by Ivan Durbak

On March 2nd, 2004, the New York City Chapter of the Ukrainian Engineers' Society of America presented a lecture by Peter Halatyn, President of KDM Aero Inc., at the Ukrainian Institute on East 79th Street, New York City, on "OPTIMAL ESTIMATION "

Mr. Halatyn combined engineering and mathematics concepts to present an informative and comprehensive look at the complex field of estimation, which he defined as "the process of extracting information from data" or, more mathematically, as "data processing methods for dealing with random variables". After introducing the topic, Mr. Halatyn began by explaining the estimation problem, involving measurements and noise in multi-sensor systems, and noting how the different types of estimation filtering, smoothing, and predicting have widespread applicability to thousands of real-world applications. He then went on to review the basic underlying mathematical concepts such as mean, variance, co-variance, probability, normal or gaussian probability distributions, and vector matrices.

Mr. Halatyn next provided a broad historical perspective, beginning with the deterministic least-squares estimation techniques invented by Gauss (in 1809), and continuing with the work of R.A. Fisher (in 1912) with probability density functions and maximum likelihood estimation techniques. He then moved to the work of N. Wiener (in 1940), who used the frequency domain approach to design statistically optimal filters used to solve the problem of estimating signals in noise in important applications such as radar. The next and possibly most-important development was the seminal work of R.E. Kalman (in 1960) who used optimal recursive filter techniques, based on vector modeling of state-space and time-domain formulation, to develop a very efficient and robust "least-squares" estimation methodology.

Mr. Halatyn explained how the Kalman filter is now the most commonly used optimal filtering technique: for example, a recent “Google” search on the internet revealed over 15,000 applications using Kalman Filtering methods. These applications span a broad array of science and engineering areas, including flood prediction and atmospheric model forecasts, wireless networks, GPS pedestrian navigation, real-time estimation of human body postures, cellular networks, lidar and microwave radiometers, trace gas concentration measurements, probabilistic video stabilization, glottal closed-phase location & analysis, neural networks, weather models, and even stock market forecasting. The power of Kalman filtering lies in its ability to combine the dynamic process model with the measurement model to efficiently, recursively, and robustly estimate unknown random parameters and missing states based on a sequence of noisy measurements. Kalman filtering has also been extended to nonlinear models and reformulated to use functions instead of matrices.

Mr. Halatyn finished with a detailed example of the GPS (global positioning system), where a 24 satellite-based navigation system uses the linearization techniques of the extended Kalman filter to precisely locate any position on earth.

Throughout this presentation, which lasted over two hours into the night, Mr. Halatyn kept the audience engaged and involved with an artfully combined balance of highly technical material and practical real-world problem examples.

The evening finished with informal and convivial discussions over food and drinks.

Mr. Halatyn, one of many brilliant Ukrainian engineers, has conducted research, published recent papers, and worked on practical applications using leading-edge mathematical modeling techniques that span a broad array of application areas, including cybernetics, aeronautical science, electrical engineering, navigational control, and stock market forecasting. He now runs his own engineering consultant company; previously he had worked for many of the major aerospace / engineering companies, including Sikorsky, Boeing, Lockheed, and Honeywell.

This was the third in a series of engineering & scientific lectures presented by the New York City Chapter of the Ukrainian Engineers' Society of America during the 2003/2004 year. The next lecture will be presented on Tuesday April 20, 2004 by Ivan Durbak on "Computer Security".