Sequential parameter estimation for dynamical systems in the presence of multiplicative and additive noises in the observations (Q1069899)

The paper considers the estimation of the parameters in linear-in- parameters models which include two noise sources. The description of the first noise source is by means of its second-order properties but that of the second noise source is less standard. This second noise is assumed to be bounded by some known function of the measurements. A modified least- squares method for estimating the parameters in this type of models is proposed, and its properties are established. Next, it is shown that the problem of estimating the parameters of an autoregressive model with both additive and multiplicative noise can be reduced to the type of problem analysed previously. The estimates proposed are shown to be robust in the sense that they possess a prescribed accuracy which holds for a whole class of distribution functions of the measurements.