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Isomorphic state observers and system signal robust filtering


V.S. Kulabukhov – JSC MRPC «Avionica» (Moscow)

The use of algorithms and programs for signal observation and filtering is fairly widespread in radio systems. The best known are two approaches to observer synthesis – on the ground of the Kalman filter and on the ground of the Luenberger observer. The approaches are mainly applied to the linear systems and allow to synthesize asymptotic observers that generate precise estimates of unmeasurable state vector components at the sufficient long observation time. The observers realize simultaneously the signal filtering function too. Besides, the heuristic compromise is reached between qualities of observation and filtering. Insufficient robustness of the mentioned observers is eliminated heuristically and only partly. Luenberger observers as simpler are used in many practical tasks in view of Kalman filter “redundancy”. They represent the arbitrarily selectable dynamic system which state vector is connected linearly with the state vector of the observed object and therefore can serve as its estimation.
In whole the current methods of the observer synthesis are complicated and heuristic. This refers even to simple linear systems often applied practically. For the general solution of the observation and filtering problem the geometrical methods and Lie algebra apparatus, as well as current algebra apparatus based on morphisms are used. In the article the structure of the new type observers – isomorphic observes – is formally defined on the ground of the general isomorphism principle in the system theory and the observability concept to an accuracy of any isomorphic model. Was demonstrated that in contrast to conventional additive observers the isomorphic observers have simple multiplicative form allowing to decompose the general synthesis task into separate tasks of observer synthesis and filter synthesis. The robust observer synthesis method is proposed that provides in conjunction with filters high quality of reproduction and filtering of linear system input signals in conditions of significant noise and parametrical disturbances. The isomorphic observer advantages include the strict formalization of synthesis procedures and assurance of maximum attainable quality of observation and filtering. Examples of isomorphic observers and filters synthesis are given.

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