This book is downloadable from http://www.irisa.fr/sisthem/kniga/. Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs.

Detection of abrupt changes: theory and application

https://ntrs.nasa.gov/api/citations/19760004259/downloads/19760004259.pdf

Paper: A survey of design methods for failure detection in dynamic systems

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

We consider a class of stochastic linear systems that are subject to jumps of unknown magnitudes in the state variables occurring at unknown times. This model can be used when considering such problems as estimation for systems subject to possible component failures and the tracking of vehicles capable of abrupt maneuvers. Using Kalman-Bucy filtering and generalized likelihood ratio techniques, we devise an adaptive filtering system for the detection and estimation of the jumps. An example that illustrates the dynamical properties of our filtering scheme is discusssed in detail.

A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems

Detection of Abrupt Changes: Theory and Applications.

Adaptive control of linear stochastic systems

An adaptive approach is presented for optimal estimation of a sampled stochastic process with finite-state unknown parameters. It is shown that for processes with an implicit generalized Markov property that the optimal (conditional mean) state estimates can be formed from (i) a set of optimal estimates based on known parameters, and (ii) a set of "learning" statistics which are recursively updated. The formulation thus provides a separation technique which simplifies the optimal solution of this class of nonlinear estimation problems. Examples of the separation technique are given for prediction of a non-Gaussian Markov process with unknown parameters and for filtering the state of a Gauss-Markov process with unknown parameters. General results are given on the convergence of optimal estimation systems operating in the presence of unknown parameters. Conditions are given under which a Bayes optimal (conditional mean) adaptive estimation system will converge in performance to an optimal system which is "told" the value of unknown parameters.

Optimal estimation in the presence of unknown parameters

For the non-linear estimation problem with non-linear plant and observation models, white gaussian excitations and continuous data, the state-vector a posteriori probabilities for prediction and smoothing are obtained via the 'partition theorem'. Moreover, for the special class of non-linear estimation problems with linear models excited by white gaussian noise, and with non-gaussian initial state, explicit results are obtained for the a posteriori probabilities, the optimal estimates and the corresponding error-covariance matrices for filtering, prediction and smoothing. In addition, for the latter problem, approximate but simpler expressions are obtained by using a gaussian sum approximation of the initial state-vector probability density. As a special case of the above results, optimal linear smoothing algorithms are obtained in a new form.

Optimal non-linear estimation†

Recent results of Middleton and Esposito (1968) and Lainiotis (1969) on single-shot joing detection-estimation for discrete data are extended to the single-shot continuous data case and generalized to joint Bayesian detection-estimation-system identification. Moreover, previous results were generalized to the case of causal estimator. Specifically, it is shown that the above problem constitutes a class of nonlinear mse estimation problems, with the attendant difficulties in realizing the optimal nonlinear estimators. However, by utilizing the adaptive approach, closed form integral expressions are given. These are given in terms of the generalized likelihood ratio gλ(t) , which is a sufficient statistic for Bayes-optimal compound detection. The latter in turn is specified by a continuum (for continuous θ ) θ -conditional likelihood ratious λ(t/θ) each of which is the LR for testing for the model specified by the parameter value θ . The latter LR's are, moreover, given in terms of optimal mse causal estimators. In essence then, it has been shown that system identification is equivalent to multihypothesis testing, with a continuum or finite sequence of hypotheses, respectively, for continuous or finite discrete range of θ .

Joint detection, estimation and system identification

The recent results of Lainiotis (1971 a, b, 1971) on single-shot, as well as multishot, joint detection, estimation and system identification for continuous data and dynamics are extended to multishot, discrete data and discrete dynamical systems. The results are given for the signals generated by the linear dynamical systems with unknown parameter vectors and driven by white gaussian sequences, where the observation contains additive white gaussian noise. Specifically, it is shown that the above problem constitutes a class of non-linear mean-square estimation problems. By utilizing the adaptive approach, closed-form integral expressions are obtained for simultaneously optimal detection, estimation and system identification. In addition, several approximate algorithms that utilize linear Kalman estimators are presented to limit the storage requirement to finite size and reduce computational requirements. The results presented in this paper are applicable to both independent and Markov signalling sources

Demetrios G. Lainiotis

Papers

Adaptive control of linear stochastic systems

Optimal estimation in the presence of unknown parameters

Optimal non-linear estimation†

Joint detection, estimation and system identification

On joint detection, estimation and system identification: discrete data case†