From space: the survey inside every spacecraft

On 1 July 2025 the ATLAS survey reported a faint, fast object on a hyperbolic path: the third interstellar visitor ever found, soon designated 3I/ATLAS. Within weeks a team went back to the Transiting Exoplanet Survey Satellite (TESS), a spacecraft built to watch stars dim when planets cross them. TESS had been staring at the patch of sky the object was crossing from 7 May to 2 June, beginning 55 days before the discovery. In no single 200-second TESS image was the object visible. But once the trajectory was known, the team could cut out a small moving window, model the background, stack thousands of frames along the path and pull out a light curve: the object brightened from TESS magnitude $T=20.9\pm0.29$ to $19.57\pm0.15$ over the weeks before anyone knew it existed (Martinez-Palomera et al. 2025).

That small result contains the whole subject of this chapter. Space telescopes built for stars, galaxies and exoplanets also record reflected sunlight from asteroids, comets and distant planets, and they do so with a quality no ground site can match: no atmosphere, no day–night cycle, stable point-spread functions and, for some missions, a vantage point far from Earth. The archives therefore contain a second survey inside the primary one. But each spacecraft also imposes its own rules on what gets recorded. TESS keeps every pixel but makes them 21 arcseconds wide. Gaia measures a source with exquisite precision but transmits only a small window around it. Euclid’s long exposures turn asteroids into streaks. Roman averages its detector reads on board before downlink. New Horizons sees a Kuiper belt object from a few tenths of an astronomical unit away, but through a field smaller than the full Moon.

This chapter treats these missions as different observation operators acting on one underlying signal: a moving point of light. Its main lesson is about where the algorithmic room lies. A good deal of it sits before and around the final search: preserving moving flux during data reduction, fitting the right observer-dependent trail, controlling the combinatorics of candidates, and keeping enough information in what is transmitted and archived. A faster final GPU kernel cannot restore photons that a cosmic-ray filter has already thrown away.

Thermal-infrared physics belongs to Chapter 24, streak detection in general to Chapter 11, and orbit-space stacking to Chapter 20. Here those tools appear in their mission-specific roles.

One signal, many operators

The moving-source model

Every mission in this chapter observes the same thing: a body on a heliocentric orbit $q$ seen from a spacecraft that is itself moving. Let $\mathbf r(t;q)$ be the body’s position and $\mathbf R_o(t)$ the spacecraft’s barycentric position. The direction in which the spacecraft sees the body is

where $\tau$ is the light travel time, so the body is seen where it was, not where it is. For precision astrometry one adds aberration, gravitational light bending and reference-frame transformations. Gaia’s processing performs all of these explicitly (Tanga et al. 2023), and the NEO Surveyor simulator includes observer ephemerides, light-time and relativistic orbital terms (Masiero et al. 2023). The point to hold on to is simple: the observer is the spacecraft, not Earth. For Gaia, about 0.01 au from Earth, the difference is already large enough that the predicted position of a nearby asteroid differs between Gaia and a ground telescope by arcminutes or, for close asteroids, by degrees (Carry et al. 2021).

An exposure does not record a direction. It records charge in pixels. For exposure $k$ starting at $t_k$ and lasting $T_k$, the expected signal in pixel $p$ is

where $b_{kp}$ is the static sky and instrumental background, $P_k$ the point-spread function convolved with the pixel response, $\mathcal W_k$ the map from sky to detector coordinates, and $F_k(t)$ the source flux, which can vary as the body rotates. The time integral is the trail template. Treating the source as a point is justified only when its motion during the exposure is small compared with the PSF. In Euclid’s simulated images, with $0.1''$ pixels and 565-second exposures, a body moving at $10''$ per hour smears into a trail $10\times565/3600=1.57''$ long, about 15.7 pixels (Pöntinen et al. 2020). The same motion in a 21-arcsecond TESS pixel over a 30-minute frame is a quarter of a pixel.

The detection statistic

If the background has been subtracted and the noise is approximately Gaussian with covariance $C$, the optimal statistic for a source of unknown constant flux along a trial orbit is the matched filter of Chapter 1. Writing $d$ for the data and $h(q)$ for the unit-flux template,

$A$ is a weighted sum of data along the track, $B$ is the information (inverse variance) of the flux estimate, and $\nu$ is the signal-to-noise ratio. If flux must be non-negative, the log-likelihood ratio is $2\log\Lambda=\max(0,A)^2/B$. With diagonal noise this suggests a concrete recipe used, in some form, by every good stacking code: make a per-exposure “numerator” image (PSF-filtered, inverse-variance-weighted data) and a per-exposure “information” image, sample both along each trial path, sum, and divide. Masked pixels drop out of both sums. A raw flux sum, by contrast, can favour noisier paths or paths with more valid samples.

Two cautions follow from the same algebra. First, for $M$ independent Gaussian trials the expected number of noise peaks above threshold $\nu_*$ is $M\,\bar\Phi(\nu_*)$, where $\bar\Phi$ is the upper-tail probability. With $10^{12}$ trials, a one-sided $5\sigma$ threshold ($\bar\Phi\approx2.9\times10^{-7}$) yields about $2.9\times10^{5}$ false peaks. Real templates overlap, so the effective trial count is smaller and usually unknown, and artefacts can fatten the tails far beyond the Gaussian prediction. Second, a CNN score, a morphological segmentation threshold and a likelihood ratio are calibrated differently. A “false-positive fraction” in a simulated output catalogue is not the probability of a false discovery over a mission. Papers in this field report all of these, and they are not interchangeable.

Reversible and irreversible steps

The most useful distinction in the chapter is between what can be redone on the ground and what cannot. Splitting a long exposure into shorter ones avoids integrating irreversibly along an unknown motion, at the cost of read noise, data volume and telemetry. Once an exposure has been integrated, or once reads have been averaged on board, the temporal information inside it is gone. If a fixed flux $F$ is spread along a trail of length $L$ and width $w$ on a background $b$, the background-limited matched-filter signal-to-noise scales approximately as $F/\sqrt{bLw}$, while a compact source pays only for a PSF-sized noise area. That is an analytic scaling, not a mission sensitivity curve, but it shows what trailing costs.

The table below collects the mission parameters that matter for moving bodies. They differ by orders of magnitude in pixel scale, field and cadence, and those differences decide which algorithm makes sense.

All values are from the mission papers cited in the sections below.

Kepler and K2: properties in preselected pixels

Kepler’s stellar photometry was designed around telemetry. Only pixels selected in advance around target stars were returned at high cadence. After a reaction-wheel failure, the extended K2 mission pointed near the ecliptic to balance solar radiation pressure. That put the planets’ plane in the field, and small-body astronomers began to request pixels along the predicted paths of known asteroids and trans-Neptunian objects (TNOs). Disjoint stamps were then stitched into moving-object image sequences (Pál, Molnár & Kiss 2018; Kecskeméthy et al. 2022).

This was never a blind survey. András Pál, Csaba Kiss, Gyula Szabó, László Molnár and colleagues built a programme of long, uninterrupted light curves of known bodies, with early observations of the TNOs 2002 GV31 and (278361) 2007 JJ43 (Pál et al. 2015). The mature collection of Kecskeméthy and colleagues covers campaigns C03 to C19, from November 2014 to September 2018: 66 targets, frequency assignments for 37 (ten of them tentative) and amplitude limits for 29.

The method is ephemeris-based differential photometry. Build mosaics of the target pixels along the allocated path and from nearby stellar stamps, register them, and subtract a median image built without the target. Kecskeméthy et al. enlarged images by about a factor of three before subtraction to reduce residual fringing, then measured aperture photometry at the predicted position. Pixels typically followed about 30 days of apparent motion within campaigns lasting 60 to 80 days. The period search fitted

over a grid of frequencies $f$, accepting peaks that stood at least $5\sigma$ above the residual spectrum with Fourier amplitude at least $3\sigma$, and calling amplitudes between $2.5\sigma$ and $3\sigma$ tentative. Noise was estimated locally in frequency, because low-frequency noise was elevated.

