Interpolation Method for Update with Out-of-Sequence Measurements: The Augmented Fixed-Lag Smoother

Abstract

In this study, the authors propose a novel method to handle OOSMs in Kalman filtering. The proposed method, called the augmented fixed-lag smoother (AFLS), is based on the fixed-lag smoother (FLS) formulation, which has been shown to be optimal [10]. We generate the OOSM node from the two adjacent nodes, plug the generated estimations into the state vector and the covariance matrix, and update the filter with OOSMs using the FLS update equation. This approach gives a generalized solution that can handle any number of OOSMs. We also extend the AFLS algorithm to nonlinear system, called the extended AFLS (EAFLS), and give an application example on a satellite-tracking problem.