Set-Theoretic and Game-Theoretic Estimation

The first part of this dissertation is focused on parameter estimation problems where proper statistical description of the system uncertainties is not available. We develop adaptive filtering algorithms based on the set-membership filtering (SMF) framework which aims to upper bound the magnitude of filtering errors. Novel convergence results for the sequence of parameter estimates of the set-membership normalized least-mean squares (SM-NLMS) algorithm are established. Sufficient conditions are identified under which the sequence of parameter estimates of the SM-NLMS algorithm converges to the unknown true parameter almost surely. Utilizing the built-in selective update feature of the SM-NLMS algorithm, we develop an energy- and bandwidth-efficient diffusion scheme for distributed estimation problems. Furthermore, kernel methods are employed to extend two linear SMF algorithms to solve nonlinear adaptive filtering problems. These two proposed kernel SMF algorithms are equipped with several appealing features, including data-dependent selective update of filter parameter estimates without compromising MSE performance, sparse kernel expansions and asymptotically upper bounded filtering error magnitude.

The second part of this dissertation is concerned with crowdsensing applications where uncertainties arise due to the interactions of human participants who influence the system performance by adopting different strategies to meet their own interests. The challenges with regards to user participation and data quality are addressed by designing appropriate incentive mechanisms that encourage desired behaviors of the strategic agents. We solve the optimization problem of minimizing total payment to be made to strategic agents while ensuring a certain level of estimation accuracy. The proposed framework provides an insightful guideline for building cost-efficient crowdsensing platforms. Finally, we take a further step to address the problem of estimation in the presence of adversarial agents whose objective is to degrade the estimation accuracy. An optimal linear fusion scheme is presented to mitigate the effect of the adversarial attack. We show that when the attack of the adversarial agent is restricted, the estimator can obtain a better estimate by properly fusing the information from the adversarial agent rather than simply discarding it.