Estimation, Decision and Applications to Target Tracking

This dissertation mainly consists of three parts. The first part proposes generalized linear minimum mean-square error (GLMMSE) estimation for nonlinear point estimation. The second part proposes a recursive joint decision and estimation (RJDE) algorithm for joint decision and estimation (JDE). The third part analyzes the performance of sequential probability ratio test (SPRT) when the log-likelihood ratios (LLR) are independent but not identically distributed. The linear minimum mean-square error (LMMSE) estimation plays an important role in nonlinear estimation. It searches for the best estimator in the set of all estimators that are linear in the measurement. A GLMMSE estimation framework is proposed in this disser- tation. It employs a vector-valued measurement transform function (MTF) and finds the best estimator among all estimators that are linear in MTF. Several design guidelines for the MTF based on a numerical example were provided. A RJDE algorithm based on a generalized Bayes risk is proposed in this dissertation for dynamic JDE problems. It is computationally efficient for dynamic problems where data are made available sequentially. Further, since existing performance measures for estimation or decision are effective to evaluate JDE algorithms, a joint performance measure is proposed for JDE algorithms for dynamic problems. The RJDE algorithm is demonstrated by applications to joint tracking and classification as well as joint tracking and detection in target tracking. The characteristics and performance of SPRT are characterized by two important functions—operating characteristic (OC) and average sample number (ASN). These two functions have been studied extensively under the assumption of independent and identically distributed (i.i.d.) LLR, which is too stringent for many applications. This dissertation relaxes the requirement of identical distribution. Two inductive equations governing the OC and ASN are developed. Unfortunately, they have non-unique solutions in the general case. They do have unique solutions in two special cases: (a) the LLR sequence converges in distributions and (b) the LLR sequence has periodic distributions. Further, the analysis can be readily extended to evaluate the performance of the truncated SPRT and the cumulative sum test

Image processing and pattern recognition for industrial robotic vision

Imperial Users onl

Application of statistical decision theory to the detection of radiotelegraph signals

Imperial Users onl

Statistical Tests of the Rank of a Matrix and Their Applications in Econometric Modelling

Testing the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics literature where these tests are required.Multiple time series, Model specification, Tests of rank

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

Statistical inverse problems for population processes

Population processes are stochastic processes that record the dynamics of the number of individuals in a population, and have many different applications in a broad range of areas. Population processes are often modelled as Markov processes, and have the important feature that transitions correspond either to an increase or a decrease in the population size. These two types of transitions are often referred to as births and deaths. A specific class of population processes is the class of birth-death processes, where transitions can only increase or decrease the population by one at a time. In many real-life situations the dynamics of a population is affected by exogenous, often unobservable, factors. Therefore, this thesis considers population processes of which the parameters are affected by an underlying stochastic process, referred to as the background process. The aim is to find reliable inference techniques to estimate the parameters, including those related to the background process, from discrete-time observations of the population size. The statistical inference is complicated severely by the fact that a substantial part of the process is unobserved. First, the underlying background process is not observed. Second, only the population size is observed, which is the net effect of all the transitions in the dynamics of the population. Last, the population size is observed in discrete time, hence the transitions in between two consecutive observations are not observed. In this thesis we show a collection of techniques to overcome these complications for a variety of population processes. The aspects in which the models differ, ask for specific inference techniques. For a certain class of Markov-modulated population processes, we show how the well-known EM algorithm can be used to estimate the model parameters. In these models, the background process is a finite, continuous-time Markov chain and the parameters of the population process switch between distinct values at the jump times of this Markov chain. An algorithm is presented that iteratively maximizes the likelihood function and at the same time updates the parameter estimates. A generalization of the conventional birth-death process, involving a background process, is the quasi birth-death process. We use the Erlangization technique to evaluate the likelihood function for this kind of processes, which can then be maximized numerically to obtain maximum likelihood estimates. A specific model in the class of quasi birth-death processes is a birth-death process of which the births follow a hypoexponential distribution with L phases and are controlled by an on/off mechanism. We call this the on/off-seq-L process, and use it to model the dynamics of populations of mRNA molecules in single living cells. Numerical complications related to the likelihood maximization are analyzed and solutions are presented. Based on real-life data, we illustrate the estimation method, and perform a model selection procedure on the number of phases and on the on/off mechanism. Last, we consider a class of discrete-time multivariate population processes under Markov-modulation. In these models, the population process is defined on a network with finitely many nodes. In addition to the births and deaths that can occur at each of the nodes, the individuals follow a probabilistic route through the network. We introduce the saddlepoint technique and show how it can be used to evaluate the likelihood function based on observations of the network population vector. The likelihood function can again be maximized numerically to obtain maximum likelihood estimates. Throughout the thesis, the accuracy of the inference methods is investigated by extensive simulation studies

Control of Finite-State, Finite Memory Stochastic Systems

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems