Robust Information Filtering Under Model Mismatch for Large-Scale Dynamic Systems

The Kalman filter (KF) loses its optimality properties when the system model is misspecified to a certain extent, that is, when the assumed system knowledge does not perfectly match the true system dynamics, which in turn can severely impact its performance in real-life applications. The same goes for its extended counterpart (EKF). Linear constraints were recently shown to be a possible way to mitigate the impact of system model mismatch, which led to the derivation of a linearly constrained KF and EKF (LC-KF and LC-EKF). In this contribution, we build on these new robust filters to provide their information form counterparts, the so-called linearly constrained (extended) information filters (LC-IF and LC-EIF). In the unconstrained case, both IF and EIF are mathematically equivalent to the KF and EKF, respectively, but better suited to systems without priors or with a measurement dimension much larger than the state one. Actually only the IF and EIF can be used for large-scale real-time dynamic systems in which computational time and memory are at a premium. Hence the essential need of IF forms of the LC-KF and LC-EKF for such systems, which are introduced in this article. Furthermore, LC-(E)IF still adapts to systems without priors, even though some restrictions apply. Their computational advantages are shown through representative applications, i.e., large array processing and multi-sensor localisation.