Geometrically Intrinsic Nonlinear Recursive Filters II: Foundations

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dc.creatorDarling, R. W. R.
dc.date1998-09-06
dc.date.accessioned2026-07-07T05:25:54Z
dc.date.available2026-07-07T05:25:54Z
dc.descriptionThis paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random initial condition. There is a single observation consisting of a nonlinear function of X(T), corrupted by noise, and with values in another manifold M. The noise covariance of X and the observation covariance themselves induce geometries on M and N, respectively. Using these geometries we compute approximate but coordinate-free formulas for the "best estimate" of X(T), given the observation, and its conditional variance. Calculations are based on use of Jacobi fields and of "intrinsic location parameters", a notion derived from the heat flow of harmonic mappings. When any nonlinearity is present, the resulting formulas are not the same as those for the continuous-discrete Extended Kalman Filter. A subsidiary result is a formula for computing approximately the "exponential barycenter" of a random variable S on a manifold, i.e. a point z such that the inverse image of S under the exponential map at z has mean zero in the tangent space at z.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/9809029
dc.identifierhttp://arxiv.org/abs/math/9809029
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77360
dc.subjectProbability
dc.subjectDifferential Geometry
dc.subject60G35, 58G32, 53B20
dc.titleGeometrically Intrinsic Nonlinear Recursive Filters II: Foundations
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