Estimation for rotational processes with one degree of freedom--Part I: Introduction and continuous-time processes
- 1 February 1975
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 20 (1) , 10-21
- https://doi.org/10.1109/tac.1975.1100829
Abstract
A class of bilinear estimation problems involving single-degree-of-freedom rotation is formulated and resolved. Continuous-time problems are considered here, and discrete-time analogs will be studied in a second paper. Error criteria, probability densities, and optimal estimates on the circle are studied. An effective synthesis procedure for continuous-time estimation is provided, and a generalization to estimation on arbitrary Abelian Lie groups is included. Applications of these results to a number of practical problems including frequency demodulation will be considered in a third paper.Keywords
This publication has 18 references indexed in Scilit:
- An optimal phase demodulatorStochastics, 1975
- Signal detection of rotational processes and frequency demodulationInformation and Control, 1974
- An innovations approach to least-squares estimation--Part III: Nonlinear estimation in white Gaussian noiseIEEE Transactions on Automatic Control, 1971
- Global properties of diffusion processes on cylindrical type phase spaceJournal of the Franklin Institute, 1970
- Conditions for absolute continuity between a certain pair of probability measuresProbability Theory and Related Fields, 1970
- Nonlinear filtering of multiplied and convolved signalsProceedings of the IEEE, 1968
- Asymmetric non-mean-square error criteriaIRE Transactions on Automatic Control, 1962
- Conditional Markov ProcessesTheory of Probability and Its Applications, 1960
- Non-mean-square error criteriaIEEE Transactions on Information Theory, 1958
- A Theorem on Convex Sets with ApplicationsThe Annals of Mathematical Statistics, 1955