Error Analysis for Rotating-drift-scan Charge-coupled Device Observation of Near-Earth Asteroids

The apparent velocities of near-Earth asteroids (NEAs) are usually high when they pass by Earth. Observing these fast-moving objects with long exposure times would cause their images to streak and significantly decrease the precision of astronomical measurements. The rotating-drift-scan (RDS) charge-coupled device technique is a promising approach to observe fast-moving NEAs during their close approaches to Earth. By rotating the camera of a telescope, an NEA can be observed in the time delay integration mode. This allows the asteroid to be imaged as a point source, even with a long exposure time. Here, we thoroughly present the RDS follow-up observation and orbit determination of a newly discovered NEA 2023 BJ7. This technique makes an impactful contribution to improving the NEA's orbit accuracy by extending the observation arc. A detailed statistical analysis of the astrometric error was conducted, revealing that RDS observations can achieve a competitive accuracy with an rms error of 0.″24 in right ascension and 0.″32 in declination. The instability of the telescope is thought to be the main reason affecting the internal precision. Furthermore, the RDS technique excels at observing fast-moving NEAs, as well as newly discovered NEAs without accurate ephemerides. For NEAs with rates of motion exceeding 10 deg day−1, the rms of RDS observation residuals is 0.″35 in the along-track direction and 0.″23 in the cross-track. With this technique, a network of small-aperture telescopes would substantially benefit our global NEAs monitoring system to ensure Earth’s safety from any asteroid impacts.


Introduction
Near-Earth asteroids (NEAs) are asteroids with perihelion distances of less than 1.3 au and orbits that approach or cross Earth's orbit.When an NEA is larger than 140 m in diameter and has a minimum orbital intersection distance (MOID) with Earth of less than 0.05 au, it is denoted as a potentially hazardous asteroid (PHA). 4A PHA could cause significant damage if it impacts Earth.As of September 2023, the International Astronomical Union (IAU) Minor Planet Center (MPC) has cataloged nearly 33,000 NEAs, including over 2000 PHAs. 5 Observing these NEAs, especially PHAs, is essential to improving their orbits by extending observation arcs and to ensuring Earth's safety from asteroid impacts by predicting them in advance.
To detect and reduce the risk of asteroid and comet impacts, a great number of resources are devoted to NEA observations.Wide-field survey telescopes are the first line of defense, scanning the night sky for moving objects against the background stars.NEA survey projects, including the Catalina Sky Survey (Christensen et al. 2012), Pan-STARRS (Kaiser et al. 2002), and ATLAS (Tonry et al. 2018), have discovered a large number of asteroids.Once an NEA is detected, groundbased optical telescopes follow up to obtain more position measurements for orbit refinement.Additional observations may be gathered from other sources, such as planetary radars and space-based telescopes.Finally, the MPC collects and archives NEA observational data from around the world.The MPC is responsible for NEA identification, designation, and orbit computation.It also designates newly discovered asteroids, assists observers with its ephemeris service, and alerts the community to close approaches.
Small-aperture optical telescopes are attractive for building a global observation network because they are inexpensive.However, their limited aperture means that they can only follow up relatively bright NEAs, especially when the NEAs are traveling near Earth.At close approach, the apparent velocities of these asteroids are usually high, which can make it difficult to obtain accurate positional measurements.This is because it is challenging to simultaneously obtain point-like images of a fast-moving NEA and field stars using long exposures, regardless of whether the telescope is tracking the stars or the NEA.
The rotating-drift-scan (RDS) charge-coupled device (CCD) technique (hereinafter referred to as the "RDS technique") has been proposed for conducting precise and reliable positional measurements of fast-moving NEAs during their close approaches to Earth, especially with small-aperture telescopes (Tang et al. 2014).The technique involves mounting a CCD camera that supports the time delay integration (TDI) mode on a rotation platform attached to a telescope.By controlling the rotation angle of the camera and the CCD charge transfer speed according to the apparent motion of the target NEA, point-like images of the fast-moving NEA can be acquired.The RDS technique has been used to observe hundreds of NEAs, as reported by Maigurova et al. (2018), Pomazan et al. (2021), and Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Pomazan et al. (2022).In this article, we present a detailed overview of the RDS technique by observing a newly discovered NEA 2023 BJ 7 .We investigate potential sources of error during the observation process and perform a statistical analysis of the RDS observation residuals to assess its astrometric precision and accuracy.
The rest of this article is structured as follows.In Section 2, we briefly introduce the RDS technique for NEA observation, covering the equipment upgrade, observation procedure, and data reduction.The NEA 2023 BJ 7 ʼs follow-up observation and orbit determination are presented in Sections 3 and 4, respectively.Section 5 is about the statistical analysis of RDS astrometry.Finally, Section 6 summarizes the advantages and disadvantages of the RDS technique.