What K2 discovered was usually a property, not a body. Uninterrupted coverage exposed slow rotators and corrected periods that sparse ground data had aliased. The median light-curve period in the K2 TNO sample is about 24 hours, against about 8.9 hours in the comparison ground-based database, though selection effects contribute to that contrast. K2’s depth is best stated as modulation sensitivity on a known track: a constant-amplitude fit to the non-detections gives nominal three-sigma amplitude limits of 0.0133 mag at mean brightness 20 mag and 0.21 mag at 23 mag (Kecskeméthy et al. 2022). These are neither single-frame source limits nor blind-discovery completeness. And because only allocated pixels were recorded, no later search can find a body that wandered outside them.

TESS: a wide, shallow camera as a deep survey

What TESS records

TESS launched on 18 April 2018 and began routine observations on 25 July. Its four cameras each carry four $2048\times2048$ CCDs at about $21''$ per pixel, giving a $24^\circ\times24^\circ$ field per camera and a combined strip of about $96^\circ\times24^\circ$. Each sector is watched for about 27 days. Unlike Kepler, TESS downlinks full-frame images (FFIs): 30-minute cadence in the original mission, 10 minutes in the first extension, 200 seconds afterwards (Pál, Molnár & Kiss 2018; Martinez-Palomera et al. 2025). In their 2018 paper “TESS in the Solar System”, Pál, Molnár and Kiss argued that the huge pixels did not rule out minor-body work: the downlinked full frames gave a spatial coverage K2’s stamps never had.

The photon budget

In October 2019 Matthew Holman, Matthew Payne and András Pál made the distant-planet case explicit in a two-page research note (Holman, Payne & Pál 2019). For a solar-coloured source of Cousins magnitude $I_C$, the signal in one frame is

with effective area $A=69$ cm², $s_0=1.45\times10^6$ photons s⁻¹ cm⁻² and a 600–1000 nm bandpass. The noise is

with $n_{\rm pix}$ aperture pixels, zodiacal light $Z_L\approx47$–135 photons per pixel per second, $n_r$ readouts and read noise $R_N\approx10$ electrons per pixel per read. TESS takes 2-second exposures without a shutter and sums them on board; cosmic-ray rejection reduces the effective 30-minute FFI integration to 1,440 seconds. The pixel response function encloses about 90% of the light within four pixels. At faint magnitudes zodiacal light dominates.

Their conclusion: combining about 1,300 exposures from one sector gives a 50% detection threshold of $I_C\approx22.0\pm0.5$. The ideal background-limited gain from stacking $N$ frames is $\Delta m=1.25\log_{10}N$, which for $N=1300$ is $1.25\times3.11\approx3.9$ magnitudes. Subtracting the mean background does not remove its shot noise, and at fixed total integration a shorter cadence mostly redistributes photons rather than adding them. A camera with 69 cm² of effective area reaching magnitude 22 by stacking is the whole basis of every TESS outer-Solar-System search.

The trajectory bank

Holman et al. then asked how many trajectories a blind search needs. Over a TESS sector a distant body’s apparent motion is dominated by the spacecraft’s parallax, which depends on distance $d$ through the parallax constant $\gamma=1/d$. Following the parametrisation of Bernstein & Khushalani (2000), a local short-arc model is

where $\boldsymbol\mu$ is the residual angular velocity, $\mathbf R_{\perp,\rm obs}$ the spacecraft’s displacement projected perpendicular to the line of sight (in au, with angles in radians), and $\boldsymbol\delta_{\rm orb}$ the curvature that a linear model omits. Shift each frame to cancel the parallax for a trial $\gamma$, and the remaining motion is a straight line.

The bank is set by the requirement that the template stay within one resolution element $P$ of the true path over the baseline $T$, so $\Delta\mu\lesssim P/T$. Bound orbits move at angular speeds that scale as $d^{-3/2}$. Holman et al. obtained

for the two angular-velocity axes, and

for distance, with a floor of one bin on each axis. A month later Payne, Holman and Pál corrected the work normalisation (Payne, Holman & Pál 2019):

These are search operations, not measured FLOPs or GPU time. The striking term is $d^{-4}$: a search restricted to distant objects is far cheaper than one that must also cover nearby asteroids. At 100 au the count drops by $4^4=256$ relative to 25 au. That is why a TESS search for Planet Nine is computationally modest even though a TESS search for every asteroid is not.

Payne et al. also forecast yields under their assumptions: an effective KBO area of about 7,000 square degrees containing roughly 1,400 KBOs brighter than $I_C=22$, about 200 of them potentially new, and about 750 new Centaurs and scattered-disk objects. Their criterion that a body move about five pixels to separate from stationary sources implies a distance horizon near 900 au in their geometry. All of these are conditional forecasts and a method-dependent horizon, not discoveries or a physical boundary.

Known-object photometry

The first large TESS Solar System product went the other way: predict where known objects are and measure them. Pál et al.’s TSSYS-DR1 processed camera 1 (the one nearest the ecliptic) in sectors 1–13 of the southern survey, 52 CCD-sector blocks in all, and extracted 9,912 asteroid light curves (Pál et al. 2020). Their FITSH pipeline built a median background reference from about a dozen exposures spanning two days, modelled scattered light with median filtering and splines on a $64\times64$-pixel grid, and convolved the reference to match each image, absorbing PSF changes and differential velocity aberration of up to about a tenth of a pixel across a sector. The EPHEMD service supplied positions for a TESS observer; Gaia DR2 calibrated astrometry and photometric zero points.

A 2025 reanalysis by Dmitrii Vavilov and Benoît Carry is a reminder that better inference can mean a smaller catalogue. From the same 9,912 curves they kept 4,839 periods with relative uncertainty at most about one third, and 4,521 better than 10%, after comparing Fourier orders, counting extrema and reporting alternative aliases (Vavilov & Carry 2025).

A blind search in the Galactic plane

In 2020 Malena Rice and Greg Laughlin, at Yale, ran the first real blind shift-and-stack search for distant bodies in TESS (Rice & Laughlin 2020). They chose sectors 18 and 19, crowded northern fields along the Galactic plane, where optical surveys tend not to look and where some Planet Nine models placed the planet.

Their pipeline shows how much of a “stacking search” is not stacking. They divided each CCD into $256\times256$-pixel cutouts at 128-pixel spacing, so that most positions appeared in four overlapping cutouts. They discarded problematic time intervals, the 10% of remaining frames with the largest median flux gradient, and the 10% of pixels with the highest peak flux. The final sectors kept 574 and 540 frames, well short of the nominal forecast’s 1,300.

Background removal came in two versions. One fitted temporal polynomials of degree one to five to each pixel’s light curve, segment by segment. The other used Lightkurve’s RegressionCorrector with three principal components drawn from the nearest 2,000 pixels, excluding a five-pixel neighbourhood around the target pixel. The polynomial version rejected systematics better but also absorbed slow-moving sources; the PCA version preserved distant bodies but let through more false positives. Requiring a candidate to appear in both inherited the weaker method’s sensitivity.

The search itself summed along integer-displacement linear tracks and kept, at each starting pixel, the largest flux over all tracks: a “best-ever” image. Their sector 18 example takes 748 whole-array operations across the displacement grid. A maximum over trajectories does not have ordinary Gaussian statistics, so local maxima were inspected by eye and checked against the other background model. On Yale’s Grace cluster each cutout took one CPU about 1–3 hours with polynomial subtraction or 7–8 hours with PCA, run in parallel across cutouts. The summation was a small part of that.

Injection tests placed 24 Gaussian sources into each tested cutout before preprocessing. The reliable region for the joint method was $V<21$ with total displacement above about 30 pixels, corresponding to $d\lesssim150$ au. PCA alone recovered slower sources, about $V=20$ out to 800 au, but that did not define the final completeness. The search produced 17 candidates with weak orbital constraints: their distances came mostly from displacement under a circular-orbit assumption and their magnitudes from an imperfect peak-flux calibration.

The story ends with a validation problem, not a planet. Carlos and Raúl de la Fuente Marcos, Ovidiu Vaduvescu and Marcel Stanescu used the William Herschel Telescope to search areas larger than a square degree around candidates 9 and 11. They recovered neither down to Sloan $r'\le23$ and concluded that the two were much fainter than predicted or false positives (de la Fuente Marcos et al. 2022). Two of 17 were tested; the rest remain untested.

