Design and complexity analysis of marginalized Gaussian filtering for nonlinear systems with multi-step random measurement delays and packet dropouts

For nonlinear systems with multi-step random measurement delays and packet dropouts, the existing state-augmented Gaussian filtering (SAGF) has a high computational complexity in the case of large delay steps as the dimension of augmented state increases with delay step. To overcome this drawback, this paper firstly points out that there exist analytical linear substructures in the augmented systems. Then by applying the marginalization technique to these substructures, a marginalized Gaussian filtering (MGF) is developed, where integrals are w.r.t. a single original state rather than w.r.t. the augmented state. Further, on the premise that sigma-point methods are applied to integrals in both SAGF and MGF, a quantitative computational complexity analysis is provided by counting floating-point operations, showing that MGF has a lower theoretical computational complexity than SAGF. Finally, a simulation experiment on target tracking illustrates that MGF has the same estimation accuracy as SAGF, but requires less running time.