This paper considers the problem of finding the directions of narrow-b
and signals using a time-varying array whose elements move during the
observation interval in an arbitrary but known way. We derive the cond
itional maximum likelihood (CML) estimator for the directions-of-arriv
als, and the corresponding Cramer-Rao bound (CRB). Using small-error a
nalysis we derive analytical expressions for the bias and variance of
the estimates. The CML is derived using a deterministic signal model.
Its performance for Gaussian signal is, therefore, suboptimal. However
, we demonstrate that for the case of two uncorrelated sources, and su
fficiently high signal-to-noise ratio, the accuracy of the CML is clos
e to the CRB derived for Gaussian signals. Thus, the closed-form expre
ssions for the performance of the CML are useful for evaluating the pe
rformance of time-varying arrays. For uncorrelated sources, these expr
essions are significantly simpler than the corresponding expressions f
or the Gaussian signal model, and provide more insight into the proble
m. Furthermore, these expressions provide a simple quality measure for
time-varying arrays which depends only on the time-varying geometry o
f the problem.