Multivariate Statistics in Single Observation Space

The observation data collected from continuous industrial processes usually have two main categories: process data and quality data, and the corresponding industrial data analysis is mainly for the two types of data based on the multivariate statistical techniques.

On the performance of particle filters with adaptive number of particles

We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models. To be specific, we propose a family of block-adaptive PFs based on the methodology of Elvira et al. (IEEE Trans Signal Process 65(7):1781–1794, 2017). In this class of algorithms, the number of Monte Carlo samples (known as particles) is adjusted periodically, and we prove that the theoretical error bounds of the PF actually adapt to the updates in the number of particles. The evaluation of the predictive statistics that lies at the core of the methodology is done by generating fictitious observations, i.e., particles in the observation space. We study, both analytically and numerically, the impact of the number K of these particles on the performance of the algorithm. In particular, we prove that if the predictive statistics with K fictitious observations converged exactly, then the particle approximation of the filtering distribution would match the first K elements in a series of moments of the true filter. This result can be understood as a converse to some convergence theorems for PFs. From this analysis, we deduce an alternative predictive statistic that can be computed (for some models) without sampling any fictitious observations at all. Finally, we conduct an extensive simulation study that illustrates the theoretical results and provides further insights into the complexity, performance and behavior of the new class of algorithms.

Interpreting estimated observation error statistics of weather radar measurements using the ICON-LAM-KENDA system

Assimilation of weather radar measurements including radar reflectivity and radial wind data has been operational at the Deutscher Wetterdienst, with a diagonal observation error (OE) covariance matrix. For an implementation of a full OE covariance matrix, the statistics of the OE have to be a priori estimated, for which the Desroziers method has been often used. However, the resulted statistics consists of contributions from different error sources and are difficult to interpret. In this work, we use an approach that is based on samples for truncation error in radar observation space to approximate the representation error due to unresolved scales and processes (RE) and compare its statistics with the OE statistics estimated by the Desroziers method. It is found that the statistics of the RE help the understanding of several important features in the variances and correlation length scales of the OE for both reflectivity and radial wind data and the other error sources from the microphysical scheme, radar observation operator and the superobbing technique may also contribute, for instance, to differences among different elevations and observation types. The statistics presented here can serve as a guideline for selecting which observations are assimilated and for assignment of the OE covariance matrix that can be diagonal or full and correlated.

A Case of Application of Data Transforms

The recent implementations of Industry 4.0 and allied mathematical applications such as machine learning and big data analytics are conditioned by mathematizing the basic features of the observed system. For example, the key phenomena in a number of man-made processes are controlled by an orifice, an opening through which is passing a medium of interest. When the observed process is recursive, the related records indicate the possibility of extracting from the accumulating observations knowledge useful for the system optimisation. Many of the process variables such as chemical composition, velocities, temperatures, and forces, are recorded in a convenient digital format. This, however, is not always the case with the orifice geometry. Mathematical transforms presented hereby demonstrate how a broad variety of the orifice geometries can be defined in a generic mathematical format that allows for analysing them within the same observation space

Interpreting estimated Observation Error Statistics of Weather Radar Measurements using the ICON-LAM-KENDA System

Assimilation of weather radar measurements including radar reflectivity and radial wind data has been operational at the Deutscher Wetterdienst, with a diagonal observation error (OE) covariance matrix. For an implementation of a full OE covariance matrix, the statistics of the OE have to be a priori estimated, for which the Desroziers method has been often used. However, the resulted statistics consists of contributions from different error sources and are difficult to interpret. In this work, we use an approach that is based on samples for truncation error in radar observation space to approximate the representation error due to unresolved scales and processes (RE) and compare its statistics with the OE statistics estimated by the Desroziers method. It is found that the statistics of the RE help the understanding of several important features in the variances and correlation length scales of the OE for both reflectivity and radial wind data and the other error sources from the microphysical scheme, radar observation operator and the superobbing technique may also contribute, for instance, to differences among different elevations and observation types. The statistics presented here can serve as a guideline for selecting which observations to assimilate and for assignment of the OE covariance matrix that can be diagonal or full and correlated.

New fixed point of on-orbit calibration scale based on the In-Bi eutectic alloy for application in novel high-stable space-borne standard sources

The problem of ensuring stability of Earth observation space-borne instruments undertaking long-term temperature measurements within thermal IR spectral range is described. For in-flight reliable control of the space-borne IR instruments characteristics the stability of onboard reference sources should be improved. The function of these high-stable sources will be executed by novel onboard blackbodies, incorporating the melt↔freeze phase transition phenomenon, currently being developed. As a part of these works the task of realizing an on-orbit calibration scale within the dynamic temperature range of Earth observation systems 210−350 K based on fixed-point phase transition temperatures of a number of potentially suitable substances is advanced. The corresponding series of the onboard reference blackbodies will be set up on the basis of the on-orbit calibration scale fixed points. It is shown that the achievement of the target lies in carrying out a number of in-flight experiments with the selected fixed points and the prospective onboard fixed-point blackbodies prototypes. The new In-Bi eutectic alloy melt temperature fixed point (~345 K) is proposed as the significant fixed points of the future on-orbit calibration scale. The results of the new fixed point preliminary laboratory studies have been analyzed. The results allowed to start preparation of the in-flight experiments investigating the In-Bi alloy for the purpose of its application in the novel onboard reference sources.

Legal Problems on the Compensation for Space Damage Caused by Space Debris and Space Liability Convention

This chapter mentions the space debris, observation, space debris' accidents, and the legal problems on the compensation for space damage caused by space debris and relation to the 1972 Space Liability Convention. Space debris is an enemy for mankind. The author comments on the new Draft for the International Instrument on the Protection of the Earth Environment from Damage Caused by Space Debris and presents his proposal on the new legal frame for the prevention and mitigation of space debris and the damage caused by space debris. Frequently, space debris falls back to the Earth, which poses a potential threat to man's exploration and use of outer space activities. Space debris comprise the ever-increasing amount of inactive space hardware in orbit around the Earth as well as fragments of spacecraft that have broken up, exploded, or otherwise become abandoned. It is the author's firm opinion that only international and regional cooperation could solve the problem of environmental pollution including damage caused by space debris.