This paper considers the problem of finding the directions of narrowba
nd signals using a time-varying array, whose elements move during the
observation interval in an arbitrary but known way. Assuming a Gaussia
n signal model, we derive the Cramer-Rao bound (CRB) and the maximum l
ikelihood estimator for the directions of arrival. The single source c
ase is studied in detail, Time-varying arrays are shown to be more rob
ust to ambiguity errors than static arrays of comparable dimensions.