Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances

Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms

Discrete-time optimal preview control

There are many situations in which one can preview future reference signals, or future disturbances. Optimal Preview Control is concerned with designing controllers which use this preview to improve closed-loop performance. In this thesis a general preview control problem is presented which includes previewable disturbances, dynamic weighting functions, output feedback and nonpreviewable disturbances. It is then shown how a variety of problems may be cast as special cases of this general problem; of particular interest is the robust preview tracking problem and the problem of disturbance rejection with uncertainty in the previewed signal. . (', The general preview problem is solved in both the Fh and Beo settings. The H2 solution is a relatively straightforward extension ofpreviously known results, however, our contribution is to provide a single framework that may be used as a reference work when tackling a variety of preview problems. We also provide some new analysis concerning the maximum possible reduction in closed-loop H2 norm which accrues from the addition of preview action. / Name of candidate: Title of thesis: I DESCRIPTION OF THESIS Andrew Hazell Discrete-Time Optimal Preview Control The solution to the Hoo problem involves a completely new approach to Hoo preview control, in which the structure of the associated Riccati equation is exploited in order to find an efficient algorithm for computing the optimal controller. The problem tackled here is also more generic than those previously appearing in the literature. The above theory finds obvious applications in the design of controllers for autonomous vehicles, however, a particular class of nonlinearities found in typical vehicle models presents additional problems. The final chapters are concerned with a generic framework for implementing vehicle preview controllers, and also a'case study on preview control of a bicycle.Imperial Users onl

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Dynamic Network Reconstruction in Systems Biology: Methods and Algorithms

Dynamic network reconstruction refers to a class of problems that explore causal interactions between variables operating in dynamical systems. This dissertation focuses on methods and algorithms that reconstruct/infer network topology or dynamics from observations of an unknown system. The essential challenges, compared to system identification, are imposing sparsity on network topology and ensuring network identifiability. This work studies the following cases: multiple experiments with heterogeneity, low sampling frequency and nonlinearity, which are generic in biology that make reconstruction problems particularly challenging. The heterogeneous data sets are measurements in multiple experiments from the underlying dynamical systems that are different in parameters, whereas the network topology is assumed to be consistent. It is particularly common in biological applications. This dissertation proposes a way to deal with multiple data sets together to increase computational robustness. Furthermore, it can also be used to enforce network identifiability by multiple experiments with input perturbations. The necessity to study low-sampling-frequency data is due to the mismatch of network topology of discrete-time and continuous-time models. It is generally assumed that the underlying physical systems are evolving over time continuously. An important concept system aliasing is introduced to manifest whether the continuous system can be uniquely determined from its associated discrete-time model with the specified sampling frequency. A Nyquist-Shannon-like sampling theorem is provided to determine the critical sampling frequency for system aliasing. The reconstruction method integrates the Expectation Maximization (EM) method with a modified Sparse Bayesian Learning (SBL) to deal with reconstruction from output measurements. A tentative study on nonlinear Boolean network reconstruction is provided. The nonlinear Boolean network is considered as a union of local networks of linearized dynamical systems. The reconstruction method extends the algorithm used for heterogeneous data sets to provide an approximated inference but improve computational robustness significantly. The reconstruction algorithms are implemented in MATLAB and wrapped as a package. With considerations on generic signal features in practice, this work contributes to practically useful network reconstruction methods in biological applications

Adaptive filtering-based multi-innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi-innovation identification theory, an adaptive filtering-based multi-innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi-innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering-based multi-innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm

A framework for non-Gaussian signal modeling and estimation

"June 1999."Includes bibliographical references (p. [225]-240).Sponsored by the U.S. Air Force. F49620-96-1-0072 Supported by the U.S. Army Research Laboratory under Cooperative Agreement, DAAL01-96-2-001Shawn M. Verbout