Robust Kalman tracking and smoothing with propagating and non-propagating outliers

A common situation in filtering where classical Kalman filtering does not perform particularly well is tracking in the presence of propagating outliers. This calls for robustness understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. Based on optimality results for distributional-robust Kalman filtering from Ruckdeschel[01,10], we propose new robust recursive filters and smoothers designed for this purpose as well as specialized versions for non-propagating outliers. We apply these procedures in the context of a GPS problem arising in the car industry. To better understand these filters, we study their behavior at stylized outlier patterns (for which they are not designed) and compare them to other approaches for the tracking problem. Finally, in a simulation study we discuss efficiency of our procedures in comparison to competitors.Comment: 27 pages, 12 figures, 2 table

On general systems with network-enhanced complexities

In recent years, the study of networked control systems (NCSs) has gradually become an active research area due to the advantages of using networked media in many aspects such as the ease of maintenance and installation, the large flexibility and the low cost. It is well known that the devices in networks are mutually connected via communication cables that are of limited capacity. Therefore, some network-induced phenomena have inevitably emerged in the areas of signal processing and control engineering. These phenomena include, but are not limited to, network-induced communication delays, missing data, signal quantization, saturations, and channel fading. It is of great importance to understand how these phenomena influence the closed-loop stability and performance properties

Ensemble updating of binary state vectors by maximising the expected number of unchanged components

In recent years, several ensemble-based filtering methods have been proposed and studied. The main challenge in such procedures is the updating of a prior ensemble to a posterior ensemble at every step of the filtering recursions. In the famous ensemble Kalman filter, the assumption of a linear-Gaussian state space model is introduced in order to overcome this issue, and the prior ensemble is updated with a linear shift closely related to the traditional Kalman filter equations. In the current article, we consider how the ideas underlying the ensemble Kalman filter can be applied when the components of the state vectors are binary variables. While the ensemble Kalman filter relies on Gaussian approximations of the forecast and filtering distributions, we instead use first order Markov chains. To update the prior ensemble, we simulate samples from a distribution constructed such that the expected number of equal components in a prior and posterior state vector is maximised. We demonstrate the performance of our approach in a simulation example inspired by the movement of oil and water in a petroleum reservoir, where also a more na\"{i}ve updating approach is applied for comparison. Here, we observe that the Frobenius norm of the difference between the estimated and the true marginal filtering probabilities is reduced to the half with our method compared to the na\"{i}ve approach, indicating that our method is superior. Finally, we discuss how our methodology can be generalised from the binary setting to more complicated situations