Optimal Estimation of Dynamic Systems

A distributed finite-time observer for linear systems

“…The problem of state estimation for dynamical systems has a long history of research and many extensions were obtained for various models: linear, nonlinear, switched, sampled, time-delay, etc., [1]- [4]. The majority of the proposed observers in all solutions aim to optimize essential properties in their design, such as robustness to measurement noises, overshooting of estimates, time of convergence, tolerance to model uncertainties and parametric errors [5], [6].…”

Performance Comparison of the Kalman Filter Variants for Dynamic Mobile Localization in Urban Area Using Cellular Network

“…for non-linear processes the Extended Kalman Filter (EKF) is the most widely used approach. The main concept of the EKF is the propagation of Gaussian random variables which approximates the state distribution through the first order linearization of the nonlinear model [13]. Therefore, the degree of accuracy of the EKF relies on the validity of the linear approximation and is not suitable for highly non-Gaussian conditional probability density functions, since it only updates the first two moments (mean and covariance) [13].…”

Terrain-Relative and Beacon-Relative Navigation for Lunar Powered Descent and Landing

“…Kalman published his original work in 1960 [19] and is now extremely well-known and welldocumented in the literature [20,21]. It provides an optimal method to take advantage of a priori models of the system and noisy, imperfect, asynchronous measurements from physical sensors to estimate the state of a system.…”

“…The 4-dimensional quaternion state,q i , is replaced by a 3-dimensional rotation vector state,θ i , and the quaternion kinematics are replaced by the Bortz equation [24]. The navigation state covariance update equation [20] is given bŷ…”