Milestones

Research Objectives

• To develop a spectrum of computationally efficient state of the art conditional probability density and parameter  estimation algorithms that collectively solve the gamut of real time detection, tracking, path-space filtering,   prediction,and image processing problems based upon possibly incompletely determined predictive models.

• To advance the art of predictive modeling through increased realism, mathematical complexity, and efficient computer tractable approximations.

• To analyze, compare, and evaluate our algorithms and models on prototype problems suggested by our corporate sponsors or with real world applications.

• To promote the use of sophisticated mathematics in industry.

• To determine the additional skills necessary for graduates of the mathematical sciences to be sought by industry.     Subsequently, to train students accordingly.

• To develop a set of course materials to help train graduate students in applications of stochastic analysis.

Sub-Topics

• Develop and advance efficient, computer workable filtering algorithms;

• Develop combined parameter and state estimation algorithms for tracking, prediction and image processing;

• Create computer workable nonlinear filtering and estimation algorithms using our SERP, REST, IDEX and combined

• parameter-state estimation methods as well as other particle filter, convolutional, chaos, or Markov chain techniques.  Compare methods empirically on benchmark problems;

• Prove consistency and rates of convergence for the algorithms in 1) and 2);

• Develop prediction systems to control lighting, microphones, etc. for live theatre performers. (Acoustic Positioning Research problem);

• Improve model approximation and robustness;

• Generate filters for signals in random environments;

• Further basic filtering theory including uniqueness, particle representation, existence, and the innovations theorem.