ONE (Optimal Nonlinear Estimation)

Shortly obout Optimal Nonlinear Estimation (cloud physics)

I came across Optimal Nonlinear Estimation during my industrial internship at the University of Warsaw (Institute of Geophysics, Department of Atmospheric Physics). One of the directions of research was to learn about the mixing processes between a cloud and the surrounding air. A cloud is made of droplets with variable spatial concentration. We would like to learn the most accurate course of changes in the concentration of droplets at the boundary of the cloud and its surroundings. Airplanes with additional research equipment are used to study clouds. The plane flies through the cloud and the equipment records changes in the parameters being investigated. A single-particle spectrometer is used to measure the concentration of cloud particles. This device uses the optical properties of droplets (they work a bit like lenses). A single-particle spectrometer has a laser. The air surrounding the plane passes through the laser beam area. If a cloud droplet is in the laser beam, the beam parameters will change and this will be recorded as a droplet count. The output data from a plane flying through a cloud contains a series of counts (a list of times between successive counts). It remains to analyze this data.

However, mathematical problems arise. If we want to know exactly the course of changes in particle concentration, we have a problem with relative measurement uncertainty. This is because there are large fluctuations in particle concentration. The concentration in the cloud is high. The tested intermediate layer is very thin. This causes a problem with the "ordinary" moving average method. If the droplet concentration is significantly reduced, the relative error of the counting process becomes large. For this reason, it was decided to use the ONE method. In this method, it is assumed that the counting process is described by a Poisson distribution. The ONE method allows to remove the inherent noise of the counting process and to learn more about the structure of the cloud.

ONE - what next?

Removing the noise from the counting process seemed quite interesting and unique to me. I started to wonder what this method could be used for. A few suggestions came to mind

• I have read that the authors of this method use it in many other applications (G.Salut at Google Scholar) e.g. in RADAR / SONAR devices.
• Perhaps the ONE method can be used to denoise Particle In Cell simulations for plasma and space charges (e.g. high gradients).
• Perhaps the ONE method can be used in data analysis, e.g. in mass spectrometry. Maybe someone will invent a method where it will be possible to identify particles based on time parameters of counting. Or e.g. testing the stability of particles to some radiation (suddenly some class of particles is missing - it means that they have decayed).
• I've read about Burkhard Heim's somewhat high-flown "theory of everything". Its feature is a "spatially quantized" world. Perhaps one could do some simulations "in a quantized world" and simplify it with the help of ONE to models in the continuum world.

Links

• H. Pawlowska, J. L. Brenguier, and G. Salut, "Optimal Nonlinear Estimation for Cloud Particle Measurements" - https://www.igf.fuw.edu.pl/en/publications/33/
• H. Pawlowska, J. L. Brenguier, and G. Salut, "Optimal Nonlinear Estimation for Cloud Particle Measurements"- https://journals.ametsoc.org/view/journals/atot/14/1/1520-0426_1997_014_0088_onefcp_2_0_co_2.xml
• Donald L. Snyder , Michael I. Miller, "Random Point Processes in Time and Space " - https://link.springer.com/book/10.1007/978-1-4612-3166-0

I do not recommend searching "shadow libraries" (copyright violation, etc.).

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