Signal Interpretation of Multifunction Radars: Modeling and Statistical Signal Processing With Stochastic Context Free Grammar

Multifunction radars (MFRs) are sophisticated sensors with complex dynamical modes that are widely used in surveillance and tracking. Because of their agility, a new solution to the interpretation of radar signal is critical to aircraft survivability and successful mission completion. The MFRs' three main characteristics that make their signal interpretation challenging are: i) MFRs' behavior is mission dependent, that is, selection of different radar tasks in similar tactic environment given different policies of operation; ii) MFRs' control mechanism is hierarchical and their top level commands often require symbolic representation; and iii) MFRs are event driven and difference and differential equations are often not adequate. Our approach to overcome these challenges is to employ knowledge-based statistical signal processing with syntactic domain knowledge representation: a signal-to-symbol transformer maps raw radar pulses into abstract symbols, and a symbolic inference engine interprets the syntactic structure of the symbols and estimates the state of the MFR. In particular, we model MFRs as systems that "speak" a language that can be characterized by a Markov modulated stochastic context free grammar (SCFG). We demonstrate that SCFG, modulated by a Markov chain, serves as an adequate knowledge representation of MFRs' dynamics. We then deal with the statistical signal interpretation, the threat evaluation, of the MFR signal. Two statistical estimation algorithms for MFR signal are derived - a maximum likelihood sequence estimator to estimate the system state, and a maximum likelihood parameter estimator to infer the system parameter values. Based on the interpreted radar signal, the interaction dynamics between the MFR and the target is studied and the control of the aircraft's maneuvering models is implemented.