Nonlinear State Estimation Algorithms and their Applications

State estimation is a process of estimating the unmeasured or noisy states using the measured outputs and control inputs along with process and measurement models. The extended Kalman filter (EKF) has been an important approach for nonlinear state estimation over the last five decades. However, EKFs are only suitable for ‘mild’ nonlinearities where the first-order approximations of the nonlinear functions are available and they also require evaluation of state and measurement Jacobians at every iteration. This thesis presents a few linear and nonlinear state estimation methods and their applications. To start with, we investigate the use of the linear H∞ filter, which can deal with non-Gaussian noises, in a control application. The efficacy of the linear H∞ filter based sliding mode controller is verified on a quadruple tank system. The main tools for nonlinear state estimation are cubature Kalman filter (CKF) and its variants. A solution to simultaneous localisation and mapping (SLAM) problem using CKF is proposed. The effectiveness of the nonlinear CKF-SLAM over EKF- and UKF-SLAM is demonstrated. We propose a couple of new nonlinear state estimation algorithms, namely, cubature information filters (CIFs) and cubature H∞ filters (CH∞Fs), and their square root versions. The CIF is derived from an extended information filter and a CKF. The CIF is further extended for use in multi-sensor state estimation and its square root version is derived using a unitary transformation. For non-linear and non-Gaussian systems, we fuse an extended H∞ filter and CKF to form CH∞F which has the desirable features of both CKF and an extended H∞ filter. Further, we derive a square root CH∞F using a J-unitary transformation for numerical stability. The efficacies of the proposed algorithms are evaluated on simulation examples.