Event Triggered Cubature Kalman Filter

Abstract

The Event-triggered state estimation problem has been at the forefront of systems research for several decades and has seen multiple successful applications in diverse areas such as signal processing, target tracking, and navigation systems. Event-triggered state estimation offers a promising solution to data traffic congestion, in which information between sensors and estimators, takes place aperiodically in an event-based manner. In this research, we tackle some practical problems encountered in this field and endeavor to improve the state of the art. In the first part, we develop the necessary theory to develop a discrete-time event-triggered cubature Kalman filter for nonlinear systems with noisy measurements. We show that the proposed filter offers excellent performance in the state estimation of the high dimensional nonlinear systems compared to the other previously proposed nonlinear filters which typically suffer from possible divergence, or curse of dimensionality. In addition, the proposed filter has bounded state estimation error while reducing the communication burden. In the next part of this research, we study the effect of the packet dropout in the transmission of information on the state estimator performance. Packet dropouts are caused by imperfect communication channels, and are therefore unavoidable when information is received by the filter via a communication network. We first develop the nonlinear filter to reduce the estimation error. Then we show that if the packet arrival rate is lower bounded, then the error covariance matrix is bounded. In addition, by properly tuning the value of the event-triggered threshold, one can guarantee the boundedness of the estimation error. Then, we consider the effect of transmission delay in the triggered measurement from the sensors to the remote nonlinear estimator. We first discuss the difficulties involved in dealing with time-delays in the context of state estimation and formulate the need for a new algorithm. Then we develop a proper nonlinear filter and show that by using the proposed event-triggered cubature Kalman filter, accurate estimates of the states can be achieved despite time delays, while reducing transmission of information between system and the filter. To show the advantages of the proposed filters, we evaluate the performance of the proposed filters applied to a synchronous machine. In the next part, we turn our attention to the developing of a nonlinear filter for more realistic scenario. We develop a nonlinear event-triggered adaptive filter for high dimensional nonlinear systems. The adaptive mechanism is important whenever there are sudden changes in the system states. We show that although the upper bound of the error covariance matrix and the estimation error could be affected, one can guarantee the convergence and the boundedness of the state estimation error by properly designing the nonlinear filter and tuning the event-triggered threshold value and the rate of the packet arrival. Finally, the effect of the transmission delay and the sudden changes of the states are considered and we develop a nonlinear filter for high dimensional nonlinear systems which could tackle these issues while reducing the amount of data transferring between the sensors and the remote state estimator.