Rotating-drift-scan Technique
TDI is an operating mode for CCDs that allows for cumulative exposures of an object by transferring the charges generated by incident light from one CCD line to the next at the same speed as the object moving across the camera.TDI mode is widely used in long exposure astronomical imaging of wide regions of the sky, also known as drift-scan imaging.In driftscan imaging, the telescope is kept stationary and the stars drift across the CCD camera in the direction perpendicular to the lines of the CCD.In TDI mode, the photoelectrons are transferred in synchronization with the movement of the sky.This means the intensity value for the corresponding image location continues to be increased, and the star appears as a point.Through this drift-scan technique, a strip of the sky can be imaged as it passes over the telescope's field of view (Sabbey et al. 1998).
After being upgraded to the RDS technique, the drift-scan method can be used to capture fast-moving NEAs as well.As depicted in the schematic of Figure 1, the RDS technique involves mounting the camera on a rotation platform that changes the CCD charge transfer direction.This allows the target NEA to move parallel to the CCD lines and be scanned at a rate commensurate with its velocity.The telescope is kept in a fixed position during the drift-scan observation.The exposure time is adjusted in agreement with the apparent magnitude of the target object and is limited by the time it takes the NEA to move across the CCD from one side to the other.This technique allows point-like images of the asteroid to be acquired.
Following the method described above, an RDS observation of an NEA can be broken down into four steps (Tang et al. 2014): 1. Slew the telescope to the NEAʼs predicted position and rotate the camera as needed according to the NEA's ephemeris.Then keep the telescope stationary.2. Take a short exposure of field stars in TDI mode.3. Make a drift-scan observation of the NEA with a required exposure time as it moves across the CCD. 4. Take another image of field stars as in Step 2.
Then, repeat these steps for the next round of observation.The date of the RDS observation is set to the exposure midpoint of Step 3. Additionally, Steps 2 and 4 denote RDS observations at the sidereal rate.In practice, the camera is not rotated in the sidereal direction, and the short exposure shots ensure that the images of field stars are not streaked.
Because the NEA and field stars have different apparent velocities, a long exposure causes the images of stars to be streaked in the CCD frame of the NEA obtained in Step 3. Therefore, two auxiliary CCD frames of field stars need to be acquired in Steps 2 and 4, respectively, for the following RDS astrometric reduction, which differs from a typical one.First, reference stars are extracted from a reference catalog and identified on the two CCD frames of field stars.For each frame of field stars, the coefficients of a polynomial model (also known as a plate model) representing the transformation between measured rectangular coordinates and standard coordinates are determined, according to these stars' celestial coordinates in the reference catalog.Since the telescope is kept stationary during the observation process, we can assume that there is a linear dependence among the three sets of coefficients related to the three CCD frames.This allows us to obtain the polynomial model for the frame of the NEA using the linear interpolation method or a combination method from Yu et al. (2018).Then, the newly determined standard coordinates of the NEA are derived, along with its celestial coordinates.A detailed description of the RDS data reduction process can be found in Pomazan et al. (2021), Pomazan et al. (2022), and Pomazan (2022).It is important to note that the values of camera rotation angle and CCD charge transfer speed, key parameters for RDS observations, are calculated according to the NEA's ephemeris.An inaccuracy in the ephemeris could cause the scanning to be inconsistent with the target movement on the CCD and may make the images elongate.However, this effect is small and relatively changeless during a single RDS observation round.The trailed image's center can still approximate the target's true position.And fairly good astrometric results could be achieved with traditional centroid methods, such as two-dimensional Gaussian fitting or a modified moment algorithm (Stone 1989).Therefore, the RDS technique is less sensitive to an inaccuracy in the NEA's ephemeris.This makes the RDS technique particularly valuable for newly discovered NEAs, which often lack sufficient observational data for precise orbit determination.

