Limits on Velocity Recovery from the PURSUE Sensor Videos

Abstract: This paper analyzes the 112 sensor videos released by the U.S. Department of War under the PURSUE (Presidential Unsealing and Reporting System for UAP Encounters) initiative. Redactions to the on-screen displays limit the information available for identifying the nature of the reported unidentified anomalous phenomena (UAP). The rate at which any object transits across part or all of a frame can be measured in pixels per frame; however, converting this to a physical velocity also requires (1) the range to the object, (2) the velocity of the observing aircraft, (3) the aspect angle between the object's path and the observer, and (4) the field angle of the camera sensor. No sensor video in the PURSUE corpus provides this complete set of information. In one clip (DOW-UAP-PR113), the object crosses visible depression-angle markings, allowing the camera's field of view to be reconstructed. Even this clip does not provide sufficient information to distinguish between a bird flying past the sensor at close range and a large craft traveling at Mach 5 a kilometer away. A second clip (DOW-UAP-PR149) includes a vessel of known size in the frame, which can be used as a reference to calculate an upper bound of Mach 0.4 on the object's relative velocity. Without further information, the PURSUE sensor videos in their present form cannot fully resolve unidentified cases or conclusively indicate anomalous velocities.

• The paper finds that none of the 112 PURSUE videos contains enough information to constrain relative velocity, because range, angular scale, aspect angle or range rate, and platform motion are missing.
• The paper’s two strongest case studies remain inconclusive: PR113 permits angular-rate reconstruction but allows speeds from subsonic to supersonic, while PR149 limits transverse motion to roughly 99–132 m/s under stated assumptions.
• The analysis shows that single-camera imagery measures angular motion rather than physical kinematics, making unredacted telemetry, range estimates, flight logs, or corroborating radar and multi-sensor data essential for testing anomalous claims.

Overview

This paper examines the 112 sensor videos released by the U.S. Department of War under the PURSUE (Presidential Unsealing and Reporting System for UAP Encounters) initiative between late 2025 and mid-2026, and asks a narrow but consequential question: to what extent can an object's velocity be constrained from these videos alone? The answer is essentially "not at all, in physical units." The authors show that no video in the corpus provides the complete set of information required for a velocity determination, and they demonstrate this with two worked examples that represent the best cases available. The central conclusion is that the PURSUE corpus, in its redacted form, cannot resolve unidentified cases or establish anomalous kinematics.

The velocity equation

The analysis begins with the kinematic framework that any single-sensor velocity estimate must satisfy. From pixels alone one can measure the image rate $\dot{x}$ (pixels per frame), the object's image extent $p$, the frame rate $f$, and frame dimensions $W \times H$. Converting $\dot{x}$ into an angular line-of-sight rate requires the sensor's angular scale $k$:

$\omega = \frac{\dot{x} f}{k}$

The angular rate itself is generated by the transverse component of the relative velocity between object and observing platform:

$$\omega R = |\mathbf{v}_{\rm obj} - \mathbf{v}_{\rm ac}| \sin\theta$$

where $R$ is range, $\theta$ is the aspect angle between the relative velocity vector and the viewing direction, and $p$0 is not a free parameter—it is tied to the range rate $p$1 via $p$2. Solving for ground speed requires four additional quantities beyond what pixels provide: $p$3, $p$4, $p$5 (or equivalently $p$6), and the platform velocity $p$7.

A key technical point concerns the angular scale. For a rectilinear lens, $p$8 varies across the frame; at a wide field such as $p$9, the small-angle approximation overstates the central scale by 8%, and $f$0 itself varies by 34% between frame center and corner. This matters because targeting-pod cameras typically operate at wide fields where the common approximation $f$1 is unreliable.

Two routes exist toward recovering scale. The first uses a direct measurement or reconstruction of $f$2. The second exploits an object of known size in the same frame: the angular scale cancels algebraically, yielding a relative velocity that depends only on the range ratio $f$3—no field-of-view knowledge required.

Census of the corpus

Each of the 112 videos was individually reviewed for availability of every variable in the framework. The results are unambiguous: no video contains complete information to constrain relative velocity. Frame constants are present everywhere, but angular scale and field of view are unreported in all clips; observer velocity and aspect angle (or range rate) are absent from all 112.

