Lattice Kalman Filters: Theory and Applications
This thesis presents a new estimation strategy called the lattice Kalman filter (LKF) which is based on the nonlinear Kalman filtering framework and lattice rules. The proposed LKF algorithm uses the Korobov type (rank-1) lattice rule to deterministically generate sample points utilized to compute the multivariate integrals in the Gaussian filtering context. The mathematical formulation of the proposed LKF algorithm along with its error-bound propagation and error boundedness are discussed in this study. The main superiorities of the LKF over other sigma point filtering methods are its relatively low computational complexity while maintaining accuracy at an asymptotically same level. However, the LKF accuracy and robustness decline for the systems with a high level of nonlinearity and uncertainty. A second major contribution found within this thesis includes a robust version of the LKF formulated utilizing the relatively new sliding innovation filter (SIF), which resulted in a new filter called the sliding innovation lattice filter (SILF). Another contribution includes a derivative-free formulation of SILF which is developed using statistical linear regression to relax the requirement for Jacobian calculations to approximate the nonlinearities. A single-machine infinite bus (SMIB) power system was studied under a highly noisy environment, fault occurrence, and sequence of measurement outliers. Results demonstrate improvements in the proposed algorithms over the well-known unscented Kalman filter (UKF), standard LKF, and extended sliding innovation filter (ESIF). Finally, the proposed SILF is reinforced with the iterated sigma point filtering and strong tracking filtering strategies to further boost SILF’s accuracy, robustness, and convergence behavior against abrupt changes in the system model or parameters. This new robust formulation is referred to as reinforced LKF (RLKF). The RLKF was used to estimate the harmonic parameters of a power signal; the estimation results are compared with those obtained by some other well-known filters in terms of accuracy and robustness of the filters. Experimental results show that SILF and RLKF outperform other filters, particularly under model uncertainty and noisy environments.