Coherent long-time integration and Bayesian detection with Bernoulli track-before-detect

We consider the problem of detecting small and manoeuvring objects with staring array radars. Coherent processing and long-time integration are key to addressing the undesirably low signal-to-noise/background conditions in this scenario and are complicated by the object manoeuvres. We propose a Bayesian solution that builds upon a Bernoulli state space model equipped with the likelihood of the radar data cubes through the radar ambiguity function. Likelihood evaluation in this model corresponds to coherent long-time integration. The proposed processing scheme consists of Bernoulli filtering within expectation maximisation iterations that aims at approximately finding complex reflection coefficients. We demonstrate the efficacy of our approach in a simulation example.