EFFICIENT AND ROBUST ALGORITHMS FOR THE REAL-TIME OPTICALTRACKING OF SPACE DEBRIS

Julian Rodriguez-Villamizar and Thomas Schildknecht

Astronomical Institute University of Bern (AIUB), Sidlerstrasse 5, 3012 Bern , Switzerland, Email:julian.rodriguez@aiub.unibe.ch

ABSTRACT

The latest European Space Agency Annual SpaceEnvironment Report [4] confirms, once more, the everincreasing amount of space debris orbiting around theEarth. Collisions between resident space objects willonly accelerate the growth rate of the current debrispopulation endangering space-related activities. In thatcontext, the surveillance of the outer space becomesof paramount relevance. Current existing surveillancenetworks make extensive use of different observationtechniques to retrieve not only updated information ofthe orbital elements of the object, but also evidence aboutits attitude and attitude motion.One on-going limitation for the tracking of space debriswith optical sensors (active or passive) comes fromthe lack of accurate ephemerides that will not allowpinpointing the object within the field of view of thesensor. The constraint imposed by the field of view issignificantly less stringent in passive-optical systems, butbecomes critical for active systems such as laser rangingstations.The presented work focuses on the development ofalgorithms that allow an automated real-time correctionof the pointing of the telescope while the object is withinthe field of view of the wide angle camera. The final aimis the centring of the target within the narrow field ofview of the laser beam, thus facilitating the acquisitionof laser ranges. We choose estimators according tostatistical properties such as efficiency and robustnessto enable the tracking even in the most challengingobservation conditions: daytime. All experiments wereconducted using real data derived from a tracking camerawith a scientific-CMOS sensor on the ZimmerwaldLaser and Astrometry Telescope (ZIMLAT) at the SwissOptical Ground Station and Geodynamics ObservatoryZimmerwald (SwissOGS) operated by the AstronomicalInstitute of the University of Bern, Switzerland.

Keywords: Satellite Laser Raning, Object Recognition,Active Tracking.

1. INTRODUCTION

The last revision of the Space Debris Mitigation Guide-lines issued by The Inter-Agency Space Debris Coordina-tion Committee (IADC) [6] supports the sustainable useof the outer space through:

• Limiting the probability of accidental collision in or-bit.

• Limiting the long-term presence of spacecraft andlaunch vehicle orbital stages in the low-Earth orbit(LEO) region after the end of their mission.

The previous two guidelines, out of the total of 7, high-light the importance of a surveillance and tracking globalnetwork. Note that the second mitigation guideline asksfor surveillance to ensure that the disposal of decom-missioned satellites and launch vehicle orbital stages arecompliant with the original proposal and will not pose afuture risk for space-related activities.The ground-based monitoring of the outer space isusually conducted by sky surveys and specific target’sfollow-up observation schemes. Nonetheless, when thereduction of uncertainty in the target state becomes im-perative due to a close conjunction, or due to the oc-currence of a re-entry event, a combination of the priorobserving techniques raises: the stare and chase. Thisobservation strategy could be implemented either usingprior information of the target, or for first discoveries fix-ing the telescope in a given direction, e.g. in the zenith.The one pass real-time observation of targets with poorephemerides presents a challenge: we want to maximizethe portion of the observed arc and maximize the likeli-hood to retrieve range and angular measurements. In pre-vious studies [8], we showed that the use of merged ob-servations, distributed along the maximal observable or-bital arc, will facilitate the re-acquisition of targets for thesame station and to other stations by disseminating thenew ephemerides through the propagation of the newlyestimated state. Through this work we will present thecore algorithms used by the stare and chase. Specifically,we will derive efficient and robust estimates for the objectrecognition and the tracking modules. The combinationof the two modules define our active tracking approach

Proc. 8th European Conference on Space Debris (virtual), Darmstadt, Germany, 20–23 April 2021, published by the ESA Space Debris Office

Ed. T. Flohrer, S. Lemmens & F. Schmitz, (http://conference.sdo.esoc.esa.int, May 2021)

where the system starts the tracking using existing orbitalinformation from the target. Next, once images are ac-quired, and the target object is successfully identified inthe camera reference frame, differential corrections areestimated and the pointing of the telescope is rectifiedwith respect to the initial pointing derived from the givenorbit.

