On 14 November 2004, the U.S. Navy’s Carrier Strike Group Eleven (CSG 11), which includes the USSnuclear aircraft carrier and the Ticonderoga-class guided missile cruiser USS, was conducting training exercises off the coast of Southern California when the’s radar systems detected as many as 20 anomalous aerial vehicles, which could not be identified. The UAVs were entering the training area and were deemed a safety hazard to the upcoming exercise. The Captain of the USSordered an interception with two F/A-18F Super Hornet fighter jets. The available data consists of eyewitness information from both the pilots and the radar operators, Freedom of Information Act (FOIA) releases of four Navy documents, and a Defense Intelligence Agency (DIA) released infrared (IR) video of a similar encounter later that day taken by an F/A-18F jet using an AN/ASQ-228 Advanced Targeting Forward Looking Infrared (ATFLIR) system [ 22 ]. We estimated the accelerations of the UAVs relying on (1) radar information from USSformer Senior Chief Operations Specialist Kevin Day, (2) eyewitness information from CDR David Fravor, commanding officer of Strike Fighter Squadron 41 and a second jet’s weapons system operator, LCDR Jim Slaight, and (3) analyses of a segment of the DIA-released Advanced Targeting Forward Looking Infrared (ATFLIR) video from an encounter later that day. The following descriptions of theencounters were summarized from the more detailed study published by the Scientific Coalition for UAP Studies (SCU) [ 22 ].

With acceleration estimates in hand, we obtained a ballpark estimate of the power involved to accelerate the UAP. Of course, this required an estimate of the mass of the UAP, which we did not have. The UAP was estimated to be approximately the same size as an F/A-18 Super Hornet, which has a weight of about, corresponding to. Since we want a minimal power estimate, we took the acceleration asand assumed that the UAP had a mass of. The UAP would have then reached a maximum speed of aboutduring the descent, or 60 times the speed of sound. The power,, required to accelerate the UAP is given byfor whichis the force,is the mass of the UAP,is its velocity, andis its acceleration. The power required varies as a function of velocity, and hence as a function of time. Figure 3 C illustrates the power required to accelerate the UAV as a function of time, assuming that the UAV is propelled in a conventional way. The required power peaks at a shocking, which exceeds the total nuclear power production of the United States by more than a factor of ten. For comparison, the largest nuclear power plant in the United States, the Palo Verde Nuclear Generating Station in Arizona, provides aboutof power for about four million people [ 24 ].

We also employed sampling for which the change in altitude and the elapsed time were described by Gaussian distributions withand, respectively. The most probable acceleration was found to bewhile the mean acceleration was found to be Figure 3 B).

In the first analysis, we assigned a joint Gaussian likelihood,for the measured altitude change,, and the duration,, of the maneuver. Since the altitude change and the duration are independently measured, the joint likelihood is factored into the product of two likelihoods, and one can marginalize over the duration of the maneuver to obtain a likelihood for the altitudewhere the symbolrepresents the fact that these probabilities are conditional on all prior information. Assigning Gaussian likelihoods, we have thatThe integrand is the exponential of a quartic polynomial in, which was solved numerically. Assigning a uniform prior probability for the acceleration over a wide range of possible accelerations results in a posterior that is proportional to the likelihood (13) above resulting in a maximum likelihood analysiswhich gave an estimate of, as illustrated in Figure 3 A.

The data consisted of the change in altitude y ± σ y = 8530 ± 90 m ( − 28 , 000 ft ± 295 ft ) and the duration t ′ ± σ t = 0.78 ± 0.08 s . The the dominant source of uncertainty in altitude was due to the observed variation in altitude among the observed UAPs, which was on the order of 200 to 300 ft leading to our assigned uncertainty of σ y = 295 ft . For the duration, we assigned a conservative 10 % uncertainty resulting in σ t = 0.08 s . The goal was to estimate the acceleration, a , of the UAP during this maneuver.

An important role of the USSis to act as air defense protection for the strike group. Thewas equipped with the SPY-1 radar system which provided situational awareness of the surrounding airspace. The main incident occurred on 14 November 2004, but several days earlier, radar operators on the USSwere detecting UAPs appearing on radar at about 80,000+ feet altitude to the north of CSG11 in the vicinity of Santa Catalina and San Clemente Islands. Senior Chief Kevin Day informed us that the Ballistic Missile Defense (BMD) radar systems had detected the UAPs in low Earth orbit before they dropped down to 80,000 feet [ 23 ]. The objects would arrive in groups of 10 to 20 and subsequently drop down to 28,000 feet with a several hundred foot variation, and track south at a speed of about 100 knots [ 23 ]. Periodically, the UAPs would drop from 28,000 feet to sea level (estimated to be 50 feet), or under the surface, in 0.78 s. Without detailed radar data, it is not possible to know the acceleration of the UAPs as a function of time as they descended to the sea surface. However, one can estimate a lower bound on the acceleration, by assuming that the UAPs accelerated at a constant rate halfway and then decelerated at the same rate for the remaining distance as in ( 2 ) and ( 3 ).

