A Qualitative Introduction to Linear Least square Estimation

Abstract

The filtering theor ies we discussed are us ually classified as linear
r.ecursive estimation theory. Non-recursive estimation theory is in fact
the forerunner of the estimation theory; dating back to the time of GaussKepler, etc . Present research however, focusses on the development of
recursive estimation, as th is is the case where physical implementation is
an a ttractive practical proposition.
OUf di~.cussion has been concentrated upon the continuous-time
filtering. In modern communication, however, most systems are more appropriately
described as discrete - time model. The actual transmitted signals
are often continuous-time. Sampling takes place at the receiving end and
the signals are processed using both digital and ana log equipments. The
estimate obtained from the discrete-time measurement sequence is given
both as discrete-time and continuous-time. This estimation procedure is
known as discrete-continuous filtering. This concept can also be applied to
fixed-lag smoothing (15). The smoother obtained normally possesses the
same stability property as that possessed by the Kalman-Bucy filter.