Abstract
In this paper we consider several applications of bilinear stochastic models in which state estimation is an important problem. Bilinear stochastic models occur naturally in many communication problems, including noisy oscillators and phase-lock loops, in which the system evolves on the circle Sl. Similar models arise in the estimation of the position of an orbiting body (in which the state evolves on the 2-sphere S2) and in the estimation of the orientation of a rotating rigid body (which evolves on SO(3)).
Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent Lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed.
The work of this author was supported in part by NASA under Grant NGL-22-009-124 and in part by NSF under Grant GK-42090.
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Willsky, A.S., Marcus, S.I. (1975). Estimation for Bilinear Stochastic Systems. In: Ruberti, A., Mohler, R.R. (eds) Variable Structure Systems with Application to Economics and Biology. Lecture Notes in Economics and Mathematical Systems, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-47457-6_7
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DOI: https://doi.org/10.1007/978-3-642-47457-6_7
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