Follow-up Observations
Follow-up observations are essential for refining NEAs' orbits to ensure reliable predictions and recovery at their next apparition.The RDS technique allows small-aperture telescopes with CCD cameras to observe NEAs during their close approach to Earth.In this study, we demonstrate the power of the RDS technique by observing fast-moving NEAs.A computer program was developed to select interesting and observable NEAs considering factors such as the asteroids' apparent rates of motion, apparent magnitudes, topocentric positions, and other criteria.One such NEA that caught our attention is the newly discovered 2023 BJ 7 .It was scheduled to pass by Earth on 2023 January 30 at a distance of 0.0024 au.Its maximum apparent angular rate in the plane of the sky, or rate of motion, is about 112 deg day −1 .
NEA 2023 BJ 7 is an Aten-type asteroid.Over three days as it passed by Earth, telescopes around the world recorded 80 positions of this asteroid.All astrometric data points are distributed along a distance-time line in Figure 2.For subsequent analysis, all observed data were apparently split into three data sets (DSs) according to their observation periods.DS1: observations near 2023 January 28.4 (UTC) by the Zwicky Transient Facility (ZTF) at the Palomar Observatory (MPC code: I41).DS2: observations around 2023 January 30.0 (UTC).DS3: observations on 2023 January 30.5 (UTC) by the LiShan Observatory (MPC code: O85).As this asteroid was close to Earth, its apparent speed became very high.The closest moment was recorded by a 0.5 m Cassegrain telescope at the LiShan Observatory in China, and a total of 11 positions were obtained using the RDS technique.The focal length of the telescope is 3445 mm.The full width at half-maximum (FWHM) is 2 3. We used an Alta U9000 CCD detector without a filter.This CCD supports the TDI scanning mode and has 3056 × 3056 pixels of size 12 μm.The field of view (FOV) is 36 7 × 36 7 with a pixel scale of 0 72.
Follow-up RDS observations and data reduction of 2023 BJ 7 were carried out as described in Section 2. The orbital elements of 2023 BJ 7 provided by the MPC database were used to generate its ephemeris for coordinating follow-up observations.Two parameters were notably calculated for subsequent RDS observations: drift-scanning speed and camera rotation angle.An example of one observation round is shown in Figure 3.It includes two CCD frames of field stars with a 3 s exposure, and one CCD frame of 2023 BJ 7 (apparent magnitude: 16.7) with an exposure time of 90 s.A point-like image of 2023 BJ 7 appears in the central panel of Figure 3, while all field stars trail owing to the long exposure.The other two auxiliary frames in the right and left panels of Figure 3 provide the information of reference stars for the RDS astrometric reduction.The positional precision of optical observations is limited by the number of photons recorded and the image resolution.A higher signal-to-noise ratio (SNR) and smaller FWHM value for the point-spread function (PSF) can improve the precision.For this RDS observation, the SNR of the target in Figure 3 is 17.374.The FWHM is 2 3.
Reference stars are typically used to calibrate astrometric measurements.For this case, we used the Gaia Data Release (DR) 2 star catalog, which has position uncertainties of about 2 mas for sources at brightness equal to 20 mag (Gaia Collaboration et al. 2016, 2018).The number of reference stars in the FOV depends on many factors, including the observed sky area, weather conditions, exposure time, and the telescope's size.For this RDS observation of 2023 BJ 7 , the number of reference stars is greater than 50 (as depicted in Figure 3), which meets the requirement for astrometric reduction.
The astrometric reduction process is also sensitive to errors in the measured coordinates of the reference stars and the target.The repeatability of one object's measured coordinates in different frames indicates the precision.First, we eliminated the systematic errors caused by atmospheric refraction using the reference stars that appear simultaneously in two frames.Then, we obtained the measured coordinates of stars in different frames and calculated their standard deviation to reflect the repeatability.The results are illustrated in the right panel of Figure 4.The abscissa is the logarithm of brightness in analog-to-digital units (ADU).Around 7000 reference stars were selected in 10 rounds of observation, where four adjacent sky areas were imaged per round by the LiShan telescope.As the brightness increases, the repeatability of the measurement coordinates generally shows a better trend, with an average value of 0 12 uncertainty.Note that the RDS astrometric reduction is performed using reference stars that are not on the same frame as the target.This strategy is conditional on the assumption that the telescope's pointing position is fixed during the RDS observation.To check the stability of the telescope, 2-4 frames of reference stars were obtained in a manner comparable to one round of RDS observation.The azimuth and elevation of the center of each frame were acquired, and their standard deviation in each round was calculated.The right panel of Figure 4 displays these standard deviations and indicates the possible pointing deviation of the LiShan telescope, which average around 0 20.As the pointing direction of the telescope changes, it will lead to errors in the position measurement.
The NEA 2023 BJ 7 was observed using the RDS technique as described above.We conducted a detailed error analysis of the RDS observation, including calculations and analysis of the repeatability of measured coordinates and the instability of the telescope through specially designed experiments.The latter may be the largest source of error in RDS observations.To further assess the accuracy of RDS observations, we calculated the orbit of the NEA and statistically analyzed the residuals of the RDS astrometric positions as described in the following sections.

