The goal of this paper is to study a connection between the finite-horizon Kalman filtering and the LQR problems for discrete-time LTI systems. Motivated from the recent duality results on the LQR problem, a Lagrangian dual relation is used to prove that the Kalman filtering problem is a Lagrange dual problem of the LQR problem.

A deterministic least squares estimation theory of linear time-invariant systems is presented. It is demonstrated that the well-known Kalman filtering results can be obtained for purely deterministic systems with impulsive noises entering into every measurement. Applying known results from singular optimal control theory, the Kalman filtering results are extended to cases where some or all meas...

To my family, anna and ammu ACKNOWLEDGEMENT I would like to express my sincere indebtness and gratitude to my thesis advisor Dr. Dan Simon, for the ingenious commitment, encouragement and highly valuable advice he provided me over the entire course of this thesis. I would also like to thank my committee members Dr. Zhiqiang Gao and Dr. Sridhar Ungarala for their support and advice. I wish thank...

Support in R for state space estimation via Kalman filtering was limited to one package, until fairly recently. In the last five years, the situation has changed with no less than four additional packages offering general implementations of the Kalman filter, including in some cases smoothing, simulation smoothing and other functionality. This paper reviews some of the offerings in R to help th...

Kalman filtering has been widely considered for dynamic state estimation in smart grids. Despite its unique merits, the Kalman Filter (KF)-based dynamic state estimation can be undesirably influenced by cyber adversarial attacks that can potentially be launched against the communication links in the Cyber-Physical System (CPS). To enhance the security of KF-based state estimation, in this paper...

The paper deals with the Kalman filtering in the factorized form. The target application area is the urban traffic control, which main controlled variable – queue length, expressing the optimality of a traffic network most adequately, can not be directly observed and has to be estimated. Additional problem is that some state variables are of a discrete-valued nature. Thus, estimation of mixed-t...

Kalman Filtering is a computational tool with widespread applications in robotics, financial and weather forecasting, environmental engineering and defense. Given observation and state transition models, the Kalman Filter (KF) recursively estimates the state variables of a dynamic system. However, the KF requires a cubic time matrix inversion operation at every timestep which prevents its appli...

The problem of estimating the state vector of a dynamical system from vector measurements, when it is known that the state vector satisfies norm equality constraints is considered. The case of a linear dynamical system with linear measurements subject to a norm equality constraint is discussed with a review of existing solutions. The norm constraint introduces a nonlinearity in the system for w...