Distributed and Optimal State Estimation for Heterogeneous Dynamic Systems Operating Within a Strongly Connected Network

This dissertation is aimed at developing optimal and distributed state estimation algorithms for a team of cooperating nodes with the goal of improving accuracy through local sharing of relevant information. The nodes are assumed to be individually equipped with heterogeneous sensors for measuring a common target which can be dynamic and time-varying. Additionally, the nodes are assumed to be connected through a dynamically changing communication network modeled as a sequence of strongly connected digraphs allowing for local communication and distributed interactions. Using the data sharing afforded by the communication network, a weighted average state estimate consensus can be found across the neighboring nodes and then used to augment an optimized Kalman filter. Implementation of this consensus-based algorithm to nonlinear estimation approaches, like the Extended Kalman Filter, is also explored to broaden the range of applications. The presence of the state estimate consensus adds complexity to the covariance calculations by introducing cross-covariances among nodes. While these cross-covariances are found in previous work to be too difficult to handle (so they are either overestimated or ignored potentially leading to overly pessimistic or inconsistent estimators, respectively), their calculation through a distributed algorithm is one of the primary contributions of this research. The other contribution is to integrate distributed topology identification into cooperative Kalman filtering so time-varying topologies can be accommodated. These algorithms developed in this dissertation fully utilize the communication network to distribute the computational burden of maintaining these cross-covariances across the network so a truly distributed and optimized estimator can be achieved. The benefits of using these algorithms are highlighted in several examples involving the tracking of a dynamic mobile target utilizing nonlinear range and bearing measurements. Cooperative tracking by stationary and mobile nodes are shown to achieve large improvements in accuracy and robustness when compared to their decentralized counterparts