Database Reference
In-Depth Information
A graphical representation of each type of inference for a simple chain
model with a single hidden variable is shown in
figure 3.1
. Prediction
and filtering are computable online, while smoothing requires observa-
tions from future instances in order to
correct
our estimate of an object's
state given more information. In the context of data management sys-
tems, filtering and prediction would be used in a MOD, while smoothing
would be used to obtain complete historic trajectories of mobile objects
for a STDB.
Figure 10.7.
KFM Inference steps:
Prediction
predicts the value of
x
t
from the
last known position of the object,
z
t−
1
and the movement model. This is computed
in the graphical model by integrating out the unobserved value of
x
t−
1
.
Filtering
corrects
thevalueof
x
t
by incorporating the latest uncertain observation,
z
t
.
Smooth-
ing
updates the filtered estimate for
x
t
by also incorporating information from later
observations (
z
1
..T
).
In general, it is rarely possible to evaluate Eq. 10.2 exactly, and ap-
proximate methods have become quite common [13, 19, 59]. However,
under certain modeling assumptions, exact inference is tractable. Next,
we introduce the Kalman filter model (KFM), a popular model for which
exact inference is tractable. Due to the popularity of the KFM and its
widespread adoption in tracking and sequential data processing [40, 41,
74, 91, 51, 94], we discuss this model in some depth. Our objective in the
following section is to briefly introduce the Kalman filter to unfamiliar
readers, including some intuition as to how and why the model works.
3.2 Kalman Filter
The Kalman filter model [39] (KFM) is a linear dynamic system that
offers an ecient exact inference procedure. The eciency stems from
the fact that all of the variables in the model are assumed to come from
a joint Gaussian distribution. As a result, both the observation noise
(Eq. 10.4) and the system dynamics (Eq. 10.5) are assumed to be Gaus-
sian distributions. The observation noise describes how observations
are related to the actual belief state. In this case, we expect observa-
tions to be distributed normally about the true state with the degree of