2. EFFICIENT AND ROBUST ESTIMATORS

Through our work, we will use robust and efficient es-timators. The metric defined for the robustness is thebreakdown point [9], while for the efficiency we chooseestimators that yield minimum dispersion estimates [9].An example of a robust estimator is the sample median;likewise, an example of an efficient estimator is the sam-ple mean. Next, we will list situations where the selectionof a suitable estimator is of paramount relevance:

• To mitigate the impact of different error sources inthe estimation of source and background in the pas-sive system. Potential error sources could be due tohot and dead pixels in the imaging sensor, stray lightfrom the laser beam, if used in combination with anactive system, presence of clouds or star trails withinthe field of view of the sensor.

• During the object recognition phase during daylight,the terminator or nighttime if close to a celestial orartificial bright object. The brightness of the back-ground might be close to the one of the source chal-lenging the localization of the object image in theframe.

• During the active tracking, for deriving best esti-mates of the pointing of the telescope in real time.Note that inaccurate and unreliable estimates com-ing only from the object recognition module couldlead in worse-case scenarios to hardware failures,e.g. wrong slew movements of the telescope.

For the fulfilment of the previous points, a combinationof robust and efficient estimators is selected as the pre-ferred choice for estimating the properties of the objectimage, i.e. the centroid and brightness, as well as its fu-ture position in the camera reference frame using the his-torical records available from successful detections. Fi-nally, once we are able to track the object for the com-plete pass, we update its state and propagate it for nextacquisitions.

3. IMAGE PROCESSING

In this section we will analyse all steps concerning the ob-ject recognition phase and the estimation of the so-calledcentroid, i.e. the coordinates of the object image on the

camera reference system, which describe the central ten-dency for the location of the distribution of its intensityon the image plane. The input for the image process-ing module are images acquired in real time. The outputwill be estimates of the centroid coordinates for the objectimage. The latter will be the input for the tracking algo-rithm. Moreover, we will show that the implementationof our algorithm allow us to derive the apparent bright-ness of the target as a by-product of the object recognitionphase.

3.1. Problem statement

Given a raw image and the orientation of the camera ref-erence system with respect to a defined reference systemof interest, e.g. the horizon reference system, find thecoordinates of the object image so that, after applyingthe transformation between camera and horizon referencesystems, angular observations, i.e. azimuth an elevation,can be derived.To tackle the problem we divide the acquired image intotwo classes: source and background. The source cor-responds to those solar photons scattered by the target,which reach the detector. The background comprises skybackground photons, detector dark current, dead and hotpixels, etc. In general, the background represents all in-put signal which triggered an event on the detector de-spite not coming from the source. Due to the afore-mentioned variability of the background attributed to thedifferent error sources, we apply a sequence of steps tosmooth and remove the background and improve the es-timation of the centroid.

3.2. Pre-Processing

In this step we apply a lowpass filter in order to enhancethe quality of the object image by filtering potential imag-ing errors, which will affect otherwise the estimation ofthe background and the source. We refer to imaging er-rors as sample pixels that provide intensity values notdrawn from the expected probability distribution of eitherthe background or the source. The selected choice for thefilter is the robust median kernel. The operation consistson placing a matrix of a defined size in each of the imagepixels, and computing the median of all elements withinit; the resulting value will overwrite the old value for thepixel where the matrix was placed. This pre-processingstep was implemented as a discrete convolution in thespatial domain, meaning that we include another tuningparameter besides the kernel size, the step size, whichwill allow to improve the computational performance ofthe operation. In Subsection 3.5 we will show the impactof selecting different tuning parameters.

