To date, I haven’t encountered a science-based field of study that is not interesting to me. But with that said, I certainly have developed a certain level of knowledge in more specific areas. Still broadly, these areas are statistical signal processing and contact tracking. I’ve found applications within these broad areas in beamforming and direction finding, passive and active sonar contact tracking, radar contact tracking, way-point navigation, unmanned underwater vehicle navigation, tracking and navigation waveform design, and tracking accuracy prediction.
The common theme of my research has generally been those areas most well-studied during graduate school; basis pursuit and Bayesian statistics. Admitting that I am not a world-class theorist and finding the intersection of theory and application very interesting, my work (at least so far) tends to stand on known well-developed theoretical foundations and implement pragmatic solutions to practical problems.
Within this page I will list any prior and current research in which I’ve at least conducted some level of analytical and simulatory study. I’ve chosen to include all such mentioned research (and not only that published) simply because I do not know where or when I may need to re-visit the research. A chronological listing of published research is included last.
Track-Before-Detect-Like Contact Localization in Complex Sonar Scenarios
As those close to the sonar contact localization problem know, classical measurement-to-track association (MTA) is a nightmare to handle in any automated way in the real world. While a large body of research has continued to try to work around, and with, MTA, a decade ago, track-before-detect algorithms began gaining popularity for localization which has the benefit of avoiding MTA entirely. MIKEL began looking at these algorithms about a decade ago with a deterministic selection of the particles. The algorithm performed very well but had some limitations when it needed to handle differing levels of uncertainties in input parameters. Also, I wasn't able to find any track-before-detect algorithms employed in scenarios where those working closely with sonar contact localization would be interested. All of the scenarios I saw were simple and experimental. So, I decided to employ one with real data that would challenge even the most advanced automation I knew available. The results were very good and I submitted them in . I am hoping that the results will gain the interest of those working closely with sonar contact localization.
Signal Estimation for Sensor Array Failure Resilience
Typically when an array of sensors experiences an element failure the failed element is simply excluded from signal processing processes. In this work I am examining an approach to replace the failed sensor with an estimate of its appropriate signal in the context of direction-of-arrival estimation using non-linear sensor arrays. The main concept of the approach is to describe the phase of the arriving signals at the functioning sensors with a polynomial of some order (e.g. 3) and to use the functioning sensors to estimate the coefficients of the phase polynomial using a DFT. With the coefficients estimated one can predict the signal at the failed sensors. I summarized the results and submitted them for publication in .
Spectral Extrapolation for Ultra-Wide Band Breast Tumor Localization
This work is an interesting extension of a spatial extrapolation technique used in one of my collaborator's student's dissertation for improved spatial discrimination with short linear arrays to increase a wireless network's capacity. The primary motivation in this work is to offer x-ray-like breast tumor localization but at UWB microwave frequencies. In my application I've used the technique in the temporal frequency domain to synthetically expand the bandwidth of an RF pulse to improve the localization accuracy of classical and contemporary beamforming methods. I found this work very gratifying as the extrapolation technique has many temporal and spatial applications. It should appear in the Biomedical Engineering Letters journal .
DNA Copy Number Profile Estimation
My lovely bride is close to adult oncology treatment and some of her stories are quite inspiring, and sometimes honestly, quite sad. After hearing one particular story, I was motivated to try my hand at providing an alternative solution to some area within cancer research. Realizing that cancer research is quite far afield for me, I understood my contribution would quite certainly be on the periphery of cancer research. But, nonetheless I am hoping my perspective may offer some new, albeit small, advance. Currently my focus is on estimating the DNA copy number profile of the human genome. Copy number aberrations measured in the gnome can be indicative of cancerous cell reproduction. However two challenges seem to be current. First, measurements with varying (and often high) noise can make estimating the copy number difficult. Second, the profile may have very few aberrant clones thwarting the ability to detect them among noisy measurements at all.
Automated UUV Contact Localization
Unmanned underwater vehicles (UUVs) are becoming increasingly capable and versatile. Modern navies are employing UUVs in a variety of tactical applications. However, the research literature seems a little sparse when looking for means to perform contact localization without a human in the loop. So, one of my research foci is in providing an approach to do so.
Fusion of Multimodal Sensor Data for Improved Passive Contact Localization
The context of this work was passive sonar contact tracking from a single sensor array producing beamformed energy both spatially (e.g. bearing) and across a frequency band. Currently implemented approaches perform contact tracking in either one measurement space or the other, but not jointly. This work offered a joint solution for improved contact localization.
Direction-of-Arrival Estimation in the Presence of Gross Array Element Position Uncertainty
In many tactical naval applications a sonar line array is towed from a platform and used to perform contact localization in a spatial domain. However, variability of the physical forces in the water column introduce array element position uncertainty which degrades localization performance. This work offered an approach that was robust to high levels of array element position uncertainty.
