About

Todd E. Humphreys is a Professor and the Ernest Dashiell Cockrell II Chair in Engineering at the University of Texas at Austin's Department of Aerospace Engineering and Engineering Mechanics. He specializes in the application of optimal detection and estimation techniques to problems in satellite navigation, autonomous systems, and signal processing. His research interests include positioning, navigation, and timing technology and security, satellite communications and navigation, detection and estimation, and software-defined radio. Humphreys directs the Wireless Networking and Communications Group (WNCG) and the Radionavigation Laboratory, and he is also a member of the graduate study committee of UT Austin's Department of Electrical and Computer Engineering. Since joining the faculty in Fall 2009, he has contributed significantly to his field through research and leadership, earning numerous awards including the Presidential Early Career Award for Scientists and Engineers (PECASE) in 2019, the Institute of Navigation Kepler Award in 2023, and the Royal Institute of Navigation's Harold Spencer Jones Gold Medal in 2025. He has been recognized as a Fellow of both the Institute of Navigation and the Royal Institute of Navigation, reflecting his notable contributions to navigation and aerospace engineering.

Research topics

• Computer Science
• Engineering
• Telecommunications
• Computer Security
• Aerospace engineering
• Remote sensing
• Real-time computing
• Physics
• Geography
• Electronic engineering

Selected publications

• Navigation

  VTechWorks (Virginia Tech) · 2026-01-01

  articleSenior author

  This paper presents an analysis and experimental demonstration of single-satellite single-pass geolocation of a terrestrial broadcast global navigation satellite system (GNSS) spoofer from low Earth orbit (LEO). The proliferation of LEObased GNSS receivers offers the prospect of unprecedented spectrum awareness, enabling persistent GNSS interference detection and geolocation. Accurate LEO-based single-receiver emitter geolocation is possible when a range-rate time history can be extracted for the emitter. This paper presents a technique crafted specifically for indiscriminate broadcast-type GNSS spoofing signals. Furthermore, it explores how unmodeled oscillator instability and worst-case spoofer-introduced signal variations degrade the geolocation estimate. The proposed geolocation technique is validated by a controlled experiment, in partnership with Spire Global, in which a LEO-based receiver captures broadcast GNSS spoofing signals transmitted from a known ground station on a non-GNSS frequency band.

  Publisher

• npj Wireless Technology

  VTechWorks (Virginia Tech) · 2026-01-01

  articleSenior author

  We identify and characterize dedicated pilot symbols and other predictable elements embedded within the Starlink Ku-band downlink waveform. Exploitation of these predictable elements enables precise opportunistic positioning, navigation, and timing using compact, low-gain receivers by maximizing the signal processing gain available for signal acquisition and time-of-arrival (TOA) estimation. We develop an acquisition and demodulation framework to decode Starlink frames and disclose the explicit sequences of the edge pilots—bands of 4QAM symbols located at both edges of each Starlink channel that apparently repeat identically across all frames, beams, channels, and satellites. We further reveal that the great majority of QPSK-modulated symbols do not carry high-entropy user data but instead follow a regular tessellated structure superimposed on a constant reference template. We demonstrate that exploiting frame-level predictable elements yields a processing gain of approximately 48 dB, thereby enabling low-cost, compact receivers to extract precise TOA measurements even from low-SNR Starlink side beams.

  Publisher

• Analysis of the Trusted Inertial Terrain-Aided Navigation Measurement Function

  NAVIGATION Journal of the Institute of Navigation · 2025-01-01

  articleOpen accessSenior author

  <h3>Abstract</h3> The trusted inertial terrain-aided navigation (TITAN) algorithm leverages an airborne vertical synthetic aperture radar to measure the range to the closest ground points along several prescribed iso-Doppler contours. These TITAN minimum-range, prescribed-Doppler measurements are the result of a constrained nonlinear optimization problem whose optimization function and constraints both depend on the radar position and velocity. Owing to the complexity of this measurement definition, analysis of the TITAN algorithm is lacking in prior work. This publication offers such an analysis, making the following three contributions: (1) an analytical solution to the TITAN constrained optimization measurement problem, (2) a derivation of the TITAN measurement function Jacobian, and (3) a derivation of the Cramér-Rao lower bound on the estimated position and velocity error covariance. These three contributions are verified via Monte Carlo simulations over synthetic terrain, which further reveal two remarkable properties of the TITAN algorithm: (1) the along-track positioning errors tend to be smaller than the cross-track positioning errors, and (2) the cross-track positioning errors are independent of the terrain roughness.