3.3. Background Estimation and Removal

An image taken by our tracking camera contains 5.5megapixels. The object image will be represented in onlya fraction of the total number of pixels. In order to reducethe size of the image we crop the original raw image intoa smaller one. To answer the question: where do you cropyour image without also removing the object of interest?we implemented two different options. First, we use theestimated position of the laser beam on the camera refer-ence system (further details are given e.g. in [3]) and cropthe raw image according to a predefined width consider-ing an average apparent velocity of a low Earth orbiter forcrossing the diagonal field of view of the tracking camera,which is of about 9 arcminutes. That works when we haveaccurate ephemerides, e.g. those generated for active tar-gets of the International Laser Ranging Service (ILRS)[7] in the form of Consolidated Predicted Format (CPF).In the space debris domain usually the ephemerides arecomputed from the so-called Two Line Elements (TLE)[1], which can have significant offsets with respect to thetrue position of the object in the sky. In the latter case,the operator must select where the object is during thefirst frame acquired by the tracking camera and only af-terwards the image is cropped. Note that this approachwas implemented only for cases where the signal-to-noiseratio was compromised, e.g. during daylight, and the au-tomated operating mode will remove the target after thepre-processing step preventing the immediate tracking ofthe target.Once we have the subframe, and initial coordinates of thecentroid, we can compute the intensity as a function ofthe distance between all pixels within the subframe andthe centroid. By doing so, we are approximating the pointspread function (PSF) of the object image. Note that thePSF will represent mainly the on-site atmospheric see-ing, i.e. we use the mathematical function describingthe seeing-induced PSF as a first-order approximation ofthe PSF of the object image. To derive the radius of thesource on the image, we compute it using the full-width-at-half-maximum (FWHM) calculated numerically usingthe previously constructed radial distribution of intensitywith respect to the centroid. The radii for the inner andouter background apertures are the result of the productbetween the FWHM and a defined constant (more detailsare available in [2]). In our case we took twice the valuetaken in [2] to consider potential errors in the estimationof the centroid.The difference between outer and inner background radiidefines a region within the subframe that might be usedas a representative sample of the background. For the ap-proximation of the PSF, we use circular apertures assum-ing a symmetrical PSF, which might be found in idealimaging systems observing with long exposure, averag-ing the impact of the on-site atmospheric seeing. Fromthe computational point of view, the calculation of circu-lar apertures involve the computation of the distance be-tween all pixels within the subframe and the centroid ofthe object image. The previous operation can be avoidedif we take the circumscribed square of the outer minus theone of the inner aperture.

In Figure 1 we show the subframe of the image, and thearea that will be used to extract the samples for the esti-mation of the background using circular and square aper-tures. The raw image has a radiometric resolution of 16bit and, as it can be seen in the raw subframe, the useddynamic range is that of 18% of its total capacity. Theexample shows a nighttime frame acquired for Topex-Poseidon using an exposure time of 0.05 seconds. Addi-tionally, from visual inspection, we see that the extractedbackground using squares is more heterogeneous, in thiscase, than the one using circles, in particular the lowerright and left corners. It is clear that the geometrical pat-tern is not the cause, but rather the fact that the squareapertures reach a brighter region of the background thatis more heterogeneous for this specific frame.In Table 1 we compare the estimation of the backgroundfor each case evinced in Figure 1. Our ground truth isdefined by the values estimated using the circular aper-tures. The reason is that we computed the normalityKolmogorov-Smirnov statistical test, and it succeeded ata confidence level of 95% using the samples contained inthe background ring. Despite the fact that the backgroundis more heterogeneous when using squares, the estimatesfor the background using the sample mean and medianare close to the ones provided by our ground truth. Thedifference can be neglected if one considers the dynami-cal range of the image. The estimated background usingthe complete subframe, including the source, show theexpected increase in the magnitude for the backgroundestimated using the sample mean, but the impact of thesource is significantly attenuated when using the samplemedian. Note that despite including the source within theestimation of the background, due to the large number ofsamples, the impact of the source is further attenuated.Regarding the estimators measuring the dispersion, wesee no difference between the estimation of the variancewith respect to the mean or median due to the large num-ber of samples for each of the 3 cases. The latter result iscommonly found in actual symmetric distributions. Theestimated standard deviation with respect to the samplemean and sample median reflects the heterogeneity of thebackground containing the source when estimating thebackground using the subframe. Finally, when taking themedian absolute deviation, a robust estimator to measurethe dispersion of a set of samples, we see that it is ableto isolate those pixels that do not belong to the homoge-neous distribution of the background, i.e. the source.We conclude that the use of robust estimators for the reck-oning of the background, as well as for its dispersion,mitigates the impact of error sources not coming fromits expected distribution. We proved the previous state-ment computing the background including the source it-self, which may be considered an extreme case. We im-plemented the described approach in our real-time systemusing the square apertures besides the median and medianabsolute deviation as estimators for the background.

