Journal
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS
Volume 57, Issue 4, Pages 1996-2005Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAES.2021.3083419
Keywords
Grammar; Target tracking; Syntactics; Markov processes; Hidden Markov models; Context modeling; Radar tracking; Context-free grammars (CFGs); Markov random fields (MRFs); metalevel target tracking; stochastic grammars (SGs); syntactic processes
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This article discusses the problem of defining statistical models for languages derived from context-free grammars, introduces the concept of stochastic syntactic processes, and demonstrates embedding an SSP into a Markov random field for advanced machine learning algorithms. Extensions to context-sensitive grammars are also discussed.
This article addresses the problem of suitably defining statistical models of languages derived from context-free grammars (CFGs), where the observed strings may be corrupted by noise or other mechanisms. This article uses the concept of a stochastic syntactic process (SSP), which we have introduced in previous work. An SSP is a stochastic process taking values in the set of all parse trees of a CFG. Inference problems such as estimating a parse tree for noisy processes are of obvious significance, particularly in the motivating example of metalevel target tracking. This article demonstrates that by careful application of the theory of probability, an SSP can be embedded into a Markov random field (MRF), thus opening up the possibility of the application of advanced machine learning algorithms based on graphical models to inference problems involving sophisticated target behavior at the meta level. This article provides a simple example of how a simple CFG can be embedded in an MRF. Extensions to context-sensitive grammars are discussed.
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