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toni
2018-04-03 10:53:44 +02:00
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@@ -59,18 +59,20 @@ The authors of \cite{Sun2013} handled the problem by using an adaptive number of
The key idea is to choose a small number of samples if the distribution is focused on a small part of the state space and a large number of particles if the distribution is much more spread out and requires a higher diversity of samples.
The problem of sample impoverishment is then encountered by adapting the number of particles depend upon the systems current uncertainty \cite{Fetzer-17}.
However, in practice sample impoverishment is often a problem of environmental restrictions and system dynamics.
Therefore, such a method fails, since it is not able to propagate new particles into the state space due to environmental restrictions e.g. walls or ceilings.
In \cite{Fetzer-17} we deployed an interacting multiple model particle filter (IMMPF) to solve the sample impoverishment.
In practice sample impoverishment is often a problem of environmental restrictions and system dynamics.
Therefore, the method above fails, since it is not able to propagate new particles into the state space due to environmental restrictions e.g. walls or ceilings.
In \cite{Fetzer-17} we deployed an interacting multiple model particle filter (IMMPF) to solve sample impoverishment in such restrictive scenarios.
We combine two particle filter using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between both.
However, deploying a IMMPF is in most cased not a necessary step, thus we present i much simple, but also very heuristic model within this paper.
However, deploying a IMMPF is in many cases not necessary and produces additional processing overhead.
Thus a much simpler, but very heuristic method is presented within this paper.
%estimation
Finally, as the name recursive state estimation states, it requires to find the most probable state within the state space, to provide the “best estimate” of the underlying problem.
In the discrete manner of a sample representation this is often done by providing a single value, also known as sample statistic, to serve as a “best guess”.
This value is then calculated by means of simple parametric point estimators, e.g. the weighted-average over all samples, the sample with the highest weight or by assuming other parametric statistics like normal distributions
However in complex situtations like a multimodal representatio of the posterior, such methods fail to provide an accurate statement about the most probable state.
Finally, as the name recursive state estimation says, it requires to find the most probable state within the state space, to provide the "best estimate" of the underlying problem.
In the discrete manner of a particle representation this is often done by providing a single value, also known as sample statistic, to serve as a best guess \cite{Bullmann-18}.
Examples are the weighted-average over all particles or the particle with the highest weight.
However in complex scenarios like a multimodal representation of the posterior, such methods fail to provide an accurate statement about the most probable state.
Thus, in \cite{} we present a rapid computation scheme
A well known solution is KDE.
For example \cite{} used a ... in .... However it is obvious that this method has a massive computation time and is thus not practicle for smartphone-based solutions.