  To ensure reliable and effective mobility management for aerial user
equipment (UE), estimating the speed of cellular-connected unmanned aerial
vehicles (UAVs) carries critical importance since this can help to improve the
quality of service of the cellular network. The 3GPP LTE standard uses the
number of handovers made by a UE during a predefined time period to estimate
the speed and the mobility state efficiently. In this paper, we introduce an
approximation to the probability mass function of handover count (HOC) as a
function of a cellular-connected UAV's height and velocity, HOC measurement
time window, and different ground base station (GBS) densities. Afterward, we
derive the Cramer-Rao lower bound (CRLB) for the speed estimate of a UAV, and
also provide a simple biased estimator for the UAV's speed which depends on the
GBS density and HOC measurement period. Interestingly, for a low
time-to-trigger (TTT) parameter, the biased estimator turns into a minimum
variance unbiased estimator (MVUE). By exploiting this speed estimator, we
study the problem of detecting the mobility state of a UAV as low, medium, or
high mobility as per the LTE specifications. Using CRLBs and our proposed MVUE,
we characterize the accuracy improvement in speed estimation and mobility state
detection as the GBS density and the HOC measurement window increase. Our
analysis also shows that the accuracy of the proposed estimator does not vary
significantly with respect to the TTT parameter.