  PublisherOA PDFDOI

• Signal Parameter Estimation and Demodulation of the OneWeb Ku-Band Downlink

  Research Square · 2025-10-21

  preprintOpen accessSenior author
  PublisherOA PDFDOI

• Maximum Likelihood Time of Arrival and Doppler Estimation for Precise Starlink-Based PNT

  2025-04-28 · 2 citations

  articleSenior author

  We present a maximum likelihood (ML) Doppler and time-of-arrival (TOA) estimation framework for opportunistic tracking of Starlink downlink signals. Extending previous approaches that rely solely on known pilot symbols, we incorporate full-frame ML estimation to harness the data payload, significantly improving Doppler and TOA estimation accuracy. Using live Starlink transmissions, we validate our ML estimator and compare its performance against pilot-based cross-ambiguity function (CAF) and pilot-only ML estimation methods. Results show that the full-frame ML estimator achieves a 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> factor improvement in Doppler accuracy over the pilot-only CAF method and 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> factor improvement over the pilot-only ML method, reducing post-fit residual RMSE from 1469.20 Hz and 752.43 to 6.34 Hz, respectively. TOA estimation sees a smaller improvement. The findings highlight the value of leveraging the entire OFDM frame for estimation. Additionally, we newly identify two OFDM symbol modulation schemes in use by Starlink.

  PublisherDOI

• OFDM-Based Positioning With Unknown Data Payloads: Bounds and Applications to LEO PNT

  IEEE Transactions on Wireless Communications · 2025-11-18

  articleSenior author

  This paper presents bounds, estimators, and signal design strategies for exploiting both known pilot resources and unknown data payload resources in time-of-arrival (TOA)-based positioning systems with orthogonal frequency-division multiplexing (OFDM) signals. It is the first to derive the Ziv-Zakai bound (ZZB) on TOA estimation for OFDM signals containing both known pilot and unknown data resources. In comparison to the Cram´er-Rao bounds (CRBs) derived in prior work, this ZZB captures the low-signal-to-noise ratio (SNR) thresholding effects in TOA estimation and accounts for an unknown carrier phase. The derived ZZB is evaluated against CRBs and empirical TOA error variances. It is then evaluated on signals with resource allocations optimized for pilot-only TOA estimation, quantifying the performance gain over the best-case pilot-only signal designs. Finally, the positioning accuracy of maximum-likelihood and decision-directed estimators is evaluated on simulated low-Earth-orbit non-terrestrial-network channels and compared against their respective ZZBs.

  PublisherDOI

• The Effect of Coarse Doppler Resolution on the Performance of a Vertical Synthetic Aperture Radar Navigation System

  Proceedings of the Satellite Division's International Technical Meeting (Online)/Proceedings of the Satellite Division's International Technical Meeting (CD-ROM) · 2025-10-01

  articleSenior author

  The trusted inertial terrain-aided navigation (TITAN) algorithm correlates vertical synthetic aperture radar (VSAR) range-Doppler measurements against a digital terrain elevation model to determine the position and velocity of an airborne radar without input from global navigation satellite systems (GNSS). Recent work has characterized the navigation performance of the TITAN algorithm when the radar Doppler resolution is assumed to be infinitely fine. Hyperfine Doppler resolution, however, comes at a cost: synthetic aperture processing requires the length and number of radar pulses in an aperture to increase with finer Doppler resolutions. Consequently, the size of VSAR images, the computational resources required to process these enlarged images, and the total energy required by the greater number of radar pulses all increase. Therefore, for remote navigation systems with limited computational processing and energy budgets, it is desirable to keep the Doppler resolution of a navigation VSAR coarse, provided that this coarsening does not significantly degrade navigation performance. Existing work has not characterized how the performance of the TITAN algorithm varies with Doppler resolution, so it is difficult to determine an appropriate Doppler resolution given navigation accuracy requirements. This paper addresses this gap and analyzes how TITAN’s signal-to-noise ratio, ranging errors, and navigation accuracy are affected by Doppler resolution. The study concludes that there is little correlation between overall navigation performance and Doppler resolution when the number of navigation observables is fixed.

  PublisherDOI

• Ziv-Zakai-Optimal OFDM Resource Allocation for Time-of-Arrival Estimation

  IEEE Transactions on Wireless Communications · 2025-04-08 · 5 citations

  articleSenior author

  This paper presents methods of optimizing the placement and power allocations of pilots in an orthogonal frequency-division multiplexing (OFDM) signal to minimize time-of-arrival (TOA) estimation errors under power and resource allocation constraints. TOA errors in this optimization are quantified through the Ziv-Zakai bound (ZZB), which captures error thresholding effects caused by sidelobes in the signal’s autocorrelation function (ACF) which are not captured by the Cramer-Rao lower bound. This paper is the first to solve for these ZZB-optimal allocations in the context of OFDM signals, under integer resource allocation constraints, and under both coherent and noncoherent reception for both frequency-flat and frequency-selective channels. Under convex constraints, the optimization of the ZZB is proven to be convex; under integer constraints, the optimization is lower bounded by a convex relaxation and a branch-and-bound algorithm is proposed for efficiently allocating pilot resources. These allocations are evaluated by their ZZBs and ACFs, compared against a typical uniform allocation, and deployed on a software-defined radio TOA measurement platform to demonstrate their applicability in real-world systems.

