ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

The paper presents two different methods for nonlinear robust estimation. The frame of the estimation in both cases is nonlinear regression; however, they differ in the form of applied prediction: in one of the cases prediction is performed through optimum estimation of past noises, in the other case through the concept “multi intersample linearization”. To avoid consequences of model errors and not expected large noises, robust estimator design is desirable. The paper first deals with the problem of design of non – robust estimators in case of noises of unknown statistics, then it shows how to make them robust. When prediction is made through optimum noise estimation, a particular problem is the great number of variables to determine. As a rule a long horizon is desirable, but the number of variables increases linearly with extension of the horizon. However, when the dynamic optimization method “optimized stochastic trajectory / output sequence tracking” is used, only the noise and state components at the bottom of horizon and the parameter values for parameter estimation have to be considered as independent variables; the others may be computed from optimization. The estimated noise components will be the ones, which best fit the process, i.e. the ones at the values of which a suitable performance index has its minimum. In case of applying the principle “multi intersample linearization”, nonlinear evolution of states between sampling instants is followed in linear increments, computed with linear equations. The nonlinear parameter estimator gives the value of estimated states, too, together with the parameter estimates. Several methods are presented in the paper for robustification.