  We analyze the observability of motion estimates from the fusion of visual
and inertial sensors. Because the model contains unknown parameters, such as
sensor biases, the problem is usually cast as a mixed identification/filtering,
and the resulting observability analysis provides a necessary condition for any
algorithm to converge to a unique point estimate. Unfortunately, most models
treat sensor bias rates as noise, independent of other states including biases
themselves, an assumption that is patently violated in practice. When this
assumption is lifted, the resulting model is not observable, and therefore past
analyses cannot be used to conclude that the set of states that are
indistinguishable from the measurements is a singleton. In other words, the
resulting model is not observable. We therefore re-cast the analysis as one of
sensitivity: Rather than attempting to prove that the indistinguishable set is
a singleton, which is not the case, we derive bounds on its volume, as a
function of characteristics of the input and its sufficient excitation. This
provides an explicit characterization of the indistinguishable set that can be
used for analysis and validation purposes.
