The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

/pdf/unscented-filtering-and-nonlinear-estimation-44xbx5prtw.pdf

Unscented filtering and nonlinear estimation

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

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

Dynamic analysis of flexible manipulators, a literature review

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Stochastic Processes And Filtering Theory

The design of nonrobust and robust time-optimal controllers for linear systems in the frequency domain is presented. The bang-bang profile is represented as the superposition of time-delayed step inputs or the output of a time-delay filter subject to a step input. A parameter optimization problem is formulated to minimize the final time of the maneuver with the constraint that the time-delay filter cancels all of the poles of the system. The issue of robustness to errors in the model is addressed by placing multiple zeros of the time-delay filter at the estimated locations of the poles of the system. The design technique is illustrated on representative models of large space structures, for rest-to-rest, time-optimal, and robust time-optimal maneuvers. Spin-up maneuvers are shown to be special cases of the general formulation. IME-OPTIMAL control of flexible spacecraft is a topic of current interest.1 Many computational approaches and analyses have been presented in the recent literature to deal with the effects of flexibility. Most of these works deal with planar (singleaxis) rest-to-rest maneuvers under two categories: near-minimumtime control and exact-minimum-time control. The first category of methods is based on smooth approximations to minimum-time control for an equivalent rigid body. This class of methods has been shown to be well suited when applied moments or torques are produced by either throttlable thrusters or reaction wheels.2'3 Higher modes of the system are not excited due to the smoothness of the control profile. The second category of methods deals with on-off thrusters directly. Rajan4 formulates the problem including

/pdf/robust-time-optimal-control-frequency-domain-approach-4szlalemmo.pdf

Robust time-optimal control - Frequency domain approach

A Gaussian-mixture-model approach is proposed for accurate uncertainty propagation through a general nonlinear system. The transition probability density function is approximated by a finite sum of Gaussian density functions for which the parameters (mean and covariance) are propagated using linear propagation theory. Two different approaches are introduced to update the weights of different components of a Gaussian-mixture model for uncertainty propagation through nonlinear system. The first method updates the weights such that they minimize the integral square difference between the true forecast probability density function and its Gaussian-sum approximation. The second method uses the Fokker-Planck-Kohnogorov equation error as feedback to adapt for the amplitude of different Gaussian components while solving a quadratic programming problem. The proposed methods are applied to a variety of problems in the open literature and are argued to be an excellent candidate for higher-dimensional uncertainty-propagation problems.

Uncertainty propagation for nonlinear dynamic systems using gaussian mixture models

http://code.eng.buffalo.edu/jrnl/Rep_control_automatica.pdf

Brief paper: Design of noise and period-time robust high-order repetitive control, with application to optical storage

A method is presented to minimize residual vibration of structures or lightly damped servomechanisms. The method, referred to as the proportional plus multiple delay control, involves the use of multiple time delays in conjunction with a proportional part to cancel the dynamics of the system in a robust fashion. An interesting characteristic of the controller involves addition of a basic single time-delay control unit in cascade to the existing controller, for every additional requirement of robustness

Robust Time-Delay Control

Precise position control and rapid rest-to-rest motion is the desired objective in a variety of applications. The desire for reducing the maneuver time requires reducing the inertia of the structure which subsequently results in low frequency dynamics. The requirement of precise position control implies that the residual vibration of the structure should be zero or near zero. This paper presents techniques to shape the input to the system so as to minimize the residual vibration. A second class of problems which includes design of input profiles for systems with rigid-body modes driven by actuators with finite control authority, is also presented. The common thread which connects all the techniques presented in this paper is related to the design of controllers which are robust to modeling uncertainties. The proposed techniques are illustrated by simulations and experiments.

/pdf/tutorial-on-input-shaping-time-delay-control-of-maneuvering-2yz3il86ig.pdf

Tarunraj Singh

Papers

Robust time-optimal control - Frequency domain approach

Uncertainty propagation for nonlinear dynamic systems using gaussian mixture models

Brief paper: Design of noise and period-time robust high-order repetitive control, with application to optical storage

Robust Time-Delay Control

Tutorial on Input Shaping/Time Delay Control of Maneuvering Flexible Structures