Modelling the systematics on a GPU

Varun Ganapathi’s 2022 preprint attacked the preprocessing directly (Ganapathi 2022). Instead of fitting each pixel independently, it models the frame sequence as

where $S_t$ is a smooth scattered-light field on a coarse grid, $U$ its interpolation to full resolution, $B$ the fixed background, and $B_k$ per-pixel coefficients multiplying the pointing-jitter terms $\phi_k=(\delta x,\delta y,\delta x^2,\delta y^2,\delta x\delta y)$. Scattered light is estimated at low resolution and then held fixed while the per-pixel terms are fitted, with a Huber loss to suppress outliers and L-BFGS for optimisation. The point is to use the spatial smoothness of scattered light rather than rediscover it at every pixel.

Residuals are then correlated with templates that include trajectory, pixel response and jitter, recovering flux outside the peak pixel, under a constant-variance Gaussian approximation after clipping bright pixels. (The paper’s prose says a Poisson standard deviation is proportional to its mean; the correct relation is $\sigma=\sqrt\lambda$.) On an NVIDIA RTX 3090 the background model for one full-sector CCD takes about a minute, and one filter of spatial size $(25,100)$ applied to 1,116 frames of $2048\times2048$ pixels takes about 1.8 seconds: one filter, not a search. On known bodies the method reports local significances of 30.90 for Sedna, 10.36 for 2015 BP519 and 6.17 for 2007 TG422, and injections at magnitude 22 near 160 au. It demonstrates improved recovery, not discoveries.

Detect first, link later

The other branch detects sources in individual difference images and links them, the strategy of ground surveys described in Chapter 12. Deborah Woods and colleagues built the LINEAR–TESS pipeline, which reports asteroid observations to the Minor Planet Center without needing predicted ephemerides (Woods et al. 2021). A 2026 comparison quotes its completeness as about 90% at $V\approx19$ (Powell et al. 2026); the original full text could not be checked. Sparse detection lists make linking cheap for bright objects, but a source that never rises above the single-frame threshold cannot enter the chain.

Tam Nguyen, Woods, Jessica Ruprecht and Jonathan Birge then brought the shift-and-stack idea into the same group with FaXT, a fast discrete X-ray transform through the cube of two spatial axes and time (Nguyen et al. 2024). It is a dynamic program over track segments: short tracks are summed once and combined into longer ones, each child reused by several parents. Conceptually,

where a track of length $2L$ frames starting at pixel $\mathbf x$ with total displacement $\mathbf d$ is the sum of two half-length tracks with displacements $\mathbf d_L,\mathbf d_R$, the second starting at the joining shift $\mathbf s$. The exact floor-and-ceiling indexing is given by Matthews and Nguyen. The implementation needs a power-of-two frame count and integer linear displacements, and its quantised track can differ from rounding the true line independently at every frame. If image width, height, frame count and both velocity axes all scale as $N$, direct summation costs $O(N^5)$ and FaXT $O(N^4)$ (Matthews & Nguyen 2026). The same hierarchical idea, and its pitfalls, are the subject of Chapter 21.

The 2024 abstract reports more than a thousand TESS asteroid detections below the single-frame limit, without establishing how many were new. The independent 2026 assessment by Matthews and Nguyen gives a sharper picture of the trade. On a 256-frame simulated benchmark, nearest-pixel direct summation is about 100 times slower than FaXT. But FaXT’s mean photometric loss grows from 32% at 64 frames to 37% at 256 frames, against about 27–28% for nearest-pixel summation, because the hierarchical track drifts from the true line. In one inclined-geostationary case, FaXT plus refinement took longer than unrefined nearest-pixel summation. A factor of 100 in speed bought a few percent of flux, and refinement cannot restore sources that the coarse stage already rejected.

A learned three-dimensional detector

In May 2026 Brian Powell, Jorge Martinez-Palomera, Amy Tuson, Christina Hedges, Jessie Dotson and J. Caraballo-Vega presented a trajectory-agnostic detector for the original 26-sector TESS survey (Powell et al. 2026). W-Net is two stacked three-dimensional U-Nets, with extra skip connections, that predict an asteroid mask over cubes of $64\times64$ pixels by 64 time samples (32 hours at 30-minute cadence), overlapping by four pixels in space. An adaptive normalisation layer learns a mixture of logistic distributions to scale the input. Labels come from JPL Horizons predictions in TESS observer coordinates; rotations and reflections augment the motion directions. Models trained on southern sectors are applied to northern ones and vice versa, to keep sector-specific noise from leaking between training and test. Because more than 75% of random cubes contain no asteroid, training batches were enriched with cubes that did.

The compute is dominated by inference. The team evaluated about 490 million overlapping cubes, sliding the time window by one frame and averaging. Four GPUs took about 2.5 days per sector, and the whole original survey took about 6,000 GPU-hours on NASA’s NCCS PRISM system; the paper does not name the GPU model or give the training cost. A coarser temporal stride would be much faster but has not been shown to be as robust.

The results are reported at fixed pixel-level precision. At precisions of 10%, 20%, 30%, 40% and 50%, the magnitude at 50% recovery is $V_{50}=21.10$, 20.95, 20.82, 20.58 and 19.61. True- and false-positive counts are pixels, not tracks, and uncatalogued real asteroids count as false positives. Fast movers score lower: at $300''$ per hour a body crosses about seven pixels in one 30-minute frame, diluting its flux and leaving the training distribution. The authors decline to rank W-Net against other TESS searches, and that restraint is correct. Removing an explicit velocity bank does not remove a population prior: the network has learned what known asteroids look like.

Precovery: when the orbit is already known

The 3I/ATLAS precovery that opened this chapter is the cheapest kind of TESS search, because the trajectory is given. Martinez-Palomera and colleagues queried spacecraft-specific ephemerides, retrieved moving cutouts with the public tess-asteroids and tesscube packages, modelled the background with low-rank temporal structure and spatial splines, estimated an offset between predicted and actual detector positions (dominated by WCS uncertainty, not an anomalous orbit), stacked, and extracted aperture and PRF light curves. Two camera/CCD combinations contributed 4,727 and 6,364 frames before quality cuts. The final PRF light curve had 15 points above signal-to-noise 3 (Martinez-Palomera et al. 2025). This demonstrates that sub-threshold information sits in the archive. Because the trajectory came from the discovery, it says nothing about blind completeness. Precovery in general is the subject of Chapter 13, and interstellar objects of Chapter 14.

Gaia: precision that needed a discovery network

A scanning instrument with windows

Gaia is not a camera that takes pictures. It spins, sweeping its fields of view across the sky, and its CCDs are clocked in time-delay integration so that charge moves with the stars. A sky-mapper CCD detects sources down to about $G=20.7$ and assigns each a window, which then travels across the astrometric CCDs at the stellar drift rate. A typical faint-source window is $6\times12$ pixels, usually binned across the scan direction, with pixels subtending about $59\times177$ mas. Each CCD crossing takes about 4.4 seconds, and a full transit yields up to nine astrometric positions in roughly 40 seconds (Carry et al. 2021; Tanga et al. 2023).

A moving asteroid drifts relative to its window. A typical along-scan rate of 13 mas s⁻¹ moves it $13\times4.4\approx57$ mas, about one pixel, during one CCD crossing; a fast mover can leave the window entirely. Pixels outside the windows are never transmitted. No later stacking can find a faint source that the sky mapper did not detect.

Gaia’s measurement is also strongly anisotropic. A single CCD position is precise along the scan and poor across it. If $R(\psi_k)$ rotates along-scan/across-scan coordinates into the sky tangent plane at scan angle $\psi_k$, the covariance of one observation is

and DR3 adds a common systematic component $C_s$ shared by all CCDs in a transit, $C_{\rm transit}=\operatorname{blockdiag}(C_1,\ldots,C_n)+(\mathbf 1\mathbf 1^{T})\otimes C_s$. Right ascension and declination errors can each look like 500 mas while the along-scan combination is better than 1 mas. In DR3 the post-fit along-scan dispersion reaches about 0.25 mas for $G=12$–15 and stays below a milliarcsecond to about $G=17$ (Tanga et al. 2023). Treating coordinates as independent throws away the geometry; treating successive CCDs as independent overstates the information.

