Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

A method of using magnetic torque rods to do 3axis spacecraft attitude control has been developed. The goal of this system is to achieve a nadir pointing accuracy on the order of 0.1 to 1.0 deg without the need for thrusters or wheels. The open-loop system is under-actuated because magnetic torque rods cannot torque about the local magnetic field direction. This direction moves in space as the spacecraft moves along an inclined orbit, and the resulting system is roughly periodic. Periodic controllers are designed using an asymptotic linear quadratic regulator technique. The control laws include integral action and saturation logic. This system's performance has been studied via analysis and simulation. The resulting closed-loop systems are robust with respect to parametric modeling uncertainty. They converge from initial attitude errors of 30 deg per axis, and they achieve steady-state pointing errors on the order of 0.5 to 1.0 deg in the presence of drag torques and unmodeled residual dipole moments.

Magnetic Torquer Attitude Control via Asymptotic Periodic Linear Quadratic Regulation

Traffic flow optimization

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date, one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective, which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics U+0028 e.g., mean and covariance U+0029 conditioned on a system U+02BC s measurement data. This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering U+0028 KF U+0029 techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter U+002F input estimation.

Nonlinear Bayesian estimation: from Kalman filtering to a broader horizon

Estimations of on-site directional wave spectra from measured ship responses

Estimating directional wave spectrum based on stationary ship motion measurements

The problem of tuning stabilizers in multimachine power systems has been formulated here as a sequence of optimization problems. Both quadratic and linear programming problems have been considered. In the former case, stabilizers with complex zeros have been included in the compensator model. In each case a particular measure of the stabilizers' gain has been defined. The constraints have been written to represent the region allowed for eigenvalue shifting together with specific constraints. The objective has been to shift the lightly damped eigenvalues associated to the system electromechanical modes. The results have shown that the quadratic programming formulation may be an important auxiliary tool for stabilizers tuning.

An incremental approach to the coordinated tuning of power systems stabilizers using mathematical programming

Complete offline tuning of the unscented Kalman filter

This paper uses the extended Kalman filter (EKF) for estimation of position, velocity and attitude of an UAV of quadrotor type. The sensors used are low cost microelectromechanical systems (MEMS) accelerometer and gyroscope, MEMS barometer and GPS. The standard EKF is improved with adaptive approaches. Two innovation adaptive estimation methods were taken from the literature. One involves the change of the theoretical matrix of the innovation covariance, by another one which is determined experimentally; the second one involves the computation of the output noise covariance matrix of the Kalman filter (KF) via fuzzy logic. A new method for adaptive estimation was also developed by extending an approach of heuristic metrics of bias and amplitude of oscillation taken from the literature. It consists in the use of the metrics, together with fuzzy logic, for adjusting the input and output noise covariance matrices of the EKF. The adaptive and standard filters were both implemented in hardware and simulated. The hardware implementation involves rotation filters in indoor tests performed in open loop; these observations were exclusively carried out in a hand-controlled environment, with no flight of the quadrotor itself. The simulations were performed in conditions of the full capability of the filters, in a scenario representing a fault condition in the gyroscope. The tests showed the ability of the adaptive filters of correcting the covariance matrix for improving performance.

Fuzzy adaptive extended Kalman filter for UAV INS/GPS data fusion

This work presents the application of linear matrix inequalities to the optimal adjustment of power system stabilizers with pre-defined structure, much common in the power industry. Results of some tests show that gain and zeros adjustments are sufficient to guarantee power systems robust stability and performance with respect to various points of operation. Making use of the flexible structure of LMI's, we propose an algorithm that permits one to choose in the compromise between low gain and high damping factor. The technique used here is the pole placement design together with gain limitation, which places the poles of the closed loop system in a specific region of the complex plane. Results of tests with a nine-machine system (New England-New York) are presented and discussed, in order to validate the algorithm proposed

José Jaime da Cruz

Papers

Estimating directional wave spectrum based on stationary ship motion measurements

An incremental approach to the coordinated tuning of power systems stabilizers using mathematical programming

Complete offline tuning of the unscented Kalman filter

Fuzzy adaptive extended Kalman filter for UAV INS/GPS data fusion

Pole Placement and Robust Adjustment of Power Systems Stabilizers through Linear Matrix Inequalities