2 research outputs found
Kalman Filtering over Fading Channels: Zero-One Laws and Almost Sure Stabilities
In this paper, we investigate probabilistic stability of Kalman filtering
over fading channels modeled by -mixing random processes, where channel
fading is allowed to generate non-stationary packet dropouts with temporal
and/or spatial correlations. Upper/lower almost sure (a.s.) stabilities and
absolutely upper/lower a.s. stabilities are defined for characterizing the
sample-path behaviors of the Kalman filtering. We prove that both upper and
lower a.s. stabilities follow a zero-one law, i.e., these stabilities must
happen with a probability either zero or one, and when the filtering system is
one-step observable, the absolutely upper and lower a.s. stabilities can also
be interpreted using a zero-one law. We establish general stability conditions
for (absolutely) upper and lower a.s. stabilities. In particular, with one-step
observability, we show the equivalence between absolutely a.s. stabilities and
a.s. ones, and necessary and sufficient conditions in terms of packet arrival
rate are derived; for the so-called non-degenerate systems, we also manage to
give a necessary and sufficient condition for upper a.s. stability
An Improved Tobit Kalman Filter with Adaptive Censoring Limits
This paper deals with the Tobit Kalman filtering (TKF) process when the
measurements are correlated and censored. The case of interval censoring, i.e.,
the case of measurements which belong to some interval with given censoring
limits, is considered. Two improvements of the standard TKF process are
proposed, in order to estimate the hidden state vectors. Firstly, the exact
covariance matrix of the censored measurements is calculated by taking into
account the censoring limits. Secondly, the probability of a latent (normally
distributed) measurement to belong in or out of the uncensored region is
calculated by taking into account the Kalman residual. The designed algorithm
is tested using both synthetic and real data sets. The real data set includes
human skeleton joints' coordinates captured by the Microsoft Kinect II sensor.
In order to cope with certain real-life situations that cause problems in human
skeleton tracking, such as (self)-occlusions, closely interacting persons etc.,
adaptive censoring limits are used in the proposed TKF process. Experiments
show that the proposed method outperforms other filtering processes in
minimizing the overall Root Mean Square Error (RMSE) for synthetic and real
data sets.Comment: 21 pages, 32 figure