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

Developments in the theory of linear least-squares estimation in the last thirty years or so are outlined. Particular attention is paid to early mathematica[ work in the field and to more modern developments showing some of the many connections between least-squares filtering and other fields.

A view of three decades of linear filtering theory

In this expository paper, several approaches to Adaptive Filtering are discussed. The different methods are divided into four categories of (i) Bayesian Methods, (ii) Maximum Likelihood Methods, (iii) Correlation Methods, and (iv) Covariance-Matching Methods. The relationship between the methods and the difficulties associated with each method are described. New algorithms for the direct estimation of the optimal gain of a Kalman filter are given.

Approaches to adaptive filtering

In this paper, partitioning and the associated generalized partitioned estimation algorithms are shown to constitute a unifying and powerful framework for optimal adaptive estimation in linear as well as nonlinear problems. Using the partitioning framework, the adaptive estimation problem is treated from a global viewpoint that readily yields and unifies seemingly unrelated results and, most importantly, yields fundamentally new families of nonlinear and linear estimation algorithms in a decoupled parallel-realization form. The generalized partitioned estimation algorithms are shown to have several important properties from both a theoretical and a realization or computational standpoint.

Partitioning: A unifying framework for adaptive systems, I: Estimation

Optimal structure and parameter adaptive estimators have been obtained for continuous as well as discrete data gaussian process models with linear dynamics. Specifically, the essentially nonlinear adaptive estimators are shown to be decomposable (partition theorem) into two parts, a linear non-adaptive part consisting of a bank of Kalman-Bucy filters, and a nonlinear part that incorporates the learning or adaptive nature of the estimator. The conditional-error-covariance matrix of the estimator is also obtained in a form suitable for on-line performance evaluation. The adaptive estimators are applied to the problem of state-estimation with nongaussian initial state and also to estimation under measurement uncertainty (joint detection-estimation). Examples are given of the application of the proposed adaptive estimators to structure and parameter adaptation indicating their applicability to practical engineering problems.

Optimal adaptive estimation: Structure and parameter adaptation

For the nonlinear estimation problem with nonlinear 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 nonlinear estimation problems with linear models excited by white gaussian noise, and with nongaussian 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 nonlinear estimation

A class of upper bounds on the probability of error for the general multihypotheses pattern recognition problem is obtained. In particular, an upper bound in the class is shown to be a linear functional of the pairwise Bhattacharya coefficients. Evaluation of the bounds requires knowledge of a-priori probabilities and of the hypothesis-conditional probability density functions. A further bound is obtained that is independent of apriori probabilities. For the case of unknown apriori probabilities and conditional probability densities, an estimate of the latter upper bound is derived using a sequence of classified samples and Kernel functions to estimate the unknown densities.

A class of upper-bounds on probability of error for multi-hypotheses pattern recognition

A Bayesian approach to optimal adaptive estimation with continuous data is presented. Both structure and parameter adaptation are considered and specific recursive adaptation algorithms are derived for gaussian process models and linear dynamics. Specifically, for the class of adaptive estimation problems with linear dynamic models and gaussian excitations, a form of the "partition" theorem will be given that is applicable both for structure and parameter adaptation. The "partition" or "decomposition" theorem effects the partition of the essentially nonlinear estimation problem into two parts, a linear non-adaptive part consisting of ordinary Kalman estimators and a nonlinear part that incorporates the adaptive or learning nature of the adaptive estimator. In addition, a simple performance measure is introduced for the on-line performance evaluation of the adaptive estimator. The on-line performance measure utilizes quantities available from the adaptive estimator and hence a minimum of additional computational effort is required for evaluation.

D. Lainiotis

Papers

Optimal adaptive estimation: Structure and parameter adaptation

Optimal nonlinear estimation

A class of upper-bounds on probability of error for multi-hypotheses pattern recognition

Optimal adaptive estimation: Structure and parameter adaptation-Part I: Linear models and continuous data

Joint detection-Estimation of Gaussian signals in white Gaussian noise