Gerald LaMountain PhD Proposal Review

Name:
Gerald LaMountain

Title:
On the Performance of Classical Estimation Under Adverse
Conditions

Date:
4/11/2024

Time:
12:00:00 PM

Location:
EXP 459

Committee Members:
Prof. Pau Closas (Advisor)
Prof. Deniz Erdogmus
Prof. Aanjhan Ranganathan

Abstract:
System designers across all disciplines of technology face the need to develop machines capable of independently processing and analyzing data and, in many cases, subsequently predicting future data. Over the past century, numerous approaches have been developed to perform this task, including those that fall under the umbrella of “classical statistics;” that is, those that employ probabilistic analyses to isolate relationships between variables and, in particular, “statistical estimation” wherein those variables are used to make inferences about real-world quantities. To fully leverage the bevy of established estimation algorithms, it is necessary to be able to evaluate the performance of a given estimator and, where possible, make changes to the methodology to improve its performance according to pertinent metrics. In the presence of ground-truth information, the accuracy of estimations can be evaluated a posteriori for a specific set of data. But what of future data which may not be associated with the same set of ground-truth information? In these cases, we require statistical generalizations about estimator behavior based on models of observed reality. In reality, these models are rarely fully representative of the reality of the observed and latent variables of interest. In such cases, there exists a “model misspecification,” and estimators which are designed based on such an imprecise model will produce results which differ from both properly specified estimators and the truth.

The overall objective of this thesis is to evaluate and expand upon state-of-the-art approaches to estimation and estimator analysis under various types of misspecification, including modeling errors that naturally occur as a result of the sensory environment, for example, unknown or variable observation noise. We contribute a method of Bayesian covariance estimation which, when embedded within the Kalman filter architecture, may be used to adapt to real-time changes in sensor performance while maintaining the recursive structure that allows the Kalman filter to be implemented in so many different applications. Furthermore, we investigated the efficacy of signal subspace algorithms (e.g. MUSIC) for performing multi-antenna radio direction finding, again in the presence of modelling errors. Although these algorithms are considered suboptimal (in the sense of the minimum mean squared error—MMSE) in finite time, their computational efficiency motivates their use in many different applications. Our analysis shows that under certain classes of model misspecification, the candidate algorithm for misspecified multiple signal classification (MMUSIC) performs asymptotically as well as the “gold standard” maximum likelihood estimator (MMLE) under the same misspecification. The final objective of this thesis is to combine the estimation bounds analysis we have applied to static estimation and extend it to dynamical systems. Although there exist established methods for evaluating and bounding the performance of estimators on misspecified models and dynamic models, there has been limited progress in establishing a standard for performing misspecified estimator analysis under dynamic conditions. Although this work is still ongoing, preliminary results are encouraging, suggesting that there are likely multiple approaches to this bounded analysis based around different objectives. Further results will be included in the final version of our work.