  Safety-critical navigation applications require that estimation errors be
reliably quantified and bounded. This can be challenging for linear dynamic
systems if the process noise or measurement errors have uncertain time
correlation. In many systems (e.g., in satellite-based or inertial navigation
systems), there are sources of time-correlated sensor errors that can be well
modeled using Gauss-Markov processes (GMP). However, uncertainty in the GMP
parameters, particularly in the correlation time constant, can cause misleading
error estimation. In this paper, we develop new time-correlated models that
ensure tight upper bounds on the estimation error variance, assuming that the
actual error is a stationary GMP with a time constant that is only known to
reside within an interval. We first use frequency-domain analysis to derive a
stationary GMP model both in continuous and discrete time domain, which
outperforms models previously described in the literature. Then, we achieve an
even tighter estimation error bound using a non-stationary GMP model, for which
we determine the minimum initial variance that guarantees bounding conditions.
In both cases, the model can easily be implemented in a linear estimator like a
Kalman filter.
