Syntactic Modeling and Signal Processing of Multifunction Radars: A Stochastic Context-Free Grammar Approach

Multifunction radars (MFRs) are sophisticated sensors with complex dynamical modes that are widely used in surveillance and tracking. This paper demonstrates that stochastic context-free grammars (SCFGs) are adequate models for capturing the essential features of the MFR dynamics. Specifically, MFRs are modeled as systems that “speak” a language that is characterized by an SCFG. The paper shows that such a grammar is modulated by a Markov chain representing radar's policy of operation. The paper also demonstrates how some well-known statistical signal processing techniques can be applied to MFR signal processing using these stochstic syntactic models. We derive two statistical estimation approaches for MFR signal processing—a maximum likelihood sequence estimator to estimate radar's policies of operation, and a maximum likelihood parameter estimator to infer the radar parameter values. Two layers of signal processing are introduced in this paper. The first layer is concerned with the estimation of MFR's policies of operation. It involves signal processing in the CFG domain. The second layer is concerned with identification of tasks the radar is engaged in. It involves signal processing in the finite-state domain. Both of these signal processing techniques are important elements of a bigger radar signal processing problem that is often encountered in electronic warfare applications—the problem of the estimation of the level of threat that a radar poses to each individual target at any point in time.