Approximate Supermodularity of Kalman Filter Sensor Selection

This article considers the problem of selecting sensors in a large-scale system to minimize error estimating its states, more specifically, state estimation mean-square (MSE) and worst-case for Kalman filtering smoothing. Such selection problems are general NP-hard, i.e., their solution can only be approximated practice even moderately large problems. Due low complexity iterative nature, greedy algorithms often used obtain these approximations by one sensor at time choosing each step that minimizes performance metric. When this metric is supermodular, guaranteed (1 - 1/e)-optimal. is, however, not case MSE or error. issue circumvented using supermodular surrogates, such as log det, despite fact minimizing det equivalent MSE. Here, addressed leveraging concept approximate supermodularity derive near-optimality certificates greedily In typical application scenarios, approach 1/e) guarantee obtained functions, thus demonstrating no change original needed good performance.