Robust Data Processing in the Presence of Uncertainty and Outliers: Case of Localization Problems
Résumé
To properly process data, we need to take into
account both the measurement errors and the fact that some
of the observations may be outliers. This is especially important
in radar-based localization problems, where some signals may
reflect not from the analyzed object, but from some nearby object.
There are known methods for dealing with both measurement
errors and outliers in situations in which we have full information
about the corresponding probability distributions. There are also
known statistics-based methods for dealing with measurement
errors in situations when we only have partial information
about the corresponding probabilities. In this paper, we show
how these methods can be extended to situations in which we
also have partial inf0ormation about the outliers (and even to
situations when we have no information about the outliers). In
some situations in which efficient semi-heuristic methods are
known, our methodology leads to a justification of these efficient
heuristics – which makes us confident that our new methods will
be efficient in other situations as well.