Filtragem de kalman distribuída via predição por interação: contribuições teóricas e aplicações

Abstract

The problem of distributed Kalman filtering involves the technical challenge of migrating the well-established global Kalman filtering approach applied to complex large-scale dynamic systems with distributed measurements to simpler subsystems, without significantly compromising their performance. In this adaptation there are problems of asynotic convergence, definition of the stop criteria and the need for a fusion center that do not allow applications to be fully distributed. Thus, in this thesis two algorithms are proposed for the solution of distributed filtering problems in discrete time. These approaches use a hierarchical parallelization methodology that consists of a modification made in the structure of the calculation to decrease the dependency ratio of filter equations and decrease the convergence time. For this, algorithm 1 explores the duality between the filter and the control and applies the concepts of parametric decomposition via interaction prediction. Algorithm 2 also explores the aforementioned duality and applies the principles of convex optimization to obtain a static quadratic form with reduced dimensions, equivalent to the lagrangian associated with each subsystem, through regularization procedures, via regions of trust, without resorting to the Ricatti equations. Thus, it is possible by adjusting a scale parameter $\mu$ to obtain a family of efficient and well-conditioned solutions for each subsystem that can mitigate the impacts of process and measurement noises in the dynamic linear system. To highlight the advantages of the two proposed algorithms, five proof-of-concept examples and two other examples used in benchmarking studies are presented and discussed. In these examples, it is possible to analyze the execution time, conditioning of the system, obtain a family of gains for each subsystem, geometrically verify the robustness of the system according to the concept of matrix contraction and compare, through the mean squared error, the algorithms proposed with the state of the art in consensus-based distributed algorithms.