Modeling and Estimation for Doppler-shifted Random Processes

Signals emitted by moving sources and received at a xed sensor are subject to the Doppler eeect. For narrow-band signals the Doppler eeect amounts simply to a frequency shift. The eeect is more complex when the signals are wide-band. In this paper, a mathematical model for Doppler-shifted wide-band signal is introduced. The model assumes that the wide-band moving source can be represented by a stationary rational (ARMA) process. Several applications of the model are then described. First, a method for the generation of synthetic wide-band Doppler shifted signals is proposed. Next, a computationally eecient algorithm for the estimation of the motion of a stationary wide-band source with unknown spectrum from the recording at a single xed sensor is derived. The performance of the algorithms is illustrated on synthetic and real acoustic data. Finally, an algorithm for the estimation of the power spectrum of signals subject to unknown Doppler shifts is proposed and its eeectiveness is demonstrated on an example. Authorization to publish this abstract separately is granted.