Kalman filtering with synthetic measurements under an event-triggered sensor scheduler

This work studies the information update of the Kalman filter under a threshold-based event-triggered sensor scheduler designed to reduce the sensor-to-estimator communication cost while preserving estimation accuracy. For each sensor, when its normalized innovation is below a threshold required for data transmission (i.e., the sensor does not send measurements to the estimator), existing filtering algorithms extract this implicit information to update the estimation error covariance. However, when the low normalized innovations are insufficient indicators of the overall estimation accuracy, the state estimate may still need to be corrected. This occurs for example when the sensors directly measure only a subset of the full state vector. We propose a filtering algorithm to correct the state estimate in addition to the error covariance without requiring additional data transmission. The estimator performs the correction using synthetic measurements with bounded error compared to the true measurements, which are generated by the estimator. By correcting the estimate with synthetic measurements, the proposed filter can further reduce the estimation error at a small cost of error covariance inflation. We first show that the proposed filter is an approximate minimum mean square error estimator when the synthetic measurement is given. Second, the estimation error dynamics of the proposed filter is shown to be input-to-state stable, indicating that the estimation error is also small if the disparity between the synthetic and true measurements is small. Numerical experiments illustrate the evolution of the estimation error given by the proposed filter, and show the filter can improve the overall estimation accuracy. Supplementary source code is available at https://github.com/yesun/KFSMecc2016.