Orbit Determination
Orbit determination is the process of estimating an object's trajectory and orbital parameters based on observational data.NEA orbits are constantly perturbed by various gravitational and nongravitational influences in the solar system, resulting in increasing orbital uncertainties over time.So, it is necessary to regularly observe NEAs and update their orbits.
We developed a numerical code for the orbit calculation and analysis of solar system bodies.This code can integrate the orbit of an object and fit its initial state vectors to the observational data.It has been successfully applied to the orbit  refinement of Neptune's satellites (Tang et al. 2020(Tang et al. , 2021)).The dynamical model for calculating the NEAs' orbit includes: Newtonian and post-Newtonian accelerations induced by the masses of the Sun, eight planets of the solar system, Pluto, and the Moon; perturbations from the 16 most massive asteroids6 ; solar oblateness.Because the trajectory of 2023 BJ 7 was close to Earth, we especially took into account the gravitational interaction up to degree 10 in the spherical harmonics expansion of the gravitational potential for Earth and up to degree 4 for the Moon.Other effects are small and ignored here.
The Bulirsch-Stoer method was employed for the orbital numerical integration, along with a compensated summation algorithm to reduce round-off errors.The motion of an NEA was calculated in the Barycentric Celestial Reference System (BCRS), which is connected to the International Celestial Reference System (ICRS).Barycentric dynamical time (TDB) was set as the coordinate time.The step size used in the integration was 0.1 day.The geopotential coefficients of Earth's gravitational field were taken from the EGM2008 Model (Pavlis et al. 2012).Software routines from the IAU SOFA Collection (IAU SOFA Board 2021) were used to obtain Earth's attitude and different timescales.The positions of the Sun, planets, massive asteroids, and other required constants in the dynamical model were taken from the ephemeris DE440 (Park et al. 2021) and NASA Planetary Data System. 7bservations of asteroid 2023 BJ 7 from the MPC were measured to the International Celestial Reference Frame (ICRF) using different star catalogs, including USNO-B1.0 and Gaia DR1, DR2, and DR3.However, each star catalog has its own unique systematic relationship with the ICRF, which can introduce biases when using specific astrometric catalogs in the observation reduction process.Eggl et al. (2020) used the Gaia DR2 catalog, which has high accuracy, to identify systematic errors in 26 other star catalogs.They provided debiasing tables that can be used to alleviate these errors.After the observations were debiased, a preliminary orbit of 2023 BJ 7 was calculated from the observation DS2 using Laplace's method.The epoch t 0 = Julian Day 2459974.5 (2023 January 30.0 TDB) was chosen as the initial date.The least-squares method was then used to yield the improved position and velocity, based on all Earth-based optical observations.These observations were initially assigned equal weight, but the weights were later adjusted according to the residuals using an M-estimator in the iterative refinement procedure (Song et al. 2012).A scaling factor N 4 was also introduced to deweight the data where more than four observations per night are from the same observer, to mitigate possible effects of unresolved systematic errors (Vereš et al. 2017).The final adjusted state vectors for 2023 BJ 7 at epoch t 0 are given in Table 1.
Figure 5 shows the observation residuals in right ascension and declination.Here, the right ascension residual is corrected with the cosine of the declination.For the RDS observations from the LiShan observatory, the mean values of the residuals, with their standard deviations, are 0 07 ± 0.30 in R.A. and 0 10 ± 0.69 in decl.Despite a moderate declination deviation, these positions were obtained at the asteroid's closest approach, when it reached a very high rate of motion, approximately 112 deg day −1 .The scarcity of data elevates the importance of every measurement.RDS observations extend the observed orbital arc and are valuable for refining the orbit.Moreover, our results are consistent with the residuals computed by the NASA Jet Propulsion Laboratory (JPL), which are also plotted in Figure 5.The unweighted root-mean-square (just the rms) measures of all observation residuals are 0 60 in R.A. and 0 37 in decl.with respect to the calculated position by both JPL and us.This indicates the correctness of our computational process.
On account of the limited number of observations of 2023 BJ 7 , we performed a rough assessment of the role played by the RDS observations, DS3, in orbit determination.Specifically, we singled out DS1 and compared available ephemerides with DS1 to assess the accuracy of the ephemerides.The residuals of the observations in R.A. and decl.for all cases are listed in Table 2.We first fit the orbit of 2023 BJ 7 to (1) only DS2.However, the observation period of DS2 is too short to determine the orbit well, and the ephemeris of this fit cannot be reconciled with DS1.After we refined the orbit by fitting (2) DS2 and DS3, the residuals of DS1 decreased significantly after adding the RDS data, and the orbit determination improved greatly.This is because the longer the observation arc is extended, the more accurately the orbit is determined.
The RDS observations make an impactful contribution to improving the orbit estimates in this case.Newly discovered NEAs have the greatest need for follow-up observations.Additionally, the residuals of DS3 in Table 2 are large when the orbit of 2023 BJ 7 was only determined with (3) DS1 and DS2.This implies that the ephemeris of this asteroid was very inaccurate before we conducted an RDS observation.This could have led to errors in calculating the drift-scanning speed and camera rotation angle.However, the residuals of DS3 are still small when the orbit was fit to (4) all data sets.This suggests that RDS observation can still achieve fairly good astrometric results for newly discovered NEAs such as 2023 BJ 7 whose orbits are not well determined.

