Estimating time-varying DOA and Doppler shift in radar array processing

The authors consider the problem of retrieving information about space debris in low-Earth orbit by means of a radar system operating in a bi-static mode. More exactly, a pulse radar steers a beam in a prescribed region of space. When crossing the main lobe of the radar, a moving object will reflect energy towards a ground-based array of sensors. The signal is affected by Doppler shift, which is related to the radial speed. Additionally, its direction-of-arrival (DOA), related to the orthoradial speed, will be time-varying. Maximum likelihood (ML) solutions to the problem of estimating both the Doppler shift and the time-varying DOA are proposed. Since the exact ML solution is computationally intensive, a simpler alternative is presented that relies on the extended invariance principle. The new method is shown to be simple as it only entails Fourier transforms and linear computations. Its performance is illustrated via numerical simulations