Alerts and the follow-up network

Gaia began its survey in July 2014. François Mignard, Paolo Tanga, Karri Muinonen, Thierry Pauwels, Benoît Carry, Federica Spoto and colleagues built two Solar System chains: a short-term pipeline (SSO-ST) for discovery alerts, and a long-term pipeline (SSO-LT) that uses the final attitude and calibration for data releases. Unexpectedly heavy contamination delayed a robust alert service until November 2016 (Carry et al. 2021).

The alert chain is a sequence of filters and joins:

receive source parameters and provisional attitude
reject stationary unmatched sources and detector artefacts
fit linear motion across the CCD positions of each transit
compare with spacecraft-centric predictions for known objects
bundle unmatched transits from the last 48 h by position, motion, brightness
sample short-arc orbits compatible with each bundle (2,000 per source)
propagate the ensemble to ground observatories; issue search regions
combine ground and Gaia astrometry; require a common orbit
report accepted observations to the Minor Planet Center

The base-rate problem is severe. Carry et al. estimate about one Solar System object per 4,000 stellar sources: even 99.9% correct stellar identification leaves four unmatched stars per genuine asteroid. A motion filter, dynamically set each day and typically near $\pm2$ mas s⁻¹ along scan, does most of the separation. The provisional attitude available for alerts is uncertain by about 25 mas along scan and 40 mas across scan, far worse than the final solution, but waiting for the final solution would defeat the purpose of alerts. Then comes the hardest step: turning a 40-second arc seen from 0.01 au away into a region a ground telescope can search, when the distance is unknown. The ranging method generates 2,000 candidate orbits per new source by random-walk sampling of the range and propagates all of them.

The early hope was roughly a hundred discoveries a week. The audited outcome, to July 2020, is more than 1,700 alerts, 227 candidates successfully observed from the ground by the Gaia-FUN-SSO network, and six provisional designations credited to Gaia: 2018 XL20, 2018 XL4, 2018 YK4, 2018 YM4, 2019 CZ10 and 2019 HO4. Most other recoveries were previously observed bodies with poor orbits (Carry et al. 2021). The limit was not motion detection. It was the conversion of a very short, very precise arc into a secure orbit, which needed telescopes on the ground.

Releases: an astrometric archive, not a discovery census

Gaia DR3 was the first large Solar System release: 23,336,467 CCD-level positions in 3,214,776 transits, orbit solutions for 154,741 objects, and 60,518 mean reflectance spectra (Tanga et al. 2023). The sample is shown below.

Identification in the long-term pipeline is an instructive two-level index. Predicted positions of known objects are stored in a HEALPix grid at $N_{\rm side}=2^{10}$ in a Cassandra database; a query for a transit returns zero to a few dozen candidates, and only those are integrated accurately. DR3’s study of its 1,320 unmatched moving-source groups shows the savings: 3,541 transits against about 1.2 million orbits would require about four billion residual computations. Coarse daily geocentric positions in square-degree tiles first selected candidates, and exact Gaia-centric perturbed predictions then tested them. The result associated 712 of the 1,320 groups with 567 distinct known asteroids. The remaining groups are not automatically discoveries.

The Focused Product Release of 10 October 2023 extended the astrometry to 66 months, roughly one main-belt orbit: 46,264,083 CCD measurements of 156,823 objects and 156,762 orbit solutions. ESA states that all of them were already in DR3 (ESA FPR). The relative uncertainty in semimajor axis improved by about a factor of 50, mostly from orbital-phase coverage rather than extra samples (Gaia Collaboration, David et al. 2023). The orbit fits integrate the equations of motion and their variational equations together with a Gragg–Bulirsch–Stoer integrator, and omit direct asteroid–asteroid perturbations in the target fits; formal precision is not physical accuracy.

Gaia’s science observations ended on 15 January 2025. ESA lists Data Release 4 for 2 December 2026, after the cutoff for this book, with planned Solar System tables of 436,551 sources and 60,542,356 observations (ESA DR4). These are announced contents, not a released catalogue. Gaia’s place in the history of discovery is as a transformation of the reference frame and of small-body dynamics. It was never a leader in raw discovery counts.

Euclid: asteroids as streaks

Why Euclid sees asteroids at all

Euclid surveys the extragalactic sky and avoids the ecliptic, yet Benoît Carry’s 2017 study estimated that the planned survey could observe about 150,000 Solar System objects (Carry 2018). That is a population forecast for the survey design of the time. With $0.1''$ VIS pixels and exposures of about 560 seconds, most of those objects appear as streaks. Mikael Pöntinen, Mikael Granvik, Achille Nucita, Luca Conversi and colleagues developed three complementary detection approaches.

StreakDet: segmentation and fitting

StreakDet came from ESA-supported space-debris work by J. Virtanen and colleagues (Chapter 37 discusses the debris lineage). Pöntinen et al.’s 2020 Euclid implementation has three stages (Pöntinen et al. 2020). Segmentation applies two local mean filters, with example windows of $3\times3$ and $21\times21$ pixels, to emphasise narrow structures against broad background; thresholds the result; and cleans the binary image with erosion, morphological reconstruction and multiscale density checks. Connected-component labelling finds candidate features, and geometric tests merge fragments or split blends. A moving two-dimensional Gaussian PSF is then fitted to the original pixels by Levenberg–Marquardt optimisation, and width and curvature cuts reject what is not a streak.

The decisive addition is interdither association: transform detections to a common sky frame and require compatible position, angle, length, width and flux across the dithered exposures of a field. Cosmic rays rarely repeat along an asteroid’s motion; diffraction spikes can, so static features must be rejected. In simulations, single-streak completeness was 96.9% for objects brighter than magnitude 23 with trails longer than 15 pixels (about $10''$ per hour). That is a bright, long subset, not whole-population completeness. The paper reports about one minute on one CPU core per $4{\rm k}\times4{\rm k}$ CCD.

A learned pipeline, and Amdahl’s law

Pöntinen et al.’s 2023 pipeline delays purity to the end (Pöntinen et al. 2023). A CNN scans $20\times20$-pixel cutouts and predicts a streak label and endpoints. Long streaks appear as several “streaklets”; nearby pieces at similar angles are clustered, and a bidirectional recurrent network merges them. Candidate combinations across exposures are classified by XGBoost (644 trees of depth up to 11), with missing exposures encoded as missing features.

The paper is unusually honest about the gap between patch classification and survey detection. The cutout classifier’s purity of about 97% collapses when it is slid across mostly empty images: after CNN and RNN merging, false positives outnumber true ones by more than fifteen to one. Motion consistency across exposures supplies the missing evidence. On the final test set, completeness is 59.1% for clean associations (62.1% if associations mixing true and false streaks are counted) at a purity of 95.4%. Compared with StreakDet the authors find 0.25–0.5 magnitudes more reach and sensitivity to shorter streaks; their estimate of about 50% more detections applies a luminosity function and is not an observed count.

The timing breakdown is the most actionable compute report in this chapter. On a GeForce RTX 3060, the sliding-window CNN processes one CCD in about five seconds. For a field of 144 CCD images, the CNN takes about 12 minutes, clustering and merging 6, interdither linking 4, static-streaklet removal (in standard Python) 20, and removal of static merged streaks 4: about 46 minutes in all. XGBoost evaluation takes seconds. Training used V100 and A100 GPUs: a few hours for the CNN, tens of minutes for the RNN, minutes for XGBoost.

Amdahl’s law does the rest. If the CNN became infinitely fast, the field would take 34 minutes, a speed-up of $46/34\approx1.35$. Removing both static-rejection stages entirely would leave 22 minutes, about 2.1 times faster. A tenfold end-to-end gain would need improvements in inference, clustering, coordinate transformation, candidate generation and data movement together.

