Nota: The first four subsections are extracted from the book [25]: 3D Dynamic Scene Analysis: A Stereo Based Approach, by Z. Zhang & O. Faugeras (Springer Berlin 1992).
Kalman filtering, as pointed out by Lowe [12], is likely to have applications throughout Computer Vision as a general method for integrating noisy measurements.
The behavior of a dynamic system can be described by the evolution of a set of variables, called state variables. In practice, the individual state variables of a dynamic system cannot be determined exactly by direct measurements; instead, we usually find that the measurements that we make are functions of the state variables and that these measurements are corrupted by random noise. The system itself may also be subjected to random disturbances. It is then required to estimate the state variables from the noisy observations.
If we denote the state vector by 
and denote the measurement
vector by 
, a dynamic system
(in discrete-time form) can be
described by
where 
is the vector of random disturbance of the dynamic
system and is usually modeled as white noise:
In practice, the system noise covariance 
is usually determined
on the basis of experience and intuition (i.e., it is guessed).
In (18), the vector 
is called the
measurement vector. In practice, the measurements that can be made
contain random errors. We assume the measurement system
is disturbed
by additive white noise, i.e., the real observed measurement
is expressed as
where
The measurement noise covariance 
is either provided
by some signal processing algorithm or guessed in the same manner as
the system noise. In general, these noise levels are determined
independently.
We assume then there is no correlation between the noise process of
the system and that of the observation, that is
