  The essential of navigation, perception, and decision-making which are basic
tasks for intelligent robots, is to estimate necessary system states. Among
them, navigation is fundamental for other upper applications, providing precise
position and orientation, by integrating measurements from multiple sensors.
With observations of each sensor appropriately modelled, multi-sensor fusion
tasks for navigation are reduced to the state estimation problem which can be
solved by two approaches: optimization and filtering. Recent research has shown
that optimization-based frameworks outperform filtering-based ones in terms of
accuracy. However, both methods are based on maximum likelihood estimation
(MLE) and should be theoretically equivalent with the same linearization
points, observation model, measurements, and Gaussian noise assumption. In this
paper, we deeply dig into the theories and existing strategies utilized in both
optimization-based and filtering-based approaches. It is demonstrated that the
two methods are equal theoretically, but this equivalence corrupts due to
different strategies applied in real-time operation. By adjusting existing
strategies of the filtering-based approaches, the Monte-Carlo simulation and
vehicular ablation experiments based on visual odometry (VO) indicate that the
strategy adjusted filtering strictly equals to optimization. Therefore, future
research on sensor-fusion problems should concentrate on their own algorithms
and strategies rather than state estimation approaches.