The elapsed time is modeled as a Gaussian distribution with a mean ofand truncated for positive values of time ( Figure 4 C). The resulting acceleration distribution was a skewed distribution of accelerations ( Figure 4 D) with a most probable acceleration of, indicated in the figure by the red vertical lines and a mean acceleration of aboutindicated by the black vertical dotted line. Please note that this is a lower bound, probably far below the observed acceleration if the UAV accelerated briefly as if “shot out of a rifle” and then traveled at a constant speed.

To obtain a lower bound on the acceleration, we assume that the UAV exhibited constant acceleration so that the distancetraveled is given byduring the elapsed time. The length of the Tic-Tac UAV was estimated to be aboutwith a cross sectional width of about. Given that the acuity of human vision is aboutthe UAV, at its narrowest, would be out of sight at a maximum distance ofwhich is. It is difficult to know what Fravor’s acuity was given the viewing conditions. For this reason, we model the acuity conservatively as a truncated Gaussian distribution with a peak at Figure 4 A). The truncation atresulted in a discontinuity in the distribution of the distances ( Figure 4 B), which peaks around

The engagement lasted five minutes. With the Tic-Tac gone, the pilots turned their attention toward the large object in the water, but the disturbance has disappeared. The two FastEagles returned to the, with insufficient fuel to attempt to pursue the Tic-Tac. On their way back, they received a call from thethat the Tic-Tac UAV was waiting precisely at their CAP point. Senior Chief Day noted that this was surprising because those coordinates were predetermined and secret. Given that the CAP point was approximatelyaway, the probability of selecting the CAP point out of all the locations within the 60 mile radius, to within a one mile resolution (slightly more than the resolution of the radar system), isdiscounting the altitude. Given the improbability of this being a coincidence, it appears that the Tic-Tac UAV intentionally went to their CAP point, although it is neither clear how the UAV determined the CAP point coordinates nor why it would perform such a maneuver. However, it should be noted that the UAV was not observed on radar moving to the CAP point, but that it was discovered that a UAV had moved to the CAP point just after the encounter. Since there were several UAVs in the area at the time, it is not clear that it was the specific UAV that CDR Fravor encountered, but it was one of the UAVs in the area.

Fravor started a descent to investigate while his wingman kept high cover. As Fravor circled the area and descended, the UAV seemed to take notice of him and rose to meet him. The F-18 and the UAV circled one another. When Fravor reached the nine o’clock position, he performed a maneuver to close the distance by cutting across the circle to the three o’clock position. As he did so, the Tic-Tac UAV accelerated ([ 22 ], p. 12) across Fravor’s nose heading south. Fravor said that the UAV was gone within a second. As a comparison, Fravor noted that even a jet at Mach 3 takes 10 to 15 s to disappear from sight ([ 22 ], p. 11). LCDR Slaight described the UAV as accelerating as if it was “shot out of a rifle” and that it was out of sight in a split second ([ 22 ], p. 12)

About a half-hour after take-off, Senior Chief Day operating the SPY-1 radar system on the Princeton detected UAVs entering the training area. The training exercise was delayed and FastEagle01 and FastEagle02 were directed to intercept a UAV at a distance of 60 miles and an altitude of 20,000 feet. As the F-18s approached merge plot , which is the point at which the radar could not differentiate the positions of the F-18s and the UAV, Fravor and Slaight noticed a disturbed patch of water, where it appeared as if there was a large object, possibly a downed aircraft, submerged 10 to 15 feet below the surface. As they observed the disturbance from 20,000 ft, all four pilots spotted a white UAV, shaped like a large cylindrical butane tank, or a Tic-Tac candy, moving erratically back and forth, almost like a bouncing ping-pong ball making instantaneous changes in direction without changing speed. The Tic-Tac UAV was estimated to be about the size of an F-18, about 56 feet in length and 10–15 feet wide, but had no apparent flight surfaces or means of propulsion, and its movement had no apparent effect on the ocean surface as one would expect from something like rotor wash from a helicopter.