Slow movers and the first real data

Streak morphology misses slow, point-like objects. Nucita et al.’s SSOFinder handles motions of about $0.1$–$10''$ per hour from SExtractor catalogues: it picks a pivot exposure, excludes stationary matches, and searches an annulus in the other exposures for at least three detections consistent with constant speed and position angle (Nucita et al. 2025). In simulations purity is about 90% and completeness about 80% in bright bins at $1$–$10''$ per hour; below about $0.4''$ per hour centroid scatter and chance alignments erode purity. A self-organising map then classifies the cutouts; it is a classifier, not an orbit search.

The calibration-phase Euclid Ecliptic Survey, 23–31 December 2023, was the bridge to real data. Irureta-Goyena and colleagues’ 2026 analysis used more than 23,000 appearances of 2,321 known asteroids, found with StreakDet and interdither linking, and measured 889 high-quality rotation periods (Irureta-Goyena et al. 2026). These are physical properties, not discoveries, but they show the preparation pipeline working on mission data. They also show that flux varies along and between streaks because asteroids rotate, so linking cuts that demand constant flux will reject real objects.

The infrared survey line: NEOWISE to NEO Surveyor

NEOWISE

The Wide-field Infrared Survey Explorer (WISE), led by Edward Wright, launched in December 2009 and surveyed in four infrared bands until its coolant ran out, continued in the two shortest bands, and was put into hibernation in February 2011. Amy Mainzer’s NEOWISE team built the small-body programme on it. Reactivated observations began in December 2013; the moving-object pipeline resumed on 23 December and found its first new near-Earth object (NEO) six days later (Mainzer et al. 2014). The same paper recalls the WISE discovery of Earth’s first known Trojan asteroid, 2010 TK7, reported by Martin Connors and colleagues: infrared observations at quadrature exposed a population that night-time optical surveys sampled poorly. The thermal physics and the early WISE discovery statistics belong to Chapter 24. Here the interest is the pipeline.

NEOWISE took 7.7-second exposures every 11 seconds over a $47'\times47'$ field, looking at about $92.5^\circ$ solar elongation. A typical ecliptic position received about a dozen observations over a day and a half. The WISE Moving Object Processing System (WMOPS) linked single-exposure detections rather than stacking. The final explanatory supplement describes the chain: select artefact-clean detections above 4.5 sigma; reject poor profile fits except at high signal-to-noise, where extended comets must survive; remove stationary repeats; form motion-compatible pairs; chain pairs into longer tuples; merge overlapping sky–time regions and a legacy database across runs; reject duplicate assignments; fit great-circle motion; review images by eye; and report tracklets of at least five detections (NEOWISE Explanatory Supplement IV.3). Median reporting latency after reactivation fell below 2.5 days.

One detail shows how an algorithm can set a sensitivity limit. When a frame kept more than 250 detections after filtering, WMOPS raised the signal-to-noise cutoff in steps of 0.1 until about 100 remained; if that needed a cutoff above 10, it discarded the frame’s detections. Crowded fields were thus searched to shallower depth because of linking cost, not because of the optics.

The final archive covers operations to 1 August 2024: 10.6 years of reactivation, 21.3 sky coverages, and more than 1.6 million confirmed detections of nearly 44,600 distinct small bodies (NEOWISE Final Data Release). The single-exposure source database holds 199,762,421,143 rows, overwhelmingly stars, galaxies and artefacts (Supplement II.1). That such an archive still holds missed movers was shown by Masiero et al., whose NEO Surveyor simulator, run over NEOWISE data, recovered 21,661 previously unreported detections, including 1,166 NEOs that had no reported NEOWISE observations (Masiero et al. 2023). This was a recovery guided by known orbits, not discovery, but it shows that information survives outside the original cuts.

NEO Surveyor

NEO Surveyor is the first space telescope designed from the start around discovering asteroids (Mainzer et al. 2023). It is a 50-cm telescope at the Sun–Earth L1 point, imaging simultaneously in NC1 (4–5.2 μm) and NC2 (6–10 μm) over a $1.68^\circ\times7.08^\circ$ field with about $3''$ pixels. It looks between $45^\circ$ and $120^\circ$ from the Sun and within $\pm40^\circ$ of the ecliptic. The required five-sigma sensitivities are 65–120 μJy in NC1 and 110–280 μJy in NC2, depending on zodiacal background. NASA’s mission page gives launch no earlier than September 2027 (NASA).

Its cadence is built to make orbits, not just detections. Six dithered exposures make a Visit; four Visits over 6–9 hours make the set for a tracklet; repeat coverage yields tracks of at least two tracklets spanning about 13 days. The five-year baseline contains about 630,000 Visits. The planned ground system fits sources in both bands simultaneously, coadds each Visit, differences against references built only from other Visits, and extracts candidates from both Visit and single-exposure differences. A classifier combining a CNN on image stamps and a transformer on extracted features feeds a multilayer perceptron. The NMODE linker (which inherits methods used for ZTF) forms tracklets, with extra passes that relax tolerances for slow NEOs and use intra-Visit velocities for fast ones. Moving coadds, tracklet scoring and human review precede reporting.

The survey simulator assumes 99% efficiency for forming tracklets and another 99% for linking them, based on NEOWISE experience and still to be validated, over $0.008$–$8^\circ$ per day. Masiero et al. checked its geometry and fluxes against 1,624,795 NEOWISE positions of 128,462 main-belt asteroids, finding systematic offsets of $0.05''$ in RA and $0.12''$ in Dec; that validates geometry and photometry, not the future classifier or linker. The Level-1 requirement is to find two-thirds of potentially hazardous asteroids larger than 140 m in five years, and the paper forecasts about 200,000–300,000 new NEOs. None of this is a flown result (Chapter 14 compares it with the ground surveys).

Roman: depth, trial counts and resultants

A compute-limited forecast from 2014

In 2014 Andrew Gould asked what the planned WFIRST microlensing survey (WFIRST is now the Nancy Grace Roman Space Telescope) could do for the Kuiper belt (Gould 2014). For six 72-day campaigns with about 5,600 usable images each, he predicted roughly 5,000 KBO detections over an effective area near 17 square degrees, down to $H_{\rm Vega}=28.2$. The forecast single-image signal-to-noise near that limit is about 0.15, so detection is entirely collective.

The paper is unusual in treating computation as the limit. Over long baselines the trajectory needs position, transverse motion, inverse distance and radial motion. In Gould’s model the number of distinct trajectories grows as

At 72 days this is $1.4\times10^{24}$ trials and about $8\times10^{28}$ floating-point operations by brute force. (Gould writes “FLOPS” for what is an integrated operation count, not a rate.) His proposed hierarchy searches short segments first with a permissive threshold and follows only the surviving parameter regions through the rest of the data, cutting the work to about $8\times10^{25}$ operations at about 94% recovery under an independent-segment model. These are analytical forecasts for a historical design. The durable lesson is to reserve expensive long-baseline refinement for coherent candidates, a theme of Chapter 38.

The resultant problem

A newer and more fundamental obstacle comes from how Roman reads its detectors. The infrared arrays are read non-destructively “up the ramp” every few seconds, and the flux in each pixel is the slope of charge against time. Downlink volume does not allow every read to be sent, so reads are averaged on board into resultants. Joseph Masiero’s 2025 technical memo gives the example pattern HL300, a 300-second exposure made of two 1-read resultants, two 2-read resultants, one 4-read resultant and eleven 8-read resultants (Masiero 2025). On the ground, cosmic rays are identified as jumps between successive resultants and the affected resultants are dropped.

A moving source also produces a jump. It illuminates a pixel for a while and then leaves, so the slope changes in time exactly as a cosmic-ray hit does. With $0.11''$ pixels, even a Kuiper belt object at about $2''$ per hour moves about a pixel (the memo’s round figure) in a 300-second exposure, and an NEO, two orders of magnitude faster, moves about a pixel per 3-second read. The memo shows an example in which the jump-detection step suppressed a moving source’s flux completely. Roman’s default calibration chain treats every source as stationary.

