An improved Bayesian filter for nonlinear systems under multistep randomly delayed and lost measurements

This article addresses the Bayesian filtering problem for a class of nonlinear systems under multistep randomly delayed and lost measurements. A new measurement model is established that can characterize the random delay and loss of measurement data. First, an augmented Gaussian mixture filter framework is developed in the case of random delay of measurement data; the posterior probability density function after state augmentation is calculated by marginalizing over delay variables to extract accurate information from delayed measurements. The implementation of the filter is transformed into the computation of nonlinear numerical integrals. Second, under the proposed framework, novel expressions of the mean and covariance are generated by propagating the measurement taken at the previous moment in the event of no new measurement being received. Finally, we present two simulation examples for estimating system states, and the results demonstrate the effectiveness and superiority of our proposed filter.