**Lee and Kay (1990)** : A Kalman filter
approach for accurately estimating the 3-D position
and orientation of a moving object with respect to the robot base frame is
proposed. This approach significantly differs from other approaches in that motion is estimated with the uncertainty of the position
of a camera taken into account. Emphasis is also given to finding a solution to
the following problem of motion estimation using a
long sequence of images: the images taken from a longer distance suffer from a
larger noise-to-signal ratio, which results in larger errors in 3-D
reconstruction and, thereby, causes a series degradation in motion estimation. To solve this problem, the authors have
derived a set of discrete Kalman filter equations for
motion estimation. The measurement equation is
obtained by analyzing the effect of white Gaussian noise in 2-D images on 3-D
positional errors, and the system dynamic equation
is formulated in terms of the measurement noise in 2-D images. Simulation
results indicate that the Kalman filter equations derived present an accurate
model for the estimation of 3-D position and
orientation, thus providing significant error reduction in the presence of
large measurement noise in a long sequence of images, as well as allowing a
shorter transition period for convergence to the
true values.