform selection scheme which achieves Bellman optimality in any radar scene. 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.
• Score: 42.4297040396286
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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