The paper begins with a review of the algebras related to Kronecker products. These algebras have several applications in system theory including the analysis of stochastic steady state. The calculus of matrix valued functions of matrices is reviewed in the second part of the paper. This calculus is then used to develop an interesting new method for the identifiication of parameters of lnear time-invariant system models.

Kronecker products and matrix calculus in system theory

The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

/pdf/handbook-of-marine-craft-hydrodynamics-and-motion-control-2qu7epb0pt.pdf

Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control

Probabilistic inference is the problem of estimating the hidden variables (states or parameters) of a system in an optimal and consistent fashion as a set of noisy or incomplete observations of the system becomes available online. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive. This posterior density constitutes the complete solution to the probabilistic inference problem, and allows us to calculate any “optimal” estimate of the state. Unfortunately, for most real-world problems, the optimal Bayesian recursion is intractable and approximate solutions must be used. Within the space of approximate solutions, the extended Kalman filter (EKF) has become one of the most widely used algorithms with applications in state, parameter and dual estimation. Unfortunately, the EKF is based on a sub-optimal implementation of the recursive Bayesian estimation framework applied to Gaussian random variables. This can seriously affect the accuracy or even lead to divergence of any inference system that is based on the EKF or that uses the EKF as a component part. Recently a number of related novel, more accurate and theoretically better motivated algorithmic alternatives to the EKF have surfaced in the literature, with specific application to state estimation for automatic control. We have extended these algorithms, all based on derivativeless deterministic sampling based approximations of the relevant Gaussian statistics, to a family of algorithms called Sigma-Point Kalman Filters (SPKF). Furthermore, we successfully expanded the use of this group of algorithms (SPKFs) within the general field of probabilistic inference and machine learning, both as stand-alone filters and as subcomponents of more powerful sequential Monte Carlo methods (particle filters). We have consistently shown that there are large performance benefits to be gained by applying Sigma-Point Kalman filters to areas where EKFs have been used as the de facto standard in the past, as well as in new areas where the use of the EKF is impossible.

/pdf/sigma-point-kalman-filters-for-probabilistic-inference-in-1affrc62j6.pdf

Sigma-point kalman filters for probabilistic inference in dynamic state-space models

This is the fifth part of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I and Part II deal with target motion models. Part III covers measurement models and associated techniques. Part IV is concerned with tracking techniques that are based on decisions regarding target maneuvers. This part surveys the multiple-model methods $the use of multiple models (and filters) simultaneously - which is the prevailing approach to maneuvering target tracking in recent years. The survey is presented in a structured way, centered around three generations of algorithms: autonomous, cooperating, and variable structure. It emphasizes the underpinning of each algorithm and covers various issues in algorithm design, application, and performance.

Survey of maneuvering target tracking. Part V. Multiple-model methods

/pdf/statistical-theory-of-communication-4wy4yg9ato.pdf

Statistical Theory of Communication

This paper describes a computer-based, dynamic positioning system for floating vessels. The system is based on a detailed mathematical model of vessel motion in response to forces from thrusters, wind, waves and water current. The system uses a Kalman filter for optimal estimation of vessel motions and environmental forces from wind, waves and current. The control system is based on feedback from the motion varibles where the oscillatory, wave-induced component is removed by the estimator. Feedback from the water current estimate provides the integral action of the system, and feed forward from the wind force estimates are implemented. Simulation results and recordings from actual operation of the system indicate an excellent system performance.

/pdf/a-dynamic-positioning-system-based-on-kalman-filtering-and-2it45f4jlf.pdf

A Dynamic Positioning System Based on Kalman Filtering and Optimal Control

-A novel adaptive filtering technique is described for a class of systems with unknown disturbances. The estimator includes both a self-tuning filter and a Kalman filter. The state estimates are employed in a closed-loop feedback control scheme wbich is designed via the usual linear quadratic approach. The approach was developed for application to the dynamic ship positioning control problem and has the advantage that existing nonadaptive Kalman filtering systems may be easily modified to include the self-tuning feature. work was supported b\\l GEC Electrical Projects Ltd., and the United Manuscript received April 21, 1982: revised September 27, 1982. This Kingdom Science and Engineering Research Council. P. T.-K. Fung \\vas with the Department of Electrical Engineering, University of Strathclyde, Glasgow, Scotland. He is now with the Space and Electronic Group, Spar Aerospace Ltd.. Weston. Ont.. Canada. vrrsity of Strathclyde. Glasgow, Scotland. M. J. Grimble is with the Department of Electrical Engineering, Uni

Design and analysis of a dynamic positioning system based on Kalman filtering and optimal control

This paper describes computer-based, dynamic positioning system for floating vessels. The system is based on a detailed mathematical model of vessel motion in response to forces from thrusters, wind, waves and water current. The system uses a Kalman filter for optimal estimation of vessel motions and environmental forces from wind, waves and current. The control system is based on feedback from the motion variables where the oscillatory, wave-induced component is removed by the estimator. Feedback from the water current estimate provides the integral action of the system and feed forward from the wind force estimates are implemented. Simulation results and recordings from actual operation of the system indicate an excellent system performance. Reference is given to installations made on actual vessels.

Dynamic positioning of floating vessles based on Kalman filtering and optimal control

Automatic control: theory and structures. Process systems and process models. Process control of basic functions. Process control of the common unit processes. Process control in large industrial complexes.

Process Control: Structures and Applications

https://www.mic-journal.no/PDF/1992/MIC-1992-2-2.pdf

Jens G. Balchen

Papers

A Dynamic Positioning System Based on Kalman Filtering and Optimal Control

Design and analysis of a dynamic positioning system based on Kalman filtering and optimal control

Dynamic positioning of floating vessles based on Kalman filtering and optimal control

Process Control: Structures and Applications

State-space predictive control