The census also identifies a structural limitation: only transit events yield a measurable $f$4. For tracked objects—the pod slews to null image motion—$f$5 by design, so the transverse term $f$6 is unrecoverable regardless of the object's actual motion. Of the 112 clips, 43 contain transits, 33 are tracked-only, and 36 show both behaviors; 79 involve a single object and 33 multiple objects.

The paper situates this finding in a longer tradition, invoking James McDonald's observation that single-sensor, angular-only data cannot close kinematic questions—a point made in 1972 and still operative here. Multi-sensor observation, as pursued by the Galileo Project and UAPx, remains the only route to constraining kinematics of anomalous objects.

Case study: DOW-UAP-PR113

DOW-UAP-PR113 (infrared, Western United States, 1996) is the strongest case in the corpus because it carries a burned-in depression-angle graticule labeled 5–35 at 35.4 px per unit, allowing direct reconstruction of the angular scale: $f$7 px rad$f$8, corresponding to $f$9 horizontal. A compact dark body crosses the frame at $W \times H$0 px/frame over roughly 0.1 s, giving $W \times H$1 rad s$W \times H$2 ($W \times H$3 s$W \times H$4).

Even here, physical velocity is undetermined because $W \times H$5, $W \times H$6, and platform velocity are all unknown. The relative speed $W \times H$7 spans orders of magnitude as a function of the unknowns: subsonic for near-field objects, supersonic beyond a few hundred meters at every aspect angle. The ambiguity extends to size—the measured ~25 px extent is consistent with a bird flying past the sensor at close range or a ~37 m craft at 3 km. The paper is explicit that both the scale reconstruction and the field of view rest on the assumption that the graticule is a depression-angle scale in degrees; this assumption is inferred from image analysis rather than released metadata.

Case study: DOW-UAP-PR149

DOW-UAP-PR149 (infrared, Middle East, 2023) illustrates the second approach. A compact object crosses the frame at $W \times H$8 px/frame over 43 frames (3.2 s) on a path straight to 2.6 px rms, while a carrier ship travels beneath it. Using the ship's projected hull of 920 px against an assumed length of 150–200 m ("Handymax" class bulk carrier), the angular scale cancels and the object's motion corresponds to 0.657–0.689 ship-lengths per second. This yields an upper bound on the transverse relative velocity:

$W \times H$9

i.e., approximately Mach 0.3–0.4 at the maximum, which occurs only if object and ship are equidistant from the sensor. Because the range ratio is unknown, this is strictly an upper limit—and if the object is above the ship's altitude, the true relative velocity is lower. Supersonic relative velocities can be excluded for this case, but plausible solutions include bodies as small as 0.08 m moving at 12 m s$\dot{x}$0. Identity and precise velocity remain unconstrained.

Limitations and open questions

The paper concedes several dependencies plainly. The PR113 reconstruction rests entirely on the interpretation of the burned-in graticule as a degree-marked depression-angle scale; without released metadata confirming this, even the sole constrained $\dot{x}$1 in the corpus is provisional. The PR149 bound depends on the assumed ship class and length (150–200 m), and on the unknown range ratio. More fundamentally, a single camera records angles alone: neither $\dot{x}$2 nor platform velocity can be recovered from imagery by any amount of analytical effort, so the deficit is informational rather than methodological.

The open questions are specific: whether flight logs, sensor metadata (field of view, line-of-sight pointing angles), or correlated radar tracks exist for individual encounters and can be released; and whether the range ratios for specific clips can be bounded by independent means. The authors note that not all such data will exist for passive encounters.

Conclusion

The PURSUE sensor videos cannot demonstrate or exclude anomalous kinematics. Even the two most informative clips—one with a recoverable angular scale, one with an in-frame reference object—leave velocities spanning orders of magnitude or bounded only loosely. The corpus retains value for object morphology, sensor-artifact phenomenology, and sharpening data requests, but resolving unidentified cases requires unredacted telemetry or corroborating multi-sensor data.