Research

My academic research focuses on the areas of

  • Radar signal processing: adaptive filtering, covariance matrix estimation, and waveform design

  • Compressed sensing: Application to clutter interference, low-rank matrix approximation, and compressed detection

  • Target tracking: data association, track filtering, and information fusion

Several publications from this work are listed below.

Compressed Sensing & Radar

My principal area of research is compressed sensing applied to radar. Compressed sensing is a recently formalized concept that shows how sparse vectors can be efficiently and accurately estimated from a small number of random projections. This can be readily applied to acquisition of bandlimited continuous time signals from samples at less than the Nyquist sampling rate. The conditions for success are:

  1. The signal must be sparse or sparsifiable in some basis.

  2. The means of acquisition must be uncorrelated with the sparsifying basis.

My work has focused on describing and advancing the ability of compressed sensing algorithms to perform radar tasks like target detection in the presence of interference and error sources commonly met in real-world radar sensing problems. Papers I've published include:

  1. Sensor Calibration Errors in Compressive Distributed-Aperture Radar Sensing (pdf, link, bibtex): A study of how compressed sensing behaves in a setting with model error (multiplicative noise).

  2. Compressed Sensing Radar Amid Noise and Clutter (paper pdf, slides pdf, link, bibtex): A study of the behavior of established compressed sensing algorithms behave in the presence of measurement clutter, and a proposed solution technique to use the clutter covariance matrix to improve detection performance.

  3. Compressed Sensing Radar Amid Noise and Clutter Using Interference Covariance Information (pdf, link, bibtex): A more complete development of previous results from the previous work including comparison to established STAP methods and discussion of the impact of measurement type and quantity on performance. Published in IEEE Transactions on Aerospace and Electronic Systems.

  4. Detection Performance from Compressed Measurements (paper pdf, slides pdf, bibtex): An experiment illustrating the limitations of some compressed sensing algorithms when judged using useful detection criteria including probability of detection and probability of false alarm.

  5. Adaptive Filtering in CS for Structured Interference Suppression (link, bibtex): An invited keynote talk at NATO specialists' meeting SET-213 on how multi-dimensional radar data can be simultaneously compressed via random projections and exploited for estimation of the interference covariance.

  6. Estimating Clutter Covariance from Compressed Measurements with Low-Rank Matrix Approximation: A paper submitted to IEEE Transactions on Aerospace and Electronic Sensing that develops and tests an algorithm, based on singular value thresholding, for estimating the interference covariance from compressed measurements.

  7. Using Random Matrix Theory to Improve Radar Space-Time Adaptive Processing (link): A paper give at the 2017 Asilomar Conference on Signals, Systems, and Computers showing the utility of the Marcenko-Pastur distribution for selecting rank reduction and diagonal loading in STAP.

  8. Sample Covariance Eigenvalue Distribution (link, bibtex): A software package that calculates the spectral density for Wishart matrices, including sample covariance matrices. This has application in adaptive filtering and other fields of science and engineering.

  9. Clutter Rejection and Adaptive Filtering in Compressed Sensing Radar (link): A book chapter providing a theoretical basis and several example algorithms for adaptive processing in the context of compressed sensing.

  10. Compressed Sensing in Radar with Structured Interference (link): My dissertation collecting many of these results together into a single work.

Target Tracking

Another area in which I've done some work is multi-target tracking. Topics of interest include multiple-hypothesis tracking as well as track correlation, fusion, and association. Publications in this field include:

  1. A Comparison of Semi-Greedy Multiple Hypothesis Methods in the Radar Data Association Problem (pdf, link, bibtex): A paper to be presented at the 2014 IEEE Aerospace Conference on the performance of semi-greedy solutions to data association problems encountered in multiple hypothesis and other multi-target tracking settings.

  2. Adaptive semi-greedy search for multidimensional track assignment (link, bibtex): A paper to be presented at the 2016 FUSION Conference on the performance of adaptive semi-greedy search for improving on prior sub-optimal assignment algorithms.