On 14 November 2004, CSG11 was preparing for training exercises. Two F/A-18F Super Hornets were launched from the Nimitz for the air defense exercise to be conducted in an area 80–150 miles SSW of San Diego. Both planes, with call signs “FastEagle01” and “FastEagle02”, had a pilot and a weapons system operator (WSO) onboard. VFA-41 Squadron Commanding Officer David Fravor was piloting FastEagle01 and LCDR Jim Slaight was the WSO for FastEagle02. CDR Fravor and his wingman were headed for the Combat Air Patrol (CAP) point, which is given by predefined latitude, longitude and altitude coordinates, where they would conduct the training exercises.

2.4.3. ATFLIR Video

Nimitz , CDR Fravor requested that a crew equipped with the ATFLIR pod obtain videos of the Tic-Tac UAV. Two F/A-18Fs were launched under the guidance of an E-2 Hawkeye airborne radar plane. The two planes separated in search of the UAV, with one plane heading south toward the CAP point where the UAV was last seen on radar. That plane picked up a contact 33 miles to the south on the Range-While-Search (RWS) scan. This Tic-Tac UAV was filmed using the ATFLIR system, and the video was released to the public as the “ Nimitz video” ( Upon returning to the, CDR Fravor requested that a crew equipped with the ATFLIR pod obtain videos of the Tic-Tac UAV. Two F/A-18Fs were launched under the guidance of an E-2 Hawkeye airborne radar plane. The two planes separated in search of the UAV, with one plane heading south toward the CAP point where the UAV was last seen on radar. That plane picked up a contact 33 miles to the south on the Range-While-Search (RWS) scan. This Tic-Tac UAV was filmed using the ATFLIR system, and the video was released to the public as the “video” ( Figure 5 A) [ 25 ].

We examined the last 32 frames of the Nimitz video in which the Tic-Tac UAV accelerated to the left and the targeting system lost lock. The video frame rate was 29.97 frames / s . From 0.267 s (8 frames) before the analyzed segment of video through the end of the analyzed segment of video, the aircraft orientation was fixed and the ATFLIR orientation was fixed at a zenith angle of 5 ∘ above the aircraft axis and at an azimuthal angle of 8 ∘ left of the aircraft axis, so that the apparent motion of the UAV in the video frames is attributable only to the physical motion of the UAV. This means that, for the sake of this analysis, the UAV can be treated as if starting from rest with respect to the aircraft.

As the UAV accelerates, the image of the UAV becomes elongated and blurred. If the shutter speed was known, then this information could be used to better estimate the speed of the craft. This could be accomplished by treating the shutter speed as a model parameter, but such analysis is beyond the scope of this project. Instead, we concentrated on tracking the position of the right edge of the UAV and using those positions to estimate the kinematics. The left edge of the UAV was also estimated in the first frame to provide some information about the range, z o , to the UAV given that the UAV was estimated to be at least 40 feet in length. However, since the orientation was not known, this is modeled as a uniformly distributed unknown parameter ϕ , which allowed one to at least put an upper bound on the range z o . For clarity, it should be noted that the Tic-Tac UAVs were described as being about 40 to 50 ft in length or the size of the F-18, which is 56 ft . Here we assume that the UAV is 40 ft in length, which is probably an underestimate. As such, the estimated accelerations are expected to be underestimated, and thus more conservative.

To estimate the position of the right edge of the craft in each frame ( Figure 5 A), the row of pixels for which the UAV has a maximum intensity was examined. The pixel intensities along that row at the right edge of the UAP were fit (maximum likelihood method with a Student-t likelihood) to half of a Gaussian curve. The center position of the Gaussian plus the standard deviation was used as the position of the right side of the UAV for that frame ( Figure 5 B).

F O V p i x = 606 pixels ) corresponds to an angular field of view of 0.7 ∘ in the narrow (NAR) mode, which is indicated in the upper left hand corner of the video. At the range, z o , of the UAV this results in the proportion X s c a l e = F O V p i x / 2 z o tan 0.7 ∘ 2 (19) X s c a l e has units p i x e l s m when z o is in units of m. A similar relation holds for the vertical position of the UAV, but it was not used in this analysis. The ATFLIR has a zoom feature that can change the field of view. In the Nimitz video frames analyzed, the zoom is first set to unity in the NAR mode so that the angular field of view is 0.7 ∘ . However, at Frame 16, the zoom changes to two, so that the angular field of view in the NAR mode changes to 0.35 ∘ . This appears as a discontinuity in the data (‘+’ symbols) illustrated in Horizontal positions of the UAV are related to the pixel coordinates by noting that the entire field of view (approximately) corresponds to an angular field of view ofin the narrow (NAR) mode, which is indicated in the upper left hand corner of the video. At the range,, of the UAV this results in the proportionwherehas unitswhenis in units of m. A similar relation holds for the vertical position of the UAV, but it was not used in this analysis. The ATFLIR has a zoom feature that can change the field of view. In thevideo frames analyzed, the zoom is first set to unity in the NAR mode so that the angular field of view is. However, at Frame 16, the zoom changes to two, so that the angular field of view in the NAR mode changes to. This appears as a discontinuity in the data (‘+’ symbols) illustrated in Figure 6

