Given a Gauss-Markov signal model that consists of a linear dynamical system driven by a white noise process, the Kalman filter provides the optimal linear least-mean-squares estimator for the system states. An important premise in Kalman filter theory is that the underlying state-space model is accurate. When this assumption is violated, the performance of the filter can deteriorate appreciably. This filter sensitivity to modelling errors has led to several works in the literature on the development of robust state-space filters; robust in the sense that they attempt to limit, in certain ways, the effect of model uncertainties on the overall filter performance.
In this thesis, we develop several robust filtering schemes that address some challenges posed by unmodelled dynamics, such as uncertainties arising from mixed deterministic and stochastic sources as well as state-delayed dynamics. We also develop certain multi-objective filters that are exponentially stable, guarantee bounded error covariance matrix, and meet an Hoo prescribed performance measure. We further develop and study a class of regularized robust filters that are particularly suited for real-time operations since they do not involve existence conditions.
The tools employed in the thesis for robust filter design are then applied to problems in wireless communications and wireless networks. Specifically, a robust receiver structure is developed for DS-CDMA systems by using robust estimation and post-correlation (i.e., symbol rate) processing for channel acquisition. The proposed receiver outperforms earlier structures in the presence of channel modelling errors, multiple access interference, and low SNR. In addition, robust schemes are developed for joint rate and power control in wireless networks. These schemes are pursued by formulating state-space models with and without uncertain dynamics and by designing control signals that meet certain performance criteria (such as robustness and desired levels of signal-to-interference ratio).
As such, the dissertation focuses both on the theoretical underpinnings of robust algorithms and on their applications in the context of wireless networks.
Acknowledgment This work was supported in part by the National Science Foundation under grants CCR-0208573 and ECS-0401188. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.