Bounds on Time Delay and Doppler Estimation with Partially Coherent Signals
Richard J. Kozick, Brian M. Sadler · 2002
Abstract — Fundamental performance limits for passive time delay and Doppler estimation have been studied extensively for several decades. The fundamental limits are usually parameterized in terms of the signal-to-noise ratio (SNR) at each sensor, the spectral support of the signals (fractional bandwidth), and the time-bandwidth product of the observations. In some applications, loss of coherence between the signals measured at a pair of sensors significantly affects the time delay and Doppler estimation accuracy. For example, in aeroacoustics (low frequency sounds < 300 Hz propagating through air) and ultrasonics (sounds in the MHz range propagating through living tissue), the signals received at spatially-separated sensors are not perfectly coherent due to random motion of particles in the propagation medium. In order to quantify the effect of partial signal coherence on time delay and Doppler estimation, we present Cramér-Rao and Ziv-Zakai bounds that are explicitly parameterized by the signal coherence, along with the traditional parameters of SNR, fractional bandwidth, and time-bandwidth product. The results are applied to the processing data from an “array of arrays ” that consists of several small-aperture sensor arrays distributed over a large two-dimensional area. I.