Figure 1. Subframe of original image centered on the object image (left). Area of the subframe defined by the differencebetween outer and inner background radii (middle). Area of the subframe taking the circumscribed square of the differencebetween outer and inner background radii (right). Unit colobars: Analog-To-Digital (ADU) units.

Table 1. Estimation of the background varying the geo-metrical pattern from where samples of the backgroundare extracted. Std: standard deviation. Mad: median ab-solute deviation. We highlight in gray the combination ofestimators that minimize the impact of the source in theestimation of the background.

Circle Square SubframeNum. Samples 38300 59400 88209Sample Mean [ADU] 2661 2664 2715Sample Median [ADU] 2661 2663 2672Std. Mean [ADU] 86 89 422Std. Median [ADU] 86 89 424Mad. Mean [ADU] 58 58 70Mad. Median [ADU] 58 58 58

Figure 2. Profiles of two frames acquired during the ob-servation of a Topex-Poseidon pass using the trackingcamera. The top plot shows that there is enough contrastto distinguish the object image compared to the bottomone. The figure highlights the impact of choosing a spe-cific threshold for the removal of the background.

Once we have representative estimates for the back-ground, the next step is its removal. To see the impact ofremoving the estimated MED(back) + kMAD(back),where k is a constant,MED the median operator,MADthe median absolute deviation with respect to the medianand back is the set of background samples, we extractedtwo cross-sections from two different frames acquiredfrom the Topex-Poseidon pass, where the object wasdeeply embedded in background noise. For the statisticalinterpretation of k the reader is referred to [9]. In Figure2 we show two profiles of the object image fixing the row.After the subtraction of only MED(back), it becomesclear that a suitable threshold for masking the pixelswhich do not belong to the source is zero. Nevertheless,the zero threshold will not maximize the removal of thebackground, i.e. there will be scattered pixels which notbelonging to the source will impact the determination ofthe centroid. The thresholdMED(back)+MAD(back)was found to yield a good compromise between highand low contrast images. Larger values for k will workfor brighter targets but may remove the weak signal ofthe source for images with low signal-to-noise ratio (seebottom plot in Figure 2).

Once we are able to remove the background, we proceedwith the estimation of the centroid.

3.4. Centroid Estimation

The estimation of the centroid is given by the weightedaverage of the coordinates of the source pixels definingas weighting factor the intensity at the location of the dif-ferent N pixels within its distribution. The formula reads[5]:

XCoG =

∑N−1i=0 Ix,yX∑N−1i=0 Ix,y

, (1)

where XCoG is the coordinate component for the centerof gravity of the object image with an intensity Ix,y ata given coordinate component X . Note that the estima-tor used for finding the centroid minimizes the weightedmean square error. At this stage, after the pre-processingsteps decribed in Subsection 3.2, and the estimation and

removal of the background analyzed in Subsection 3.3,we minimize the contribution of background pixels in theestimation of the centroid for the source. In Subsection3.5 we will show the results after the two operations in asequential fashion.

