State estimation in networked systems

This thesis considers state estimation strategies for networked systems. State estimation refers to a method for computing the unknown state of a dynamic process by combining sensor measurements with predictions from a process model. The most well known method for state estimation is the Kalman filter, which assumes a linear process model and Gaussian noise distributions. The Kalman filter started as an essential part of various space and military applications. Since then, many of its successful implementations are found in the public domain as well. Motivated by this success, additional estimation methods were designed, such as the extended Kalman filter, unscented Kalman filter and particle filter, to name a few. These methods can deal with nonlinear process models and/or non-Gaussian noise distributions. Up until now, there were no critical limitations in communication and computational resources. The amount of sensor measurements and the model complexities have been sufficiently low to satisfy the requirements for a centralized implementation of state estimation algorithms. This is changing with a paradigm shift in system design towards networked systems, and ‘sensor networks’ in particular. Networked systems can manage large amount of sensors. However, they often lack communication and/or computational resources that are required for processing the large quantity of produced measurements according to a classical centralized implementation. To solve this issue, novel state estimation strategies are presented for networked systems. In the first estimation approach, the amount of measurement samples is reduced with event sampling to cope with communication channels that have a limited capacity for exchanging data. In the second estimation approach, measurements are processed directly at the sensor in a distributed state-estimator to deal with communication and computational limitations of large-scale or ad-hoc networks. A brief motivation for studying these two approaches is given, next. Limitations in the amount of exchanged data from sensor to estimator arise when a (wireless) network connection is used for transferring the data. To reduce this amount, measurements are sampled at the instants of an event on the sensor value, rather than synchronously in time. However, this complicates the estimation problem considerably, as events occur unexpectedly. Therefore, the first estimation approach proposed in this thesis focuses on stable estimation results for any type of event sampling strategy. This means that a bounded error-covariance is attained by performing an update on the estimation results not only at the instants of an event, when a new measurement is available, but also synchronously in time when no measurement is received. In the latter case, the update is based on the inherent property of event sampling that not receiving a new measurement still gives information of the current sensor value. After an in-depth study, the proposed event based state-estimator is further integrated with a feedback control system to create a new type of event based controller. The distinguishing property of this set-up, i.e., an event based estimator prior to a time synchronous controller, is that stability of the controlled system is decoupled from the event sampling strategy. To that extent, the results of the event based state-estimator are interpreted by an integration procedure, so that the employed controller (robust MPC) can optimize disturbance rejection depending on estimation errors. Communication and computational limitations in sensor networks are somewhat different. These types of networked systems consist of a large amount of so called ‘sensor nodes’ that are spatially distributed to monitor large-area processes. Some practical aspects, which prevent that the networked system is deployed with a large amount of wires, imply that sensor nodes are battery powered and exchange data via a radio. The communication range (or distance) of nodes is often limited, as it consumes too much energy, while the raised computational limitations are caused by the fact that a single node is not able to process all measurements produced by the sensor network. Therefore, distributed solutions for state estimation are being developed, in which each node typically computes a local estimate of the state based on its own measurement and on the data received from neighboring nodes. Some main drawbacks of current solutions is that they focus on minimizing the estimation error per node individually and further, impose strict requirements on shared data which are likely to be violated by system changes occurring in sensor networks. To solve these issues, the second estimation strategy proposed in this thesis does not focus on individual estimator at each node but aims to establish a cooperation in this network of estimators. Cooperation means that neighboring nodes share data not only to synchronize their estimation results but, more importantly, to reduce the (modeled) estimation error. In the proposed set-up each node employs a state estimation method locally, e.g., the (unscented) Kalman filter, to estimate the state based on its own measurement. This estimation result is then shared with neighboring nodes as input to a state fusion method, which computes a fused estimate of the state. A novel fusion method is developed for merging two of these estimates, such that the modeled estimation error (error-covariance) after fusion is reduced. A fulfillment of this property guarantees that the estimation error of each node in the network is in line with the smallest estimation error found across its nodes. Furthermore, the proposed distributed estimation approach is assessed in a comprehensive overview on distributed Kalman filtering. To that extent, the widely scattered solutions on this topic that were proposed in various research communities are studied in two real-life inspired case studies. The thesis concludes with the main contributions of the presented research, followed by ideas for future investigation.