In Chapter 3, we have analyzed which kinds of approximation have to be used in the nonlinear filters that utilize the Taylor series expansions. In addition to linearization of the nonlinear measurement and transition equations, we need to approximate the nonnormal error terms (ie.e, residuals) as the normal ones and the correlated error terms (i.e., residuals) as the uncorrelated ones. These approximations are very strong because it is known that Kalman filter models based on normality assumption are nonrobust (see Meinhold and Singpurwalla (1989)). Therefore, density approximation, rather than function approximation, has to be investigated to obtain less biased filtering estimates of the state-variables.
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