Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.Comment: To appear in the IEEE Signal Processing Magazin

Bandwidth scaling behavior in wireless systems : theory, experimentation, and performance analysis

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 167-174).The need for ubiquitous wireless services has prompted the exploration of using increasingly larger transmission bandwidths often in environments with harsh propagation conditions. However, present analyses do not capture the behavior of systems in these channels as the bandwidth changes. This thesis: describes the development of an automated measurement apparatus capable of characterizing wideband channels up to 16 GHz; formulates a framework for evaluating the performance of wireless systems in realistic propagation environments; and applies this framework to sets of channel realizations collected during a comprehensive measurement campaign. In particular, the symbol error probability of realistic wideband subset diversity (SSD) systems, as well as improved lower bounds on time-of-arrival (TOA) estimation are derived and evaluated using experimental data at a variety of bandwidths. These results provide insights into how the performance of wireless systems scales as a function of bandwidth. Experimental data is used to quantify the behavior of channel resolvability as a function of bandwidth. The results show that there are significant differences in the amount of energy captured by a wideband SSD combiner under different propagation conditions. In particular, changes in the number of combined paths affect system performance more significantly in non-line-of-sight conditions than in line-of-sight conditions. Results also indicate that, for a fixed number of combined paths, lower bandwidths may provide better performance because a larger portion of the available energy is captured at those bandwidths. The expressions for lower bounds on TOA estimation, developed based on the Ziv-Zakai bound (ZZB), are able to account for the a priori information about the TOA as well as statistical information regarding the multipath phenomena. The ZZB, evaluated using measured channel realizations, shows the presence of an ambiguity region for moderate signal-to-noise ratios (SNRs). It is shown that in a variety of propagation conditions, this ambiguity region diminishes as bandwidth increases. Results indicate that decreases in the root mean square error for TOA estimation were significant for bandwidths up to approximately 8 GHz for SNRs in this region.by Wesley M. Gifford.Ph.D

A class of Weiss-Weinstein bounds and its relationship with the Bobrovsky-Mayer-Wolf-Zakai bounds

International audienceA fairly general class of Bayesian " large-error " lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized Bayesian Cramér-Rao bound (BCRB), is introduced. In a large number of cases, the generalized BCRB appears to be the Bobrovsky-Mayer-Wolf-Zakai bound (BMZB). Interestingly enough, a regularized form of the Bobrovsky-Zakai bound (BZB), applicable when the support of the prior is a constrained parameter set, is obtained. Modified Weiss-Weinstein bound and BZB which limiting form is the BMZB are proposed, in expectation of an increased tightness in the threshold region. Some of the proposed results are exemplified with a reference problem in signal processing: the Gaussian observation model with parameterized mean and uniform prior