Iterated posterior linearization filters and smoothers with cross-correlated noises

In the article, several concise and efficient iterated posterior linearization filtering and smoothing methodologies are proposed for nonlinear systems with cross-correlated noises. Based on the Gaussian approximation (GA), the presented methods are derived via performing statistical linear regressions (SLRs) of the nonlinear state-space models w.r.t the current posterior distribution in an iterated way. Various posterior linearization methods can be developed by employing different approximation computation approaches for the Gaussian-weighted integrals encountered in SLRs. These new estimation methods enjoy not only the accuracy and robustness of the GA filter but also the lower computational complexity. Estimation performances of the designed methods are illustrated and compared with conventional estimation schemes by two common numerical examples.