1

2

3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

Improvement in Fast Particle Track Reconstruction
with Robust Statistics
M. G. Aartsen2 , R. Abbasi27 , Y. Abdou22 , M. Ackermann42 , J. Adams15 ,J. A. Aguilar21 , M. Ahlers27 , D. Altmann9 , J. Auffenberg27 , X. Bai31,1 ,M. Baker27 , S. W. Barwick23 , V. Baum28 , R. Bay43 , J. J. Beatty17,18 ,S. Bechet12 , J. Becker Tjus10 , K.-H. Becker41 , M. L. Benabderrahmane42 ,S. BenZvi27 , P. Berghaus42 , D. Berley16 , E. Bernardini42 , A. Bernhard30 ,D. Z. Besson25 , G. Binder8,43 , D. Bindig41 , M. Bissok1 , E. Blaufuss16 ,J. Blumenthal1 , D. J. Boersma40 , S. Bohaichuk20 , C. Bohm34 , D. Bose13 ,S. Böser11 , O. Botner40 , L. Brayeur13 , H.-P. Bretz42 , A. M. Brown15 ,R. Bruijn24 , J. Brunner42 , M. Carson22 , J. Casey5 , M. Casier13 , D. Chirkin27 ,A. Christov21 , B. Christy16 , K. Clark39 , F. Clevermann19 , S. Coenders1 ,S. Cohen24 , D. F. Cowen39,38 , A. H. Cruz Silva42 , M. Danninger34 ,J. Daughhetee5 , J. C. Davis17 , M. Day27 , C. De Clercq13 , S. De Ridder22 ,P. Desiati27 , K. D. de Vries13 , M. de With9 , T. DeYoung39 , J. C. Dı́az-Vélez27 ,M. Dunkman39 , R. Eagan39 , B. Eberhardt28 , J. Eisch27 , S. Euler1 ,P. A. Evenson31 , O. Fadiran27 , A. R. Fazely6 , A. Fedynitch10 , J. Feintzeig27 ,T. Feusels22 , K. Filimonov43 , C. Finley34 , T. Fischer-Wasels41 , S. Flis34 ,A. Franckowiak11 , K. Frantzen19 , T. Fuchs19 , T. K. Gaisser31 , J. Gallagher26 ,L. Gerhardt8,43 , L. Gladstone27 , T. Glüsenkamp42 , A. Goldschmidt8 ,G. Golup13 , J. G. Gonzalez31 , J. A. Goodman16 , D. Góra42 ,D. T. Grandmont20 , D. Grant20 , A. Groß30 , C. Ha8,43 , A. Haj Ismail22 ,P. Hallen1 , A. Hallgren40 , F. Halzen27 , K. Hanson12 , D. Heereman12 ,D. Heinen1 , K. Helbing41 , R. Hellauer16 , S. Hickford15 , G. C. Hill2 ,K. D. Hoffman16 , R. Hoffmann41 , A. Homeier11 , K. Hoshina27 ,W. Huelsnitz16,2 , P. O. Hulth34 , K. Hultqvist34 , S. Hussain31 , A. Ishihara14 ,E. Jacobi42 , J. Jacobsen27 , K. Jagielski1 , G. S. Japaridze4 , K. Jero27 ,O. Jlelati22 , B. Kaminsky42 , A. Kappes9 , T. Karg42 , A. Karle27 , J. L. Kelley27 ,J. Kiryluk35 , J. Kläs41 , S. R. Klein8,43 , J.-H. Köhne19 , G. Kohnen29 ,H. Kolanoski9 , L. Köpke28 , C. Kopper27 , S. Kopper41 , D. J. Koskinen39 ,M. Kowalski11 , M. Krasberg27 , K. Krings1 , G. Kroll28 , J. Kunnen13 ,N. Kurahashi27 , T. Kuwabara31 , M. Labare22 , H. Landsman27 , M. J. Larson37 ,M. Lesiak-Bzdak35 , M. Leuermann1 , J. Leute30 , J. Lünemann28 , O. Macı́as15 ,J. Madsen33 , G. Maggi13 , R. Maruyama27 , K. Mase14 , H. S. Matis8 ,F. McNally27 , K. Meagher16 , M. Merck27 , T. Meures12 , S. Miarecki8,43 ,E. Middell42 , N. Milke19 , J. Miller13 , L. Mohrmann42 , T. Montaruli21,3 ,∗ Corresponding author. Email: wellons@icecube.wisc.edu, Phone: 304-542-4464, Address:
Wisconsin Institutes for Discovery, 330 N. Orchard St., Madison, WI 53715
1 Physics Department, South Dakota School of Mines and Technology, Rapid City, SD
57701, USA
2 Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3 also Sezione INFN, Dipartimento di Fisica, I-70126, Bari, Italy
4 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

Preprint submitted to Nuclear Instruments & Methods A

October 20, 2013

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

R. Morse27 , R. Nahnhauer42 , U. Naumann41 , H. Niederhausen35 ,S. C. Nowicki20 , D. R. Nygren8 , A. Obertacke41 , S. Odrowski20 , A. Olivas16 ,A. Omairat41 , A. O’Murchadha12 , L. Paul1 , J. A. Pepper37 ,C. Pérez de los Heros40 , C. Pfendner17 , D. Pieloth19 , E. Pinat12 , J. Posselt41 ,P. B. Price43 , G. T. Przybylski8 , L. Rädel1 , M. Rameez21 , K. Rawlins3 ,P. Redl16 , R. Reimann1 , E. Resconi30 , W. Rhode19 , M. Ribordy24 ,M. Richman16 , B. Riedel27 , J. P. Rodrigues27 , C. Rott36 , T. Ruhe19 ,B. Ruzybayev31 , D. Ryckbosch22 , S. M. Saba10 , T. Salameh39 , H.-G. Sander28 ,M. Santander27 , S. Sarkar32 , K. Schatto28 , F. Scheriau19 , T. Schmidt16 ,M. Schmitz19 , S. Schoenen1 , S. Schöneberg10 , A. Schönwald42 , A. Schukraft1 ,L. Schulte11 , O. Schulz30 , D. Seckel31 , Y. Sestayo30 , S. Seunarine33 ,R. Shanidze42 , C. Sheremata20 , M. W. E. Smith39 , D. Soldin41 ,G. M. Spiczak33 , C. Spiering42 , M. Stamatikos17,4 , T. Stanev31 , A. Stasik11 ,T. Stezelberger8 , R. G. Stokstad8 , A. Stößl42 , E. A. Strahler13 , R. Ström40 ,G. W. Sullivan16 , H. Taavola40 , I. Taboada5 , A. Tamburro31 , A. Tepe41 ,S. Ter-Antonyan6 , G. Tešić39 , S. Tilav31 , P. A. Toale37 , S. Toscano27 ,E. Unger10 , M. Usner11 , S. Vallecorsa21 , N. van Eijndhoven13 ,A. Van Overloop22 , J. van Santen27 , M. Vehring1 , M. Voge11 , M. Vraeghe22 ,C. Walck34 , T. Waldenmaier9 , M. Wallraff1 , Ch. Weaver27 , M. Wellons27 ,C. Wendt27 , S. Westerhoff27 , N. Whitehorn27 , K. Wiebe28 , C. H. Wiebusch1 ,D. R. Williams37 , H. Wissing16 , M. Wolf34 , T. R. Wood20 , K. Woschnagg43 ,D. L. Xu37 , X. W. Xu6 , J. P. Yanez42 , G. Yodh23 , S. Yoshida14 ,P. Zarzhitsky37 , J. Ziemann19 , S. Zierke1 , M. Zoll34 ,and B. Recht43 , C. Ré44

61

1 III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany

62

2 School of Chemistry & Physics, University of Adelaide, Adelaide SA, 5005 Australia

63

3 Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr.,

64

Anchorage, AK 99508, USA

65

4 CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA

66

5 School of Physics and Center for Relativistic Astrophysics, Georgia Institute of67

Technology, Atlanta, GA 30332, USA68

6 Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA69

7 Dept. of Physics, University of California, Berkeley, CA 94720, USA70

8 Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

71

9 Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany

72

10 Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum,

73

Germany74

11 Physikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, Germany

75

12 Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium

76

13 Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium

77

14 Dept. of Physics, Chiba University, Chiba 263-8522, Japan78

15 Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800,

79

Christchurch, New Zealand80

16 Dept. of Physics, University of Maryland, College Park, MD 20742, USA

81

17 Dept. of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State

82

University, Columbus, OH 43210, USA

83

18 Dept. of Astronomy, Ohio State University, Columbus, OH 43210, USA

84

19 Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany

85

20 Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1

2

86

21 Département de physique nucléaire et corpusculaire, Université de Genève, CH-1211

87

Genève, Switzerland

88

22 Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium

89

23 Dept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA

90

24 Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne,

91

Switzerland

92

25 Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA

93

26 Dept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA

94

27 Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center, University of95

Wisconsin, Madison, WI 53706, USA

96

28 Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany

97

29 Université de Mons, 7000 Mons, Belgium

98

30 T.U. Munich, D-85748 Garching, Germany

99

31 Bartol Research Institute and Department of Physics and Astronomy, University of

100

Delaware, Newark, DE 19716, USA

101

32 Dept. of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK

102

33 Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA

103

34 Oskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm,

104

Sweden105

35 Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY

10611794-3800, USA

107

36 Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea

108

37 Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA

109

38 Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park,110

PA 16802, USA

111

39 Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA

112

40 Dept. of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden

113

41 Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany

114

42 DESY, D-15735 Zeuthen, Germany

115

43 Dept. of Computer Science, University of California, Berkeley, CA 94704, USA

116

44 Dept. of Computer Science, Stanford University, Stanford, CA 94305, USA

117

118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133

Abstract
The IceCube project has transformed one cubic kilometer of deep natural
Antarctic ice into a Cherenkov detector. Muon neutrinos are detected and theirdirection inferred by mapping the light produced by the secondary muon track
inside the volume instrumented with photomultipliers. Reconstructing the muontrack from the observed light is challenging due to noise, light scattering in theice medium, and the possibility of simultaneously having multiple muons insidethe detector, resulting from the large flux of cosmic ray muons.
This manuscript describes work on two problems: (1) the track reconstruction problem, in which, given a set of observations, the goal is to recover the
track of a muon; and (2) the coincident event problem, which is to determine
how many muons are active in the detector during a time window. Rather thansolving these problems by developing more complex physical models that are
applied at later stages of the analysis, our approach is to augment the detector’s
early reconstruction with data filters and robust statistical techniques. Thesecan be implemented at the level of on-line reconstruction and, therefore, improve
all subsequent reconstructions. Using the metric of median angular resolution, a3

Signal [VEM]

H. KOLANOSKI I CE T OP OVE
103

S125 = 57.2

β = 2.93

PRELIMINARY
102

10

1
High Gain
10-1

Low Gain
100

200

300

400

500
Perp. distance to show

Figure 2: Reconstruction of shower parameters frolateral distribution.

134
135
136
137

138
139

140

141
142
143
144
145
146
147
148
149
150
151
152
153
154

wide bins for a duration of 422 ns. DOMs, electroni
readout scheme are the same as for the in-ice detecto
The two DOMs in each tank are operated at different
gains (1 · 105 and 5 · 106 ) to cover a dynamic range ofthan 104 . The measured charges are expressed in un
Figure
1:
The
IceCubeObservatory
withitscomponents‘vertical
equivalent muons’ (VEM) determined by ca
Figure 1: The IceCube neutrino detector in the Antarctic ice. A picture of theEiffel Tower
DeepCoreand
IceTop.
ing
each
DOM with muons (see ref. [1]).
is shown for scale.
To initiate the readout of DOMs, a local coincidenof 1 km3 at a depth between 1450 m and 2450 m (Fig. 1). In the two high gain DOMs of a station is required. Th
sults in a station trigger rate of about 30 Hz compa
partof the detector a we
sectioncalled the
DeepCoreis instandard metricthe
forlower
track
reconstruction,
improveaccuracy
the1600
initialabout
Hz of a single high gain DOM at a thre
more densely
The mainpurposeof IceCube inreconstruction direction
byinstrumented.
13%. We alsopresent
improvements
measuring
of
about
0.1
VEM. The data are written to a permis the detection of high energy neutrinos from astrophysicalthe number of muons in coincident events: we can accurately determine
the and are thus available for analysis,storagemedium,sources via the Cherenkov light of charged particles genernumber of muonsof theinteractions
time.
ated98%in neutrino
in the ice or the rock below the readouts of six or more DOMs are launched by a loca
cidence. This leads to a trigger threshold of about 30
ice.
Keywords: IceCube,
Track reconstruction, Neutrino telescope, Neutrino
Additionally, IceTop is always read out in case of a t
astrophysics, Robust Statistics
issued by another detector component (and vice versa
IceTop: The IceTop air shower array is located above each single tank above threshold, even without a loc
IceCube at a height of 2832 m above sea level, correspond- incidence, condensed data containing integrated charg
ing to an atmospheric depth of about 680 g/cm2 . It consists time stamp are transmitted. These so-called SLC hits
1. Introductionof 162 ice Cherenkov tanks, placed at 81 stations and dis- = ‘soft local coincidence’) are useful for detecting
over detector
an area