Development of Optimal Kalman Consensus Filter and its Application to Distributed Hybrid State Estimation

Raj Deshmukh, Purdue University

Abstract

Following recent advances in networked communication technologies, sensor networks have been employed in a broad range of applications at a lower cost than centrally supervised systems. Their major functionality is to track and monitor dynamic processes using various distributed estimation techniques. Specifically, we conduct a study of the process of concurrence between agents for the state of a system. This process of concurrence is known as `consensus', and is exhibited in the distributed Kalman Consensus Filter (KCF). This estimation algorithm fuses data from different connected sensor agents by achieving two objectives for each sensor: 1) locally estimating the state of the system; and 2) reaching a consensus of the state estimate between neighboring agents through communication. Although the conventional KCF has been proven to have superior performance in terms of stability and scalability, it relies on the approximated suboptimal consensus gain to avoid algorithmic and derivational complexity. Particularly, we seek to address this concern of sub-optimality, and analytically derive the closed form solution to the globally optimal consensus gain, which is characterized by the minimum mean squared error for the estimation process. We then expand the perspective of the system dynamics to evolve in a hybrid fashion. Hybrid dynamical systems can describe a larger class of dynamics, as the state evolution is given as a combination of differential equations and discrete state (mode) transition maps. The latter part of this thesis focuses on developing a distributed hybrid estimation algorithm that builds upon the concept of the multiple model based algorithm for state estimation of stochastic hybrid systems. While previous studies have used Kalman filtering for the bank of estimators that the conventional multiple model based algorithm employs, in this research, we use a distributed network to leverage the redundancy in a network and use the measurement data available to compute the state of the system, by using the developed optimal KCF algorithm. Essentially, the hybrid estimator uses the mode-conditioned KCF, that relies on mode-specific pairwise residues among agents to compute the observer state and covariance updates. The performance of the proposed optimal KCF scheme, and its comparison to the conventional centralized and suboptimal forms are demonstrated via illustrative numerical examples. Further simulations are presented to demonstrate the application of the developed KCF for distributed hybrid estimation.

Degree

M.S.

Advisors

Hwang, Purdue University.

Subject Area

Engineering|Aerospace engineering

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