Bayesian Inverse Learning and Online Changepoint Detection of Cognitive Radar Strategies

Abstract

In this article, we introduce an online electronic countermeasure framework for learning the strategies and detecting changes in the strategy of an adversarial cognitive radar (CR) in an inverse learning framework. We model the CR as a rational, constrained utility-maximizing agent and formulate the problem in the revealed preference setting. The utility of CR is modeled as a random direction vector, that follows the von Mises-Fisher distribution with unknown parameters, and we use Bayesian machine learning with revealed preference characterization to learn the radar’s utility, and extend it to the detection of changes in strategy in an online setting. The main contributions of the article are: 1) the development of Bayesian machine learning algorithms—HBOIL and HBOCPD, for inverse learning and detection of changes in strategies of an adversarial CR, respectively; 2) HBOIL and HBOCPD use a Hamiltonian Monte Carlo (HMC) sampling algorithm that exploits the Afriat’s theorem in revealed preference as well as a subsetting structure that arises in the posterior, and hence is devoid of the computational burden of solving optimization problems in existing techniques; 3) numerical results demonstrate the ability to characterize and determine the changes in the beam allocation strategy of a CR in noise-free and noisy adversarial settings. HBOIL and HBOCPD are robust to observation noise compared to the existing approaches; 4) HBOIL outperforms classical machine learning approaches in predicting optimal radar responses; and 5) HBOCPD performs, on an average, five times faster compared to the classical offline generalized likelihood ratio (GLR) approach, while using less restrictive assumptions.