Statistical Analysis of RDS Astrometry
Numerous NEA observations using the RDS technique have already been made with the LiShan telescope (Pomazan et al. 2021(Pomazan et al. , 2022) ) from 2019 to 2023 and the Mykolaiv telescope (Maigurova et al. 2018) from 2011 to 2022.The Mykolaiv telescope is a 0.5 m Maksutov telescope with a focal length of 3000 mm and an FWHM of 2 5.It uses the same CCD detector as the LiShan telescope.The FOV is 42 5 × 42 5 with a pixel scale of 0 83.As of 2023 September, the RDS observation data set contains more than 11,000 measurements of nearly 500 NEAs.The observation uncertainty for asteroid astrometry is typically scaled from the rms of the residuals.A statistical analysis of the RDS observation residuals was performed to estimate its accuracy; refer to the approach of Vereš et al. (2017).All residuals were computed by the orbit determination process described in Section 4.
First, the rms of astrometric residuals for the LiShan and Mykolaiv telescopes was calculated to assess their data quality (Figure 6).The analysis was restricted to data from multiapparition NEAs to ensure the observation residuals reflect the actual astrometric errors.Figure 6 shows the statistical distribution of the rms residuals calculated per site, per asteroid, and per night.It shows that the LiShan telescope achieves a slightly better accuracy than the Mykolaiv telescope, but the difference is not statistically significant.The statistical results also do not exhibit obvious changes over the observation epoch.Known catalog biases in all NEA observations were treated by using debiasing tables from Eggl et al. (2020) before orbit determination.The rms values of astrometric residuals were grouped by the star catalogs used (Table 3).The errors induced by star catalogs were reduced and are not significantly apparent in the rms values of the Table .Therefore, in the following analysis, all RDS data will be uniformly processed without making any distinctions between different stations, epochs, or star catalogs.
The astrometric uncertainty is inversely proportional to the SNR.Hence, it is difficult to precisely measure faint objects, which have lower SNRs.The mean and standard deviation of astrometric rms as a function of magnitude for multiapparition NEAs are shown in Figure 7.The left panel shows that the RDS observation uncertainty increases slightly with decreasing magnitude.The limiting magnitudes for the LiShan and Mykolaiv telescopes are both 18.To observe such faint objects, an integration time of several minutes may be required.However, the RDS technique enables us to acquire unstreaked images, ensuring the precision of astrometric measurement.For the same NEAs in the RDS observation data set, their NEA survey and RDS observations were removed, leaving other follow-up observations.The right panel of Figure 7 displays the changes in rms with magnitude for all other follow-up observations.Poor astrometry for too bright asteroids can be seen here, due to the saturation of the camera sensor (Vereš et al. 2017).Statistical analysis results show the measurement accuracy for other follow-up observations remains almost the same in the magnitude range 14 to 18, with an average rms of 0 43.In this magnitude range, the RDS observation achieved rms values 0 24 in R.A. and 0 32 in decl., which is better than the average level of follow-up observations.The problem of trailed images can cause issues in positional measurements of fast-moving NEAs and increase the astrometric error along the direction of motion.The relationship between along-track (AT) residuals and cross-track (CT) residuals with the rate of motion is investigated here and displayed in Figure 8.For all other follow-up observations shown in the right panel of the figure, a significant upward trend is only evident in AT residuals.This is likely due to trailed detections or timing errors.However, the left panel of Figure 8 shows that the AT residuals of RDS observations are nearly flat with an increasing rate of motion.This indicates that the measurement accuracy of RDS observations is maintained even for fast-moving NEAs, and there is no timing error.For NEAs whose rates of motion exceed 10 deg day −1 , the rms of RDS residuals is 0 35 in AT and 0 23 in CT, which is much lower than that of other follow-up observations (1 26 in AT and 0 36 in CT).The RDS technique is effective at measuring the positions of these fast-moving NEAs.
Newly discovered NEAs urgently need more follow-up observations.Relying on short observation arcs for orbit determination leads to significant trajectory uncertainties, which accumulate with time and impede successful recoveries at their next apparitions.The RDS observation data set contains nearly 1000 positions for 69 newly discovered NEAs (1-apparition NEAs).Because the orbits of these asteroids are usually not well determined, we only calculate the standard deviation of observation residuals to estimate the precision of RDS observation.The standard deviation of residuals as a function of magnitude is plotted in the left panel of Figure 9.A slight upward trend can be seen here, similar to the result of RDS observations for multiapparition NEAs (see the left panel of Figure 7).The mean of these standard deviations for 1-apparition NEAs is 0 24 in R.A. and 0 28 in decl.Similar to the flat trend in the left panel of Figure 8, no increased uncertainty in AT residual and CT residual can be seen with increasing rate of motion for these asteroids (right panel of Figure 9).Furthermore, we fit the orbits to the data acquired before conducting RDS observations and identified NEAs with inaccurate ephemerides and observation predictions.The process is similar to comparing the rms of RDS observation residuals in case 3 and case 4 for 2023 BJ 7 mentioned in Section 4. The results for these asteroids are specially marked in red in Figure 9, while the others are in blue.No noticeable difference between the results for these two colors of dots can be seen here.This demonstrates that the RDS technique can achieve good precision even for NEAs without enough measurements and well-determined orbits.

