In many practical problems, both decision and estimation are involved. This dissertation intends to study the relationship between decision and estimation in these problems, so that more accurate inference methods can be developed. Hybrid estimation is an important formulation that deals with state estimation and model structure identification simultaneously. Multiple-model (MM) methods are the most widelyused tool for hybrid estimation. A novel approach to predict the Internet end-to-end delay using MM methods is proposed. Based on preliminary analysis of the collected end-to-end delay data, we propose an off-line model set design procedure using vector quantization (VQ) and short-term time series analysis so that MM methods can be applied to predict on-line measurement data. Experimental results show that the proposed MM predictor outperforms two widely used adaptive filters in terms of prediction accuracy and robustness. Although hybrid estimation can identify model structure, it mainly focuses on the estimation part. When decision and estimation are of (nearly) equal importance, a joint solution is preferred. By noticing the resemblance, a new Bayes risk is generalized from those of decision and estimation, respectively. Based on this generalized Bayes risk, a novel, integrated solution to decision and estimation is introduced. Our study tries to give a more systematic view on the joint decision and estimation (JDE) problem, which we believe the work in various fields, such as target tracking, communications, time series modeling, will benefit greatly from. We apply this integrated Bayes solution to joint target tracking and classification, a very important topic in target inference, with simplified measurement models. The results of this new approach are compared with two conventional strategies. At last, a surveillance testbed is being built for such purposes as algorithm development and performance evaluation. We try to use the testbed to bridge the gap between theory and practice. In the dissertation, an overview as well as the architecture of the testbed is given and one case study is presented. The testbed is capable to serve the tasks with decision and/or estimation aspects, and is helpful for the development of the JDE algorithms.

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.