The foundations of set theoretic estimation

Article Abstract:

Estimation problems are usually solved by optimizing an objective function with or without constraints, but the solvability of the resulting optimization problem may lead to the selection of an unrealistic objective function. The reliability of solutions thus becomes questionable because they may violate known constraints about the problem. Set theoretic estimation is based on feasibility and produces solutions whose sole property is to be consistent with all information arising from the observed data and a priori knowledge. All information is associated with a set in the solution space; the feasibility set, which is the intersection of the sets, represents the acceptable solutions. The various approaches to set theoretic estimation used in systems science and signal processing are synthesized into a single general framework; their fundamental philosophies, goals, and analytical techniques are examined, and they are related to conventional approaches.

Problem solving, Product introduction, Systems theory, Signal processing, Optimization, Sets, Scientific Research, New Technique

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Characterization of frequency stability: frequency-domain estimation of stability measures

Article Abstract:

The Allan (or two sample) variance is the standard characterization of frequency stability in the time domain; the spectral density function (SDF) is the standard in the frequency domain. SDFs that model sampled frequency stability data and are related to the SDF's standard characterization are described. The SDF's role in the theory of stationary processes and processes with stationary backward differences is reviewed. A systematic method of estimating SDF's frequency stability data is outlined. The relationship between the Allan variance and the SDF is considered and two nonparametric methods for the translation of stability measures between the two domains are presented.

Standard, Standardization, Stability, Measurement Techniques, Frequency

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