A correct forward model works in the resultant domain:

where $w_{ji}$ are the onboard averaging weights, $t_i$ the read times, $b_p$ the background rate and $x(u;q)$ the trajectory. The evidence for motion lives in the differences between adjacent resultants and their covariance, not in the final slope image. Scoring candidate tracks against this operator, while allowing isolated cosmic-ray jumps, is a proposed formulation, not a demonstrated Roman algorithm. The memo lists alternatives: downlink all reads for some fields, use shorter integrations, reconstruct moving flux from resultants and jump flags (no proof of concept yet), or track moving targets. Holler et al.’s 2025 paper on Roman for planetary defence likewise notes that the default pipeline does not provide the streak extraction it needs, and its forecast orbit improvements of two to three orders of magnitude are conditional (Holler et al. 2025).

Onboard averaging removes temporal degrees of freedom. It does not follow that every resultant-domain recovery is impossible. What is missing is a validated injection–recovery study using the exact read pattern, brightness, velocity, background and jump algorithm.

CSST: a forecast without a pipeline yet

The Chinese Space Station Survey Telescope, described in the CSST Collaboration’s 2026 review led by Yan Gong, is a 2-m telescope with a survey-camera field near 1.1 square degrees and $0.074''$ pixels, planned to cover 17,500 square degrees in about 150-second exposures, each field at least twice per band, plus 400 square degrees of deep fields (Gong et al. 2026). Its survey limits ($g\ge26$, at least 25.5 on average in several other bands) are static-source specifications, not the limit for a trailed asteroid in one exposure.

The processing plan includes single-frame detection, astrometry, identification of fast movers, orbit and class estimation, and machine-learning identification, but the review supplies no end-to-end discovery yield, false-alarm curve or runtime. It forecasts close to 5 PB of raw data and at least 30 PB of processed products over ten years. A 2023 simulation of asteroid mass determination by Fan Li and colleagues warns that it assumed a Gaia-like observation frequency that does not match the tentative CSST cadence (Li et al. 2023). No verified CSST discovery total exists to quote.

Hubble’s archive: trails, curvature and deep stacks

Hubble Asteroid Hunter

Hubble was never meant to look for asteroids, yet asteroids cross its images constantly. The Hubble Asteroid Hunter project, started by Sandor Kruk, Bruno Merín, Marcel Popescu, Pablo García-Martín and colleagues, searched 37,323 composite HST images (Kruk et al. 2022). Zooniverse volunteers marked trails, and their labels trained a Google Cloud AutoML Vision object detector that found candidates the volunteers had missed. Human review, duplicate rejection, a return to the original FITS files, reprocessing with cosmic-ray rejection overridden, trail extraction and matching to known objects produced 1,701 trails, 670 of them matched to 454 known bodies. Chapter 28 tells the volunteer side of the story.

The pipeline encodes a lesson that is easy to miss. Detection used display products, but measurement went back to calibrated pixels. In composite images, DrizzlePac’s cosmic-ray rejection can erase the centre of a bright moving trail and leave only its edges, so the project trained on both erased and intact morphologies and then reprocessed the originals. Measuring flux on a display image or a cosmic-ray-clipped composite would be wrong. The 1,031 unmatched trails are on average 1.6 magnitudes fainter than the matched ones and extend to about magnitude 24.5; at the ecliptic the inferred trail density is about 80 per square degree. The heterogeneous pointings, filters and exposure histories forbid reading 24.5 as a uniform completeness depth.

Distance from curvature

HST’s rapid orbital motion around Earth bends the apparent track of a nearby body within a single exposure. Over a short arc,

where $\Delta$ is the distance from the observer. The constant and linear parts of the observer’s motion are absorbed into $\boldsymbol\theta_0$ and $\boldsymbol\mu$; only the nonlinear part, the curvature, constrains $\Delta$. García-Martín et al. determined the intrinsic angular velocity from the trail endpoints at each of 1,300 trial distances, using about 300 extracted points on an average trail and a residual scale of $0.05''$, and minimised the residual over distance (García-Martín et al. 2024). After quality cuts, 632 objects remained, 454 unknown and 178 known, mostly compatible with the main belt. They also sampled 20,000 line-of-sight velocities to delimit families of bound orbits.

The information about inverse distance is proportional to the squared projected observer baseline left after removing the constant and linear parts. So a nearly straight trail can be bright and still carry little distance information. The failure case is instructive: for (58250) 1993 QU1, a bright but nearly straight trail gave a best fit near 6.695 au when the known distance from Earth was 2.382 au. The analysis rejected such solutions with cuts on distance uncertainty above 35%, non-convergence, problematic backgrounds and non-monotonic tracks. A single curved trail never yields a full six-parameter orbit; line-of-sight velocity stays poorly constrained. This is geometry, not a shortage of compute.

Deep stacks of old data

Hubble’s archive also supports searches far below the single-frame limit. In 2026 Kevin Napier, Matthew Holman, Hsing Wen Lin, David Gerdes and Thomas Ruch searched 1,118 ACS images from a 15-day campaign in 2003 with heliostack, stacking along nonlinear projected orbits (Napier et al. 2026). Their 1,148,817 orbital templates, applied across starting pixels, amount to an effective search of about $2\times10^{14}$ trials. After a permissive threshold near seven, orbit refinement on the pixels and a final cut near $\nu=8.8$, 145 candidates remained: 141 injected sources and four real objects, two of them new discoveries and two known objects below the single-frame threshold. The fitted 50% completeness magnitude is $29.21\pm0.03$. The whole process ran in a few hundred H200 GPU-hours and a few thousand CPU-hours, in under a day of elapsed time. HST’s clean noise and the restricted cold-classical orbit family help; the purity is not a guarantee for every archive. The method belongs to Chapter 20. The point here is that stable, calibrated exposures support discoveries two decades after they were taken.

New Horizons: finding a target, and looking from inside the belt

The spacecraft’s Long Range Reconnaissance Imager (LORRI) has a $0.291^\circ$ field and $1.02''$ native pixels. With 4×4 binning, a special attitude-control mode, about 30-second exposures and coadding about 100 images, it reaches $V\approx22$ at signal-to-noise near five; a single 65-second exposure in a sparse field reaches about $V=20.2$ (Weaver et al. 2020). Those are calibrated point-source capabilities, not a blind survey depth.

LORRI’s advantage is proximity. At fixed heliocentric distance and phase, apparent brightness scales as $1/\Delta^2$, and no ground-based computation can reproduce being 0.1 au from a KBO. Weaver et al. observed five known KBOs from spacecraft distances of 0.092–0.290 au, reaching resolutions of about 136–430 km (Weaver et al. 2022). The data are repeated sets of 125 native-resolution images. The pipeline removes row and column background structure, measures Gaia-based astrometric shifts, builds target-aligned and star-aligned robust stacks, and compares single-PSF with double-PSF models. Target alignment matters: a body effectively untrailed in a short exposure can move many pixels over the whole stack. The result was a confirmed close binary, 2011 JY31, with semimajor axis $198.6\pm2.9$ km and period $1.940\pm0.002$ days, and a likely close binary, 2014 OS393. These are discoveries of structure within known systems, of a kind impossible from Earth (Chapter 27 covers binaries).

The search for further targets went back to the ground: Fumi Yoshida and colleagues reanalysed Subaru Hyper Suprime-Cam images with a 32-image FPGA stacking procedure testing 263,169 trial shifts, reaching a candidate-magnitude turnover near 26.5 (Yoshida et al. 2024). Their four-GPU test suggests a future turnaround of about one-fifth, a forecast rather than a measured speed-up.

Landmark results

What the archives cannot give back

Flux preservation comes before detection. Roman’s resultant problem is the clearest case, but the HST composites that erased trail centres and the Gaia windows that truncate fast movers are versions of the same thing. There is no general rule that cosmic-ray cleaning helps moving-object searches. The filter must separate instantaneous, localised charge from PSF-convolved motion using whatever temporal and spatial information the data still contain (Masiero 2025; Kruk et al. 2022).

Confusion sets TESS’s practical depth. A 21-arcsecond pixel collects light from many unresolved stars, and removing their mean leaves their photon noise. Galactic-plane fields differ greatly from the feasibility photon budget, and slow movers are partly absorbed into the static-sky model (see the box on detrending). A single limiting magnitude without sky position, cadence, motion and threshold says little (Rice & Laughlin 2020).