Pros and Cons
The RDS technique is a promising solution for providing precise positional measurements of NEAs, especially during their close approaches to Earth.For observing faint fast-moving NEAs, long exposure times lead to streaked asteroid images, while the target tracking method introduces trailed reference stars.Both significantly impact the measurement accuracy.However, the RDS technique allows both stars and target NEAs to be observed as point sources, thereby reducing astrometric errors in their measurements.Most notably, this technique can achieve an encouraging precision independent of the target's apparent motion, which is beneficial for the orbit determination of NEAs to provide reliable predictions and estimations of the collision probability.Moreover, the longer the exposure, the fainter the limiting magnitude, allowing the RDS technique to extend the observation capability of a telescope.Furthermore, small-aperture telescopes cost much less to build and operate than large ones.The networked use of such telescopes with the RDS technique would substantially benefit the global NEA monitoring system.
In addition to the many pros associated with using the RDS technique for NEA observations, there are some cons as well.First, the RDS technique is only available for telescopes with cameras that support TDI mode.The telescope also needs to be  upgraded with a rotation platform.Corresponding software for RDS observation and astrometric reduction is also demanded.Second, although the telescope is kept stationary throughout the observation process, errors can still be introduced in the RDS data reduction, which relies on three CCD frames: two frames of field stars sandwiching a frame of the target object.The primary reason for this is most likely that the pointing direction of the telescope is not completely unchanged as expected during the observations, as described in Section 3. Further investigation is needed to improve the precision of RDS measurements.
The RDS technique presented in this article is most desirable for observing fast-moving objects, such as NEAs and artificial satellites.NEAs have short observational windows and are only bright enough to be detected when they are close to Earth.At other times, these objects are too far and too faint to be observed.This imposes higher requirements on orbit determination, which consequently requires more accurate and precise observed positions.Small-aperture telescopes can be used to full advantage with the RDS technique to observe artificial satellites, which are copious and can be observed almost every night.Medium-Earth orbit (MEO) satellites and low-Earth orbit (LEO) satellites have similar characteristics of apparent motion and observation strategy as NEAs at close approaches to Earth: they move fast and in different directions.To observe geostationary (GEO) satellites, the field stars can be observed in the drift-scan mode without rotating the camera.The observation strategies for these satellites are listed in Table 4.The differences between the strategies come from the specifics of orbital motion and the placement of orbit, which results in different observational modes and long-term strategies.The subsequent post-processing and RDS astrometric reductions for these artificial satellites are the same as for NEAs, as described in Section 3. The same strategy can also  be applied to observe space debris with similar motion characteristics.