a x to the left. The model then provides the position of the UAV as a function of time, where t i is the time of the i t h video frame: Model 1 x ( t i ) = 1 2 a x t i 2 + x o z ( t i ) = z o constant acceleration in a x , (20) a x , its initial position x o , its range z o , and its orientation ϕ in the first frame, which helps to set the scale. We consider several different kinematic models analyzed using nested sampling, and statistically test them by comparing the log Bayesian evidence. The coordinates were defined so that the x-direction corresponds to motion to the left and right, and the z-direction corresponds to motion toward and away from the camera. We used uniform prior probabilities for the kinematic parameters as well as a Student-t likelihood function, which is robust to outliers, such as those due to camera (airplane) motion. The first kinematic model assumes that the UAV started from relative rest and accelerated with a constant rate ofto the left. The model then provides the position of the UAV as a function of time, whereis the time of thevideo frame:so that there are four model parameters: the UAV’s acceleration, its initial position, its range, and its orientationin the first frame, which helps to set the scale.

x and z directions: Model 2 x ( t i ) = 1 2 a x t i 2 + x o z ( t i ) = 1 2 a z t i 2 + z o constant acceleration in a x and a z . (21) The second kinematic model considers constant acceleration in both theanddirections:

Model 3 x ( t i ) = 1 2 a x t i 2 + x o for t i < t 16 x ( t i ) = 1 2 a x t 15 2 + a x t 15 ( t i − t 15 ) + x o for t i ≥ t 16 z ( t i ) = z o limited accel . in a x (22) Model 4 x ( t i ) = 1 2 a x t i 2 + x o for t i < t 16 x ( t i ) = 1 2 a x t 15 2 + a x t 15 ( t i − t 15 ) + x o for t i ≥ t 16 z ( t i ) = 1 2 a z t i 2 + z o for t i < t 16 z ( t i ) = 1 2 a z t 15 2 + a z t 15 ( t i − t 15 ) + z o for t i ≥ t 16 lim . accel . in a x and a z , (23) x and z directions until Frame 16, at which time the UAV continues with constant velocity. The last two models describe the kinematics as acceleration followed by motion at constant velocity:andin which we consider acceleration in both theanddirections until Frame 16, at which time the UAV continues with constant velocity.

26, N = 500 samples and was run until the change in logZ from successive iterations was less than 10 − 5 , ensuring a reliable estimate of the log evidence. Tests were performed to ensure that the trial-to-trial variations in parameter estimates were within the estimated uncertainties. The models were analyzed using a nested sampling algorithm [ 17 27 ], which allowed for the estimation of the logarithm of the Bayesian evidence, logZ, as well as the logarithm of the likelihood, logL, and mean estimates of the model parameters. The analysis was performed forsamples and was run until the change in logZ from successive iterations was less than, ensuring a reliable estimate of the log evidence. Tests were performed to ensure that the trial-to-trial variations in parameter estimates were within the estimated uncertainties.

0.53 s ) is the most probable solution with acceleration components of a x = − 35.64 ± 0.08 g and a z = 67.04 ± 0.18 g for an overall acceleration of about 75.9 ± 0.2 g . While Model 4 describes the data well, the residuals indicate that a more precise model would consist of multiple episodes of acceleration and deceleration during the maneuver. This was observed in SCU’s analysis [ The results of the nested sampling analysis are listed in Table 1 . The uncertainties in the logZ estimates (not listed) were on the order of one or less. We see that Model 4, which describes the motion of the UAV as a constant acceleration to the left and away from the observer for the first 15 frames (approximately) is the most probable solution with acceleration components ofandfor an overall acceleration of about. While Model 4 describes the data well, the residuals indicate that a more precise model would consist of multiple episodes of acceleration and deceleration during the maneuver. This was observed in SCU’s analysis [ 22 ] where the accelerations were estimated to vary from around 40 to 80 g.

A more detailed analysis would involve modeling the motion of the UAV more precisely by modeling the pixel intensities on the video frames themselves. One could consider the shutter speed of the camera, which would take advantage of the blurring of the UAV image due to its motion while the shutter was open. In addition, the “change points” at which the accelerations changed could be treated as model parameters. This would allow for more precise estimates of the UAV’s behavior.