Guaranteed Parameter Estimation

Abstract

Classical estimation problems are based on the assumption that the probabilistic distributions of disturbances are known or, at least, there are known such statistical characteristics as mathematical expectations and covariance matrices. If the system is described by ordinary differential equations and the disturbances are white Gaussian noises, then the optimal estimate (i.e., the estimate with a minimal variance of estimation error) is yielded by the well-known Kaiman filter [84], [41], [79], [143], [47]. However, in many applications the stochastic description is not complete. For example, for many unique measurement systems (which are used, for example, for the ensuring of cosmic experiments) there is no sufficient amount of experimental data. Therefore, it is impossible to determine the statistical characteristics with required accuracy and reliability. Moreover, sometimes even the fact of statistical stability of experimental data is questionable. In the latter case, the stochastic description is impossible in principle. Therefore, along with the statistical description, a researcher has to use a set-membership description of uncertainty.