The orbit bottleneck follows the detection bottleneck. A reliable streak can still lack a secure orbit. Gaia needed ground telescopes because the unknown range made the Gaia-to-Earth parallax uncertain. HST curvature gives range but not radial velocity. Large local significances did not secure the Rice–Laughlin candidates. Independent visits and a common orbit matter more than an attractive stack.

Completeness denominators differ. Euclid’s bright-streak recovery, uniform-simulation recovery, patch-classifier accuracy and output purity are four different quantities. WMOPS completeness is conditional on usable detections. W-Net’s precision counts pixels. A figure plotting these as one “accuracy” would mislead.

Simulation-trained models face domain shift. Cosmic-ray residuals and diffraction spikes are strong confusers in Euclid data, and a uniform bright synthetic line is not a realistic asteroid. Catalogue labels for TESS miss uncatalogued objects and misplace poorly known ones (Pöntinen et al. 2023; Powell et al. 2026).

Compute is rarely reported. Euclid’s component timings, the W-Net inference budget, Ganapathi’s single-filter timing and heliostack’s H200 hours are the exceptions. The Gaia, WMOPS, NEO Surveyor, CSST, Hubble Asteroid Hunter and LORRI papers give no comparable end-to-end accounting. No primary source examined here demonstrates a tenfold end-to-end GPU improvement over the strongest existing baseline at equal sensitivity and false-alarm rate, for any of these missions.

Where the room is

The missions in this chapter separate cleanly into limits that computation cannot touch and limits that it can. Photon counts, the illumination during acquisition, pixels never transmitted, reads averaged on board, trails integrated within exposures, sky that a spacecraft cannot point at, and orbital arcs too short to constrain an orbit are physical or acquisition limits. Tensor cores cannot restore that information. Nuisance-model flexibility, template mismatch, candidate thresholds, linking cost and finite compute are engineering limits, and that is where new methods can win.

Candidate management before classifiers. The Euclid benchmark is a plain Amdahl warning: infinitely fast inference gives 1.35 times. The opportunity is in the other 34 minutes. Represent streaks as packed arrays, transform coordinates in batches, bin by sky position, angle, speed and epoch, and run segmented GPU joins on geometrically compatible candidates before any learned score. Replace overlapping CNN cutouts with fully convolutional feature maps where they can be shown equivalent. Keep the final PSF fit on original pixels, because learned endpoints are less accurate than StreakDet’s fitted ones (Pöntinen et al. 2023). No one has yet published a tenfold result here; the route is benchmarkable.

Weighted reusable sums with controlled mismatch. FaXT showed that sharing partial tracks buys two orders of magnitude in speed and costs a few percent in flux. The next step is a weighted version that propagates the PRF numerator $A$ and information $B$ rather than raw flux, restricts states to physical motions, and bounds mismatch. Segments must be reused without requiring each to be individually significant, because a body invisible in every segment can still be significant in the full sum. TESS’s irregular times require indexing by physical time; zero-weight padding is allowed only if motion is still evaluated at the correct times. Whether enough child-state reuse survives curved, parallax-dominated tracks is an open research question. Chapter 39 treats the transform side.

Repeated learned inference. W-Net evaluated about 490 million heavily overlapping cubes, one-frame strides of 64-frame windows. For a fixed network, cost is linear in the number of cubes, with per-cube work proportional to $\sum_\ell V_\ell k_\ell^3 c_{\ell,\rm in}c_{\ell,\rm out}$ over layers $\ell$ with $V_\ell$ output voxels, kernel size $k_\ell$ and channel counts $c$. Larger fully convolutional slabs, cached temporal features or distillation of the sliding-window ensemble could remove much of the duplication. Boundaries, pooling alignment and learned normalisation mean outputs will not match automatically, so any gain must be measured at the track level and at equal false-candidate load. A hybrid that uses learning for nuisance estimation or proposals, followed by an exact likelihood fit, is another route; the proposal stage must be tested on slow movers, extreme speeds, high inclinations and crowded fields that the training population underrepresents. Chapter 22 discusses this pattern in general.

Avoiding algorithm-driven threshold increases. NEOWISE’s crowded-frame rule, which raised the threshold until about 100 sources remained, is a case where faster linking would buy sensitivity directly. A redesigned linker with hierarchical angular-velocity cells, time-ordered spatial hashes and uncertainty-aware pair bounds could accept the original source list. The test must be paired injection–recovery at the same false-tracklet burden, including faint comets and blends; lowering a threshold while flooding human vetters is not equal sensitivity. NEO Surveyor’s much larger main-belt background makes this especially relevant.

Searching Roman resultants with the acquisition operator. Simulate moving PSFs through the actual read pattern, average them into resultants, propagate the covariance, and compare three hypotheses: static sky, moving source, isolated cosmic-ray jump. Measure completeness against default slope products and an all-reads oracle, over magnitude, rate, angle, background and resultant pattern. Batched template–readout products suit tensor cores, but no hardware inverts the null space of the averaging operator.

Using the known observer trajectory. For HST, CSST and the L1/L2 missions, observer-induced curvature is deterministic at each trial distance. Precompute projected observer basis functions, search cells in inverse distance, and reuse short-segment matched sums before refining radial velocity and curvature. Gould’s forecast and heliostack both show why: long baselines buy depth but make the naive bank enormous. Partial sums must stay signed and correctly normalised under masks; taking the maximum per segment and summing those maxima changes the null distribution and loses faint sources.

Joint archive fits. Multiple TESS sectors offer independent instrument states and a longer parallax lever arm. Jointly fitting a shared static sky, sector-dependent scattered light and an orbit-conditioned source, with the nuisance projection applied to both data and templates, could preserve faint movers that independent per-pixel detrending removes. For Gaia-like data, batched ephemerides and Jacobians and uncertainty-aware sky corridors could speed attribution, provided the covariance structure, time conventions and light bending survive the port.

Co-designing acquisition. Denser resultant sampling for some Roman fields, motion-aware window allocation for a future Gaia-like scanner, and LORRI windows chosen for discovery all trade sensitivity against telemetry. This joint optimisation may hold more discovery potential than any ground algorithm.

The decisive missing experiment is a common benchmark. On one real TESS CCD subset, withhold the known bodies, inject blind sources before detrending, and compare direct weighted GPU filtering, weighted reusable sums, and learned proposals followed by orbit refits. Record bytes read, peak memory, preprocessing, search and vetting time, completeness, flux bias and false tracks, including slow movers, missing cadences and curved tracks, and report the hardware, motion domain, passband and operating point. The same template would serve Euclid streaks and Roman resultants. Until such benchmarks exist, claims of order-of-magnitude gains in this area cannot be tested. Chapter 42 collects this and the book’s other open problems.