  PublisherDOI

• Timing Properties of the Starlink Ku-Band Downlink

  arXiv (Cornell University) · 2025-01-09 · 3 citations

  preprintOpen accessSenior author

  We develop signal capture and analysis techniques for precisely extracting and characterizing the frame timing of the Starlink constellation's Ku-band downlink transmissions. The aim of this work is to determine whether Starlink frame timing has sufficient short-term stability to support pseudorange-based opportunistic positioning, navigation, and timing (PNT). A second goal is to determine whether frame timing is disciplined to a common time scale such as GPS time. Our analysis reveals several timing characteristics not previously known that carry strong implications for PNT. On the favorable side, periods of ns-level jitter in frame arrival times across all satellite versions indicate that Starlink hardware is fundamentally capable of the short-term stability required to support GPS-like PNT. But there are several unfavorable characteristics that, if not addressed, will make GPS-like PNT impractical: (1) The v1.0 and v1.5 Starlink satellites exhibit once-per-second abrupt frame timing adjustments whose magnitude (as large as 100s of ns) and sign appear unpredictable. Similar discontinuities are also present in the v2.0-Mini frame timing, though smaller and irregularly spaced. (2) Episodic 15-s periods of high frame jitter routinely punctuate the nominal low-jitter frame arrival timing. (3) Starlink frame timing is disciplined to GPS time, but only loosely: to within a few ms by adjustments occurring every 15 s; otherwise exhibiting drift that can exceed 20 ppm. These unfavorable characteristics are essentially incompatible with accurate PNT. Fortunately, they appear to be a consequence of software design choices, not hardware limitations. Moreover, they could be compensated with third-party-provided corrections.

  PublisherOA PDFDOI

• Network-Aided Pseudorange-Based LEO PNT from OneWeb

  2025-04-28 · 5 citations

  articleSenior author

  This paper presents a framework and first experimental results for pseudorange-based positioning, navigation, and timing (PNT) exploiting OneWeb’s Ku-band downlink signal and a reference network. As the demand for accurate and resilient positioning and timing solutions grows, the proliferation of low Earth orbit (LEO) satellites, including approximately 650 in OneWeb’s constellation, offers promising opportunities for powerful new PNT services. Newly discovered synchronization sequences embedded in the OneWeb signal open the way for third-party provision of highly accurate clock and orbital models for each OneWeb satellite. Model parameters would be continually estimated by a sparse network of reference stations at known locations having access to an accurate universal time scale such as UTC. Subscribers to the third party’s data feed could treat OneWeb much like a traditional GNSS, extracting pseudorange, carrier phase, and Doppler observables directly from the OneWeb signals, either by exploiting only the newly discovered synchronization sequences or augmenting these with additional sequences decoded continuously by the reference network. The observables would then be processed together with the third-party-provided models to produce highly accurate position, velocity, and timing solutions. Because each OneWeb satellite illuminates a wide geographic area, this technique could be implemented with an attractively low density of reference stations. In this paper we develop the OneWeb satellite clock model, establish its applicability across multiple downlink beams, analyze the effect of ephemeris errors on the resulting solution, and prove the technique in a field experiment with live signals, achieving sub-meter-level positioning and timing.

  PublisherDOI

Recent grants

• CAREER: Secure Perception for Autonomous Systems

  NSF · $500k · 2015–2020

Frequent coauthors

• Mark L. Psiaki

  36 shared

• Lakshay Narula

  The University of Texas at Austin

  32 shared

• Jahshan A. Bhatti

  The University of Texas at Austin

  30 shared

• Brady W. O’Hanlon

  24 shared

• Peter A. Iannucci

  The University of Texas at Austin

  23 shared

• Matthew J. Murrian

  22 shared

• P. M. Kintner

  19 shared

• Kyle Wesson

  19 shared

Labs

• Radionavigation LaboratoryPI

Education

• Ph.D.

  Cornell University

Awards & honors

• UT Regents' Outstanding Teaching Award (2012)
• NSF Career Award (2015)
• Institute of Navigation Thurlow Award (2015)
• Presidential Early Career Award for Scientists and Engineers…
• IEEE Walter Fried Best Paper Award (2012, 2020, 2023)