Numerical method of estimating the maximal likelihood of a smooth parametric manifold

Consideration was given to the numerical estimation of the maximum likelihood for the parameter vector describing a smooth manifold. Estimation is based on the results of observing motion of a dynamic plant whose trajectory belongs to this manifold and is measured with random errors having normal distribution with certain parameters. Application of the maximum likelihood method to such problems gives rise to the problem of nonlinear highdimensionality programming. Some constructive analytical results obtained enable significant reduction in the problem dimensionality. The problem of identifying the plane of motion of a dynamic plant was examined.