3.5. Results and Discussion

In this Subsection we will analyze the sequence of op-erations performed for the extraction of the object’s cen-troid. We present one pass for the rocket body H-2A withNORAD 38341, which has an altitude of 585 km at theperigee and culminated at an elevation of 23◦on Octo-ber 11, 2019, at 15:45 UTC. Note that the observationconditions, daylight and the low elevation pass, present achallenge to distinguish the source from the background.In Figure 3 we show the sequence of operations per-formed to discriminate the source from the background.From the left to the right we show the raw subframedimage, the resulting image after the convolution be-tween the raw subframed image and the median filterusing two combinations of kernel and step size (topand bottom plots), the resulting image after subtractingMED(back) + MAD(back), and finally the resultingimage masking all non-positive pixels to zero.

We show one image out of the 750 acquired with anexposure time of 0.02 seconds. Note that we show howthe previous centroid of the image was not optimally es-timated since the background pixels were not correctlyremoved (upper sequence of images in Figure 3). De-spite being suboptimal, the solution using a kernel of 5pixels x 5 pixels with a step size of 3 pixels keeps thetarget within the subframe. On the other hand, the solu-tion using a kernel of 9 pixels x 9 pixels with a step sizeof 5 pixels keeps the target centered within the subframe,after a better removal of the background in the previousimage. The reason is clear: a larger combination betweenkernel and step size smooths better the intensity in thewhole subframe. Note also that the smoothing affects theintensity of the source. After the analysis of this series,we noticed that the dynamic range yield 76% out of itsfull capacity for the raw subframes. The impact of theon-site atmospheric seeing becomes noticeable in manyframes due to the short exposure freezing the seeing atthe acquisition of the frame. Finally, we can estimate thelimit of the kernel size by taking the atmospheric seeing.Example: for an atmospheric seeing of 2 arcseconds anda pixel scale of 0.173 arcseconds/pixel the limit will be akernel size of 11 pixels x 11 pixels. A kernel size largerthan the limit might remove the target from the subframepreventing the estimation of its centroid.Finally, after the estimation of the centroid, we can es-timate again the PSF, place the apertures for the sourceand the inner and outer apertures for the background andderive the apparent brightness of the target.

4. ACTIVE TRACKING

The output of the object recognition phase is the posi-tion of the object image in the camera reference systemand its apparent brightness. Knowing the position of thelaser beam in the camera reference system, we can es-timate the offset between the target and the laser beamposition. After the transformation between the cameraand the horizon reference systems, those offsets are ex-pressed as ∆azimuth and ∆elevation. Despite the elab-orated object recognition algorithm, nothing prevents itfrom failing in case of the presence of clouds, bright arti-ficial or celestial objects within the subframe, or very lowintensity contrast between source and background. Forthose cases, an active tracking algorithm is developed toensure the smooth tracking of the object when the esti-mates derived from the object recognition phase are ofcompromised precision or accuracy.

4.1. Problem Statement

Given a set of past records of the state vector of the objectimage in the camera reference frame, extracted from theobject recognition phase, estimate predictions at an epocht+ 1 for the state vector of the object image, updating itsstate at epoch t when a new observation becomes avail-able, using the n number of past records collected untilthe epoch t. The n last records define our sliding obser-vation window (sow).In order to model the trajectory T (t) of the object imagein the camera reference frame, we make use of the Taylorseries expansion:

T (t) =

pmax∑p=0

T (t)p

p!(t0 − t)p, (2)

where t0 is the initial entry of the sliding observation win-dow. The predictions for the epoch t+ 1 are derived afterthe estimation of the T (t)p

p! coefficients via the minimiza-tion of the mean square error using all n observationsavailable within the sliding observation window. Notethat the algebraic form of Equation 2 is simply a polyno-mial of degree pmax, but taking the pth rate of changeof the trajectory gives a dynamical definition, i.e. a statetransition matrix.The observation equation is trivial due to the fact that weobserve directly the state that we want to estimate, i.e.:

X = X + η, (3)

where η is the noise of the measurement with unknownprobability density function.

4.2. Observation and Error Windows

For the estimation of the future state and its update, weuse all measurements contained within a sliding observa-tion window of n entries. Estimators that minimize the

Figure 3. Comparison of the resulting centroid after using a different set up for the pre-processing step, i.e. convolutionbetween the raw subframed image and median kernel. The top sequence uses a median filter with a kernel of 5 pixels x5 pixels with a step size of 3 pixels, while the bottom sequence uses a kernel of 9 pixels by 9 pixels with a step size of 5pixels. Note that in the top sequence the object image is not centered in the subframe due to the impact of the non-filteredbackground pixels from the previous image. Unit colorbars: ADU.

mean square error are arguably sensitive to outliers dueto their low breakdown point. An example of an outliercoming from the object recognition phase can occur, e.g.due to a passing cloud. The estimated centroid will mostlikely correspond to the center of gravity of all the un-masked pixels which belong to the cloud not to the objectof interest. In order to filter outliers, we use a sliding errorwindow (sew) defined by the observed-minus-computed(OmC) state of the object image for the n entries of thesliding observation window.As soon as a new observation becomes available, we sub-tract it from its prediction, defining the term OmCt, andcompare it against τ = MED(sew) ± kMAD(sew)computing it over all n OmC entries in the sliding errorwindow. Our null hypothesis is that OmCt is within thebounds ±τ . If the alternate hypothesis results true, thenthe observation acquired at epoch t is marked and not ac-counted for within the sliding observation window.Note that during the tracking a sudden change in the tra-jectory can happen. In that case, the next n/2 observa-tions will be marked as outliers, however, the n/2 + 1 in-coming observation will correct the estimated τ , avoidingthe saturation of the filter marking as good observationsthose within the newly estimated ±τ .

4.3. Results and Discussion

We present an interesting case for a LAGEOS-1 passobserved on April 20, 2019. The reason for selectingthis target relies on its low signal-to-noise ratio, whichevinces a perfect case for testing the precision, accu-racy and reliability of the algorithm. For the accuracy,the solution extracted using the software AstroImageJ[2] will define our ground truth. In Figure 4 we show

the component-wise solutions obtained using Astroim-ageJ (aij), the estimated state from the object recognitionprocedure (objrec), and the predicted state derived fromthe active tracking (track). In Figure 4 we are able to see:

1. Initialization of the sliding observation window.The algorithm stores the first 10 entries to initializethe sow. The solution provided by the object recog-nition procedure is in agreement with respect to thesolution extracted using aij.

2. Change in component X and outlier in Y. We cansee how the X component is treated at the begin-ning as an outlier neglecting all incoming measure-ments, but after the 5th new measurement, the filterbecomes responsive again. In the Y component wecan see two spurious measurements neglected by theactive tracking.

3. Exclusion of outlier. We can see that an importantoutlier is neglected by the tracking solution, smooth-ing the trajectory of the object image as receivingnew observations.

The maximum error between the solution provided by aijand ours is that of 20 pixels. Considering a pixel scale of0.173 arcseconds/pixel, we conclude that the algorithmperforms at the required level, i.e. can block the targetwithin the field of view of the laser beam which is ≈ 20arcseconds.

Figure 4. Lageos-1 case study to validate the estimation of the centroid against the solution provided by AstroImageJ.We show the component-wise solutions obtained using AstroimageJ (aij), the estimated state from the object recognitionprocedure (objrec), and the predicted state derived from the active tracking (track).

5. CASE STUDY: H-2A

In Subsection 3.5 we introduced a challenging pass due tothe observation conditions: daylight, low elevation, pass-ing clouds and short exposure time. In Figure 5 we showthe observation geometry for the observed pass from theSwissOGS.

Figure 5. Observation geometry for the rocket body H-2A observed from the SwissOGS on October 11, 2019, at15:43 UTC.

Furthermore, this case highlights the benefits froman active tracking approach instead of an initial orbitdetermination. By the time that observations will becollected for the initial orbit determination and newlyephemerides will be generated and integrated into theobserving system, the target will most likely be lost.In Figure 6 we can see the different solutions for theretrieval of the object’s image centroid using only theobject recognition algorithm, using active tracking, andthe solution extracted from aij. A striking feature isthe remarkable drift starting at the 18th second. Atthat particular epoch, few clouds obscured the objectpreventing the estimation of its centroid until second 25.After ignoring the first outliers, the filter finally followsthe object until new accurate observations becomeavailable. That particular event was not successfullyovercome by the aij solution: the coordinates of theobject’s centroid for those frames covered by cloudswere introduced manually for the sake of comparison.

The other two discontinuities at seconds 54 and 104are due to the interaction of the observer to re-centerthe target while storing images. The latter two eventstriggered a halting event in aij. In our case, we wereable to process the complete pass without halts thankschiefly to the width of the subframe, which mainlypermitted the recognition of the object within a widerspace search than the one used by aij. The right subplotsin Figure 6 show that our centroid’s detection are inagreement with the ones obtained from the aij solution.The tracking solution proves its smoothness after therelatively scattered observations of the object’s centroidattributed mainly to the low intensity contrast betweensource and background, cloud presence, freezing of theseeing, etc.

Figure 6. Centroiding solutions for the H-2A pass on Oc-tober 11, 2019. We show the component-wise solutionsobtained using AstroimageJ (aij), the estimated state fromthe object recognition procedure (objrec), and the pre-dicted state derived from the active tracking (track). Theright plots depict a detailed portion of the pass for the xcomponent (top) and y component (bottom).

After the extraction of the centroid, the placement ofsource and background apertures in the original subframepermitted us to extract the apparent instrumental magni-tudes, which are shown in Figure 7.

Figure 7. Extracted instrumental magnitudes using ourreal-time solution (ZIM) and the post-processed solutionusing aij.

In general our solution and the one provided by AstroIm-ageJ show a significant dispersion due to the aforemen-tioned eventualities. Nonetheless, we can notice certainperiodicity that might correlate with the attitude and atti-tude motion of the target. Note that the represented lightcurve was detendred to remove the contribution of theslant range and phase angle. The observables collectedduring the observation of this pass are: azimuth, eleva-tion and apparent brightness. Unfortunately, for this par-ticular case we did not retrieve any laser ranges.

6. SUMMARY

The use of an active tracking approach might be criti-cal to reduce drastically the uncertainty of the target’sstate within single passes. Moreover, after the successfultracking, the newly estimated state may be propagatedand ephemerides can be sent to partner stations, whichcan reacquire the target and further improve the knowl-edge of the target’s state.The core algorithms for observation strategies such as thestare and chase are based on object recognition and track-ing modules. To be successful in the aforementioned ob-servation strategy, the derivation of robust, efficient andimplementable algorithms becomes imperative. Throughthis work, we presented:

• Centroid and apparent brightness estimationthrough a sequence of image processing steps.Those steps are the cropping of the full raw imageinto a subframe, the convolution of the subframe im-age against a median kernel, the background sub-traction, and finally the estimation of the centroid asthe weighting average of all remaining positive pix-els. Once the centroid is available we place sourceand background apertures and retrieve the apparentmagnitude of the target.

• Active tracking based on the estimation of the tar-get’s state at a future epoch besides the update ofits current state making use of its past n historicalrecords. The inclusion of the sliding error window

enhances the robustness of the otherwise sensitiveM-estimator used for the estimation of the trajectory.We presented a validation of the algorithm by com-paring our solution with the one extracted from thesoftware AstroImageJ.

• Presented a case study for the rocket body H-2A,observed with very challenging conditions: day-light, low culmination, cloud presence all in realtime. The results demonstrated an accurate proce-dure to correct for the pointing of the telescope be-side the real-time collection of azimuth, elevation,apparent brightness and ranges. For the case studyof H-2A, we did not collect ranges, but we haveother cases that prove that capability.

ACKNOWLEDGMENTS

The first author would like to thank the Swiss NationalScience Foundation for providing the funds for the cur-rent study through grant 200020-175795. Likewise, hewould like to thank Dr. Emiliano Cordelli for all fruitfuldiscussions and insights, which improved the presentedwork.

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