A. Dogandzic et A. Nehorai, Cramer-Rao bounds for estimating range, velocity, and direction with an active array, IEEE SIGNAL, 49(6), 2001, pp. 1122-1137
We derive Cramer-Rao bound (CRB) expressions for the range (time delay), ve
locity (Doppler shift), and direction of a point target using an active rad
ar or sonar array, First, general CRB expressions are derived for a narrowb
and signal and array model and a space-time separable noise model that allo
ws both spatial and temporal correlation. We discuss the relationship betwe
en the CRB and ambiguity function for this model, Then, we specialize our C
RB results to the case of temporally white noise and the practically import
ant signal shape of a linear frequency modulated (chirp) pulse sequence. We
compute the CRB for a three-dimensional (3-D) array with isotropic sensors
in spatially white noise and show that it is a function of the array geome
try only through the "moments of inertia" of the array. The volume of the c
onfidence region for the target's location is proposed as a measure of accu
racy, For this measure, we show that the highest (and lowest) target locati
on accuracy is achieved if the target lies along one of the principal axes
of inertia of the array, Finally, we compare the location accuracies of sev
eral array geometries.