Precise Relative Positioning Under GPS-Denied Conditions
In the absence of GPS, accurate positioning of any commercial or military air platform becomes quite challenging. This work offered a solution consisting of several active RF beacons with no required modifications of the air platform (assuming it had already a GPS antenna) and the solution avoided the GPS band. The solution supported accurate positioning from approach distances of several tens of kilometers to under a meter and could be used to compute an instantaneous position or integrated with an aircraft inertial measurement unit.
Data Fusion Methods for Homeland Security Emergencies
This work sought to offer actionable information to Department of Homeland Security (DHS) forces through the fusion of user-agnostic information available during DHS emergencies. For example, consider the scenario where a state evacuation is declared. How can decision makers determine if residents are indeed evacuating? Or, consider the example of a Cholera outbreak. How can decision makers determine areas with the highest probability of infection? This work was based on original work of a friend and uses information such as mobile phone locations, toll crossings, and the number of vaccinated individuals at treatment sites to provide actionable probabilistic information while completely ignoring personal user information (to protect user privacy).
Basis Pursuit-Based Medical Image Compression Using Multiple Bases
Current image compression standards such as JPEG and JPEG-2000 exploit the sparsity of an image’s representation in the Haar or Wavelet basis to allow compression. However, this is a one-size-fits-all approach and some motivating research I came across lead me to examine solutions that combine bases and, through their combination, could offer increased sparsity and higher image compression for specific medical imaging such as CT and XRAY.
Spatial Compressive Sensing Bias Mitigation
The impetus for this work was simply to build a better mouse trap. At the time of this research basis pursuit techniques had become increasingly popular as applied to direction-finding of passive and active acoustic or radio frequency signals. However, all of the approaches required the selection of a two common parameters for which the literature had not optimal selection criteria. My contribution in this area was to simply alleviate the parameter selection burden.
Expected Likelihood Contact Maneuver Detector
For many decades passive sonar contact tracking algorithms have assumed that sonar contacts maneuver highly infrequently (which is justifiable in many cases). An initial contact localization solution is usually obtained under the assumption that the contact has not maneuvered. Parallel maneuver detection algorithms are used to alert the contact tracking algorithm of maneuvers. Maneuvers are typically detected and compensated. In the very specific realm of bearings-only contact tracking there existed relatively few maneuver detectors at the time of this research and all such were based on provided bearing measurements from earlier signal processing subsystems. In my publication I discussed issues related to the current state-of-the-art at the time and proposed an alternative.
 I. Bilik, T. Northardt, Y. Abramovich, “Expected likelihood for compressive sensing-based DOA estimation”, IET conference on radar systems, Glasgow, UK, 2012.
 T. Northardt, I. Bilik, Y. Abramovich, “Spatial Compressive Sensing for Direction-of-Arrival Estimation with Bias Mitigation via Expected Likelihood”, IEEE Transactions on Signal Processing, vol. 61, March 2013.
 T.Northardt, I. Bilik, Y. Abramovich, “Bearings-Only Constant Velocity Target Maneuver Detection via Expected Likelihood,” IEEE Transactions on Aerospace and Electronics Systems, vol. 50, October, 2014.
 T. Northardt, “An approach for automated passive sonar contact localization”, IEEE Underwater Signal Processing Workgroup, Rhode Island, 2015.
 T. Northardt, D. Kasilingam, "Spectral extrapolation for super-resolution tumor localization in the breast," Biomedical Engineering Letters, 7(1), 25-30, 2017.
 T. Northardt, “Use of Basis Pursuit to detect weak sources among known strong interferers,“ IEEE UASP Workshop, Greenwhich, RI, October 2017.
 T. Northardt, S. Nardone “Track-Before-Detect Bearings-Only Localization Performance in Complex Passive Sonar Scenarios: A Case Study,” IEEE Journal of Oceanic Engineering, April, 2018.
 T. Northardt, “Array Element Signal Estimation For Non-Linear Sensor Array Fault Resiliancy,” Submitted to IEEE Journal of Signal Processing, December 2017.
 T. Northardt, “The Higher Order Ambiguity Function Used For Non-Linear Sensor Array Fault Resiliency In The Presence Of Multiple Sources,” Submitted to 2019 IEEE International Symposium on Phased Array Systems and Technology
 T. Northardt, “Track-Before-Detect applications for unmanned systems,” Submarine Technology Symposium, Laurel, MD, May 16, 2019.
 T. Northardt, “A Cramer-Rao Lower Bound for Passive Sonar Track-Before-Detect Algorithms,” IEEE Trans. On Information Theory, Vol. 66, Issue 10, October, 2020.