Conclusion
This article describes an RDS technique for obtaining precise astrometric positions of fast-moving NEAs during their close approaches to Earth.The technique involves upgrading a telescope with a rotation platform and camera, developing an observation procedure, and implementing a data reduction method.NEAs were observed in the TDI mode, and the astrometric reduction of the RDS data relied on three CCD frames: two frames of field stars sandwiching a frame of the target object.
The newly discovered NEA 2023 BJ 7 was observed at the LiShan Observatory employing the RDS technique.We fit its integrated orbits to all observations, including the RDS data.The mean values and standard deviations of the RDS observation residuals in R.A. and decl.are 0 07 ± 0.30 and 0 10 ± 0.69, respectively.The RDS technique can achieve competitive precision results even when the NEA reaches a very high rate of motion, such as the 112 deg day −1 observed for 2023 BJ 7 .Its data make an impactful contribution to improving the orbit accuracy by extending the observation arc, which is crucial for the newly discovered NEA.
A detailed error analysis of RDS observations was first conducted.The dominant error is likely due to the instability of the telescope, which is introduced into the special RDS astrometric reduction that uses three different CCD frames.A statistical analysis of the astrometric error was then performed using the historical RDS observations by the LiShan telescope and the Mykolaiv telescope from 2011 to 2023.The accuracy of RDS observations is about 0 24 in R.A. and 0 32 in decl.The RDS technique performs much better for observing fastmoving objects.For NEAs with rates of motion exceeding 10 deg day −1 , the rms of RDS residuals is 0 35 in AT and 0 23 in CT.The RDS technique can also achieve good precision for newly discovered NEAs that do not have accurate ephemerides.
The RDS technique could enable more follow-up observations of NEAs, which would allow for the acquisition of precise astrometric positions and the refinement of their orbits.A network of small-aperture telescopes using the RDS technique mode would be a significant asset to the global NEA monitoring system.

