“…1. The dynamics of the cognitive radar -target interaction and the inverse learning problem A detailed account of the general mathematical frameworks for cognitive radars are available in [9], [10], [11], [6], [12], [13], [14]. Figure 1, a generalized model adopted from [14], [5], depicts the interaction between cognitive radar and target which include: (i) the scene, which comprises the radar target and the environment, typically modelled using the parameterized transition probability, p αt (•), of the state of the target, x k , (ii) the sensor, that consists of a transceiver, which illuminates the environment and senses the reflections -modelled using a time varying sensor parameter, β t , and an observation likelihood, p β t (•), (iii) the processor, which transforms the observed data to the perception of the scene -typically modelled using a Bayesian tracker, that estimates the posterior belief π k , of target stats given past observation of the sensor, (iv) the controller, which decides the actions to be taken by the sensor and processor modules, taking into account the perception of the scene, produced by the processor, and the controller function is modelled as a constrained optimization problem.…”