Optimal Sensing for Filtering with Bounded Errors

Abstract

We address the problem of designing optimal sensing strategy for stochastic discrete- time systems. Sensors are an integral part of a system, providing knowledge about system states, through state filtering. The problem of designing optimal sensing, primarily addresses questions regarding, a) which type of sensor do we need, b) how accurate sensors do we need, and c) when and d) where do we use them. The desired performance of an optimal sensing strategy might also include minimizing energy consumption and total cost of operation or maximizing sensing accuracy or control performance, among various other metrics. Upper bounding and lower bounding the performance of a sensing strategy is tied to the notion of utility and privacy of the filtered system. The main contributions of this research are the formulations of algo- rithms and theorems that gives a structured way to manipulate sensing parameters to ensure either utility of the filtering system or privacy against the filtering system. To this end we show results on privacy and utility for Kalman Filter, Ensemble Kalman Filter, and Unscented Kalman Filter. The development of optimal sens- ing for Ensemble Kalman Filter and Unscented Kalman Filter is motivated by the space situational awareness problems regarding allocating sensing resources as well as exchanging data. The proposed contributions of this research are organized as follows. First we show preliminary results on optimal sensing for Ensemble Kalman Filter, and Unscented Kalman Filter, focusing on the utility problem. Next we address the utility and pri- vacy problem for Kalman Filter in steady state scenario using Eigen-values analysis. We then move on to the utility problem for Kalman Filter for single-step, muti-step scenario. Finally, the utility and privacy formulations for Ensemble Kalman Filter, and Unscented Kalman Filter are further developed with a focus on addressing space situational awareness problems.