Rudy Kalman, the inventor, if you will, of the Kalman Filter is being honored by the White House with a National Medal of Science and Technology & Innovation. As a young academic in the 1960s I used his paper, A New Approach to Linear Filtering, as the stepping stone to many other developments. It was in the late 1960s that using the Kalman approach we were able to measure the structure of the upper atmosphere. Kalman gave birth to so many critical ideas, including the Black Scholes model, but he also has a mind that went well beyond that. He had a view of the world and nature that led many to that paradigm change which we all benefit from today.
The key change Kalman made was to develop his estimation methods using iterative methods, either discrete or continuous. This was in contradistinction to the wonderful work of Norbert Wiener who had developed the Wiener Filter to perform estimation albeit using the paradigm of the analog computer. Wiener was one who somewhat reject the digital world for the analog. Yet it was Kalman in 1960 who took the first step in doing everything in a context which would be effected digitally. This was the major breakthrough, brilliant!
One should note that unlike the world of macroeconomics, Kalman developed a methodology which allowed men to land on the moon, it is used to control chemical plants, telecommunications, all control systems, it really does something. It works time and time again. It is an element of the real world and it has had an influence of universal scope.
Thus my congratulations to Rudy!
And if I may say so:
x*(t + 1|t) = Φ*(t + 1; t)x*(t|t – 1) + Δ*(t)y(t)
P*(t + 1) = Φ(t + 1; t){P*(t) – P*(t)M'(t)[M(t)P*(t)M'(t)]–1× P*(t)M(t)}Φ'(t + 1; t) + Q(t);
t ≥ t0
The key change Kalman made was to develop his estimation methods using iterative methods, either discrete or continuous. This was in contradistinction to the wonderful work of Norbert Wiener who had developed the Wiener Filter to perform estimation albeit using the paradigm of the analog computer. Wiener was one who somewhat reject the digital world for the analog. Yet it was Kalman in 1960 who took the first step in doing everything in a context which would be effected digitally. This was the major breakthrough, brilliant!
One should note that unlike the world of macroeconomics, Kalman developed a methodology which allowed men to land on the moon, it is used to control chemical plants, telecommunications, all control systems, it really does something. It works time and time again. It is an element of the real world and it has had an influence of universal scope.
Thus my congratulations to Rudy!
And if I may say so:
x*(t + 1|t) = Φ*(t + 1; t)x*(t|t – 1) + Δ*(t)y(t)
P*(t + 1) = Φ(t + 1; t){P*(t) – P*(t)M'(t)[M(t)P*(t)M'(t)]–1× P*(t)M(t)}Φ'(t + 1; t) + Q(t);
t ≥ t0
Posts
