  We present novel lower bounds on the localization error using a network of
satellites randomly deployed on a sphere around Earth. Our new analysis
approach characterizes the localization performance by its asymptotic behavior
as the number of satellites gets large while assuming a dense network. Using
the law of large numbers, we derive closed-form expressions for the asymptotic
Cramer Rao bound (CRB) from which we draw valuable insights. The resulting
expressions depend solely on the network statistics and are not a function of a
particular network configuration. We consider two types of estimators. The
first uses the exact statistical model, and hence employs both timing and
amplitude information. The second estimator ignores the amplitudes and hence
uses only time difference of arrival (TDOA) information. The asymptotic CRB
indicates that for practical system setup, a TDOA estimator approaches the
performance of the ideal estimator. For both estimators, the localization
accuracy improves as satellites get closer to Earth. The latter finding is
essential in light of the proliferation of low-Earth-orbit (LEO) satellites and
motivates a further study of localization-performance in such networks.
Besides, we show that the vertical localization accuracy is lower than the
horizontal accuracy and is also more sensitive to the receiver field-of-view.
