Data Smoothing using a Kalman Filter
by Vince Banes
"The analysis of continuous pricing information works well with
this form of filtering"
The concept of optimum estimation was introduced by Dr. R.E. Kalman in 1960. The first major
application of his theories was to reduce the noise found in the data of modern navigation systems. With
these theories, system designers were able to use knowledge about the noise in a system to filter out its
effects and to improve system performance without additional hardware. This led engineers to apply his
principles to many different problems. These same principles can be applied to technical analysis of stock
and commodity prices.
Because the first use of Dr. Kalman's filters was limited to certain environments, few people took the
time to understand the mathematics. A technical "cult" has been built around these equations, for many a
Ph.D. has been earned from studying them. At first glance, the original papers presented by Dr. Kalman
are an impenetrable fortress to be understood only by the highest of the most high in the world of
mathematics. This paper will present, for the common man, the simple second order case of Kalman
filtering and how to apply it to data smoothing.
The equations are quite simple but very effective in filtering out the high-frequency noise found in most
measurement systems. The analysis of continuous pricing information works well with this form of