Separating bias and state estimates in a recursive second-order filter

When recursively estimating the state of a nonlinear process using a second-order filter to process data from many sensors, the method of augmenting the state vector with those sensor systematic errors for which estimates are desired can result in a new vector of extremely large dimension. To avoid the computational problems arising from operations with large dimension matrices it is desirable to decouple the state and systematic error estimation. An efficient method of generating the estimates separately has been derived for the linear filter [1]. For the second-order filter [2] the separation can also be accomplished although unless the observation model is linear, the estimates are coupled during the discrete update stage of the two stage filter. If the observation model is linear, the estimates are completely decoupled just as in the linear filter.