References

1. Bernstein, G., Khushalani, B. (2000). Orbit fitting and uncertainties for Kuiper belt objects. AJ 120, 3323. arXiv:astro-ph/0008348
2. Buie, M. W., Spencer, J. R., Porter, S. B., Benecchi, S. D. et al. (2024). The New Horizons Extended Mission Target: Arrokoth Search and Discovery. arXiv preprint. arXiv:2403.04927
3. Carry, B. (2018). Solar System Science with ESA Euclid. A&A 609, A113. arXiv:1711.01342
4. Carry, B., Thuillot, W., Spoto, F., David, P. et al. (2021). Potential asteroid discoveries by the ESA Gaia mission: Results from follow-up observations. A&A 648, A96. arXiv:2010.02553
5. de la Fuente Marcos, C., de la Fuente Marcos, R., Vaduvescu, O., Stanescu, M. (2022). Distant trans-Neptunian object candidates from NASA's TESS mission scrutinized: fainter than predicted or false positives? MNRAS Letters. arXiv:2204.02230
6. ESA/Gaia (2023). Gaia Focused Product Release contents. ESA. cosmos.esa.int/web/gaia/fpr
7. ESA/Gaia (2026). Gaia DR4 content (updated 14 September 2026). ESA. cosmos.esa.int/web/gaia/dr4
8. ESA/Gaia (2025). Gaia end of observations. ESA. cosmos.esa.int/web/gaia/end-of-observations
9. Gaia Collaboration, David, P., Mignard, F., Hestroffer, D. et al. (2023). Gaia Focused Product Release: Asteroid orbital solution. Properties and assessment. A&A. arXiv:2310.14699
10. Ganapathi, V. (2022). Maximum Likelihood Systematic Effect Modeling and Matched Filtering to Detect Trans-Neptunian Objects with TESS. arXiv preprint. arXiv:2209.09848
11. García-Martín, P., Kruk, S., Popescu, M., Merín, B. et al. (2024). Hubble Asteroid Hunter III. Physical properties of newly found asteroids. arXiv preprint. arXiv:2401.02605
12. Gong, Y., Miao, H., Zhan, H. et al. (CSST Collaboration) (2026). Introduction to the Chinese Space Station Survey Telescope (CSST). Sci. China Phys. Mech. Astron. 69, 239501. doi:10.1007/s11433-025-2809-0
13. Gould, A. (2014). WFIRST Ultra-Precise Astrometry I: Kuiper Belt Objects. JKAS 47, 279. arXiv:1403.4241
14. Holler, B. J., Cosentino, R. G., Schultz, W. C., Brandt, T. D. et al. (2025). The Roman Space Telescope as a Planetary Defense Asset. arXiv preprint. arXiv:2508.14412
15. Holman, M. J., Payne, M. J., Pál, A. (2019). A TESS Search for Distant Solar System Planets: A Feasibility Study. RNAAS 3, 160. arXiv:1910.06383
16. Irureta-Goyena, B. Y., Altieri, B., Kneib, J.-P., Pöntinen, M. et al. (2026). Euclid: Asteroid rotation periods from the Euclid Ecliptic Survey. arXiv preprint. arXiv:2604.25652
17. Kecskeméthy, V., Kiss, C., Szakáts, R., Pál, A. et al. (2022). Light Curves of Trans-Neptunian Objects from the K2 Mission of the Kepler Space Telescope. ApJS. arXiv:2210.06571
18. Kruk, S., García Martín, P., Popescu, M., Merín, B. et al. (2022). Hubble Asteroid Hunter I. Identifying asteroid trails in Hubble Space Telescope images. A&A 661, A85. arXiv:2202.00246
19. Li, F., Yuan, Y., Fu, Y., Chen, J. (2023). Simulation study of asteroid mass determination using CSST asteroid observations. Front. Astron. Space Sci. 10. doi:10.3389/fspas.2023.1230666
20. Mainzer, A., Bauer, J., Cutri, R. M., Grav, T. et al. (2014). Initial Performance of the NEOWISE Reactivation Mission. ApJ 792, 30. arXiv:1406.6025
21. Mainzer, A. K., Bauer, J. M., Cutri, R. M., Grav, T. et al. (2023). The Near-Earth Object Surveyor Mission. PSJ 4, 224. arXiv:2310.12918
22. Martinez-Palomera, J., Tuson, A., Hedges, C., Dotson, J., Barclay, T., Powell, B. (2025). Pre-discovery TESS Observations of Interstellar Object 3I/ATLAS. ApJL. arXiv:2508.02499
23. Masiero, J. (2025). Technical Memo: The Impact of Nancy Grace Roman Telescope's default image processing on the detectability of moving Solar system objects. arXiv. arXiv:2509.20469
24. Masiero, J. R., Dahlen, D. W., Mainzer, A. K., Bottke, W. F. et al. (2023). Validation of the Survey Simulator tool for the NEO Surveyor mission using NEOWISE data. PSJ 4, 225. arXiv:2310.12919
25. Matthews, S., Nguyen, T. (2026). Performance Assessment of Track-Before-Detect Algorithms and Post-Search Refinement Methods. AMOS Conference. amostech.com
26. Napier, K. J., Holman, M. J., Lin, H. W., Gerdes, D. W., Ruch, T. R. (2026). heliostack: A Novel Approach to Minor Planet Discovery. PSJ, accepted. arXiv:2604.16731
27. NASA (2026). NEO Surveyor mission page (accessed 16 October 2026). NASA Science. science.nasa.gov/mission/neo-surveyor
28. IPAC NEOWISE team (2024). NEOWISE Final Data Release. IRSA. wise2.ipac.caltech.edu/docs/release/neowise
29. IPAC NEOWISE team (2024). Explanatory Supplement II.1: Single-exposure Source Database, General Properties. IRSA. sec2_1
30. IPAC NEOWISE team (2024). Explanatory Supplement IV.3: WISE Moving Object Pipeline Subsystem. IRSA. sec4_3
31. Nguyen, T., Woods, D. F., Ruprecht, J., Birge, J. (2024). Efficient Search and Detection of Faint Moving Objects in Image Data. AJ 167, 113. doi:10.3847/1538-3881/ad20e0
32. Nucita, A. A., Conversi, L., Verdier, A., Franco, A. et al. (2025). Euclid: Detecting Solar System objects in Euclid images and classifying them using Kohonen self-organising maps. arXiv preprint. arXiv:2501.05023
33. Pál, A., Molnár, L., Kiss, C. (2018). TESS in the Solar System. PASP. arXiv:1809.07403
34. Pál, A., Szabó, R., Szabó, Gy. M., Kiss, L. L., Molnár, L. et al. (2015). Pushing the limits: K2 observations of the trans-Neptunian objects 2002 GV31 and (278361) 2007 JJ43. ApJL 804, L45. doi:10.1088/2041-8205/804/2/L45
35. Pál, A., Szakáts, R., Kiss, C., Bódi, A. et al. (2020). Solar System Objects Observed with TESS: First Data Release. Bright Main-belt and Trojan Asteroids from the Southern Survey. ApJS 247, 26. arXiv:2001.05822
36. Payne, M. J., Holman, M. J., Pál, A. (2019). A TESS Search for Distant Solar System Objects: Yield Estimates. RNAAS 3, 172. arXiv:1911.03676
37. Pöntinen, M., Granvik, M., Nucita, A. A., Conversi, L. et al. (2020). Euclid: Identification of asteroid streaks in simulated images using StreakDet software. A&A 644, A35. arXiv:2011.05297
38. Pöntinen, M., Granvik, M., Nucita, A. A., Conversi, L. et al. (2023). Euclid: Identification of asteroid streaks in simulated images using deep learning. A&A 679, A135. arXiv:2310.03845
39. Powell, B. P., Martinez-Palomera, J., Tuson, A., Hedges, C., Dotson, J., Caraballo-Vega, J. (2026). Trajectory-Agnostic Asteroid Detection in TESS with Deep Learning. arXiv preprint. arXiv:2605.12391
40. Rice, M., Laughlin, G. (2020). Exploring Trans-Neptunian Space with TESS: A Targeted Shift-Stacking Search for Planet Nine and Distant TNOs in the Galactic Plane. PSJ 1, 81. arXiv:2010.13791
41. Tanga, P., Pauwels, T., Mignard, F., Muinonen, K. et al. (2023). Gaia Data Release 3: The Solar System survey. A&A 674, A12. arXiv:2206.05561
42. Vavilov, D. E., Carry, B. (2025). Rotation periods of asteroids from light curves of TESS data. A&A. arXiv:2501.07189
43. Weaver, H. A., Cheng, A. F., Morgan, F., Taylor, H. W. et al. (2020). In-Flight Performance and Calibration of the LOng Range Reconnaissance Imager (LORRI) for the New Horizons Mission. arXiv preprint. arXiv:2001.03524
44. Weaver, H. A., Porter, S. B., Spencer, J. R. et al. (2022). High Resolution Search for KBO Binaries from New Horizons. arXiv preprint. arXiv:2201.05940
45. Woods, D. F., Ruprecht, J. D., Kotson, M. C., Main, E. L. et al. (2021). Asteroid Observations from the Transiting Exoplanet Survey Satellite: Detection Processing Pipeline and Results from Primary Mission Data. PASP 133, 014503. doi:10.1088/1538-3873/abc761
46. Yoshida, F., Yanagisawa, T., Ito, T., Kurosaki, H. et al. (2024). A deep analysis for New Horizons' KBO search images. arXiv preprint. arXiv:2407.05673