Figure 1 .
Figure 1.A schematic of the RDS technique for observing an NEA.The red dots represent the photoelectrons generated by the incident light from the NEA, and the blue dots are those from the background.

Figure 2 .
Figure 2. Distribution of 2023 BJ 7 observations along a distance-time line.The left y-axis shows the distance to Earth, and the right y-axis shows the corresponding approximate rate of motion.The observations DS1, DS2, and DS3 are presented by green, blue, and red circles, respectively.

Figure 4 .
Figure 4. Left panel: distribution of standard deviations of reference stars' measured coordinates with the log of their brightness.X coordinates are blue solid circles, and Y coordinates are red circles.The distribution has a mean of 0 11 for X and 0 12 for Y, with a standard deviation of 0 09 and 0 11, respectively.Right panel: distribution of standard deviations of frames' center coordinates.Azimuth measures are blue solid circles, and elevation measures are red circles.The mean values of the distribution with their standard deviations are 0 20 ± 0.21 in azimuth and 0 20 ± 0.18 in elevation.

Figure 3 .
Figure 3. CCD frames of field stars and 2023 BJ 7 obtained with the RDS technique through the 0.5 m Cassegrain telescope at the LiShan Observatory on 2023 January 30.

Figure 6 .
Figure 6.Mean and standard deviation of rms residuals in R.A. (top panel) and decl.(bottom panel) for multiapparition NEAs observed by the LiShan telescope (blue) and Mykolaiv telescope (red).

Figure 8 .
Figure 8. Mean/standard deviation of rms residuals in AT (top panels) and CT (bottom panels) with rate of motion (<60 deg day −1 ) for multiapparition NEAs.

Figure 9 .
Figure 9. Changes of standard deviation of observation residuals with magnitude (left panel) and rate of motion (right panel) for 1-apparition NEAs.The results for NEAs with inaccurate ephemerides are marked in red circles, while others are blue circles.

Table 1
State Vectors and 3σ Uncertainties of 2023 BJ 7 in the BCRS and Corresponding Heliocentric Ecliptic Orbital Elements Figure 5. Observation residuals in R.A. (top panel) and decl.(bottom panel) for 2023 BJ 7 .The observations DS1, DS2, and DS3 are presented in green, blue, and red circles separately.The residuals computed by JPL are presented in orange dots.

Table 2
Observation Residuals of the NEA 2023 BJ 7 Note.The orbits of 2023 BJ 7 were respectively fit to (1) only DS2; (2) DS2 and DS3; (3) DS1 and DS2; (4) all data sets.For DS2, only the residuals of the first and the last observations are listed here.