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B. Dong, T. Burgess, H.-B. Neuner:
"Graphical Kalman Filter";
Talk: ION PLANS 2018 Conference, Monterey, USA (invited); 2018-04-23 - 2018-04-26; in: "ION Plans 2018", (2018), 12 pages.

The Extended Kalman Filter is a proven method
for efficient Markov Chain inference. It is ubiquitous in indoor
localization applications for combining relative motion often
with absolute positioning. However, an unmodified Extended
Kalman Filter struggles to handle common problems in indoor
applications. For instance, the presence of large and hard to
estimate noise terms, large correlated outliers, and other nonlinear
effects. Typically, this necessitates the introduction of
large smoothing propagation errors to ensure stability and avoid
converging on false results. As a result, the memory of filter
rapidly decays and estimates only are influenced by the last few
observations.
This work introduces the Graphic Model Kalman Filter
which combines an Adaptive Kalman Filter with a probabilistic
Graphical Model. In the filter, the adaptive component uses
historical data to dynamically estimate observation and propagation
errors. The states prior and after will be predicted
from the target state. The relations between predictions and
each observation are used to form the graphical model. The
Kalman update then replaced by an optimization of the graphical
model, which improves trajectory smoothness and robustness to
outliers. Extensive simulations are used to show that this design
outperforms regular Extended or Adaptive Kalman Filters.

Indoor navigation, Kalman filter, graphical models, adaptive algorithm, Simultaneous Localization And Mapping (SLAM)