Inverse Cognitive Radar - A Revealed Preferences Approach.
Vikram Krishnamurthy, Robin J. Evans, William Moran · arXiv (Cornell University) · 2019
We consider an adversarial signal processing problem involving us versus an enemy radar equipped with a Bayesian tracker. By observing the emissions of the enemy radar, how can we detect if the radar is cognitive (constrained utility maximizer)? Given knowledge of our state and the observed sequence of actions taken by the enemy radar, we consider three problems: (i) Are the enemy radar actions (waveform choice, beam scheduling) consistent with constrained utility maximization? If so how can we estimate the cognitive radar utility function that is consistent with its actions. We formulate and solve the problem in terms of the spectra (eigenvalues) of the state and observation noise covariance matrices, and the algebraic Riccati equation. (ii) How to construct a statistical test for detecting a cognitive radar (constrained utility maximization) when we observe the radar actions in noise or the radar observes our probe signal in noise? We propose a statistical detector with a tight Type 2 error bound. (iii) How can we optimally probe (interrogate) the enemy radar by choosing our state to minimize the Type 2 error of detecting if the radar is deploying an economic rational strategy, subject to a constraint on the Type 1 detection error? We present a stochastic optimization algorithm to optimize our probe signal. Our state can be viewed as a probe signal which causes the enemy's radar to act; so choosing the optimal state sequence is an input design problem. The main analysis framework used in this paper is that of revealed preferences from microeconomics.