Efficient Velocity Estimation in Distributed RF Sensing

In this paper, we examine the problem of velocity estimation for a moving object using distributed measurements. The system employs a non-cooperative transmitter and multiple receivers to collect targets echoes. The problem is formulated by modelling the unknown transmitted waveform as a deterministic process. The exact maximum likelihood estimator (MLE) is developed which requires a multi-dimensional search procedure. To reduce the computational load, an efficient two-step estimator (TSE) is proposed. The TSE first finds the maximum likelihood estimates of pairwise differences of the Doppler frequencies observed by the receivers. Then, the target velocity can be estimated from the frequency differences in closed-form. We show that the maximum likelihood estimation of each frequency difference reduces to a cross-correlation process followed by peak finding, which can efficiently be implemented by the fast Fourier transform (FFT). As a result, the TSE is significantly more efficient than the MLE. Numerical results show the TSE achieves a similar estimation accuracy as that of the MLE except for very low signal-to-noise ratio (SNR) scenarios.