On Analysis of Active Querying for Recursive State Estimation

In stochastic linear/non-linear active dynamic systems, states are estimated with the evidence through recursive measurements in response to queries of the system about the state to be estimated. Therefore, query selection is essential for such systems to improve state estimation accuracy and time. Query selection is conventionally achieved by minimization of the evidence variance or optimization of various information theoretic objectives. It was shown that optimization of mutual information-based objectives and variance-based objectives arrive at the same solution. However, existing approaches optimize approximations to the intended objectives rather than solving the exact optimization problems. To overcome these shortcomings, we propose an active querying procedure using mutual information maximization in recursive state estimation. First we show that mutual information generalizes variance based query selection methods and show the equivalence between objectives if the evidence likelihoods have unimodal distributions. We then solve the exact optimization problem for query selection and propose a query (measurement) selection algorithm. We specifically formulate the mutual information maximization for query selection as a combinatorial optimization problem and show that the objective is sub-modular, therefore can be solved efficiently with guaranteed convergence bounds through a greedy approach. Additionally, we analyze the performance of the query selection algorithm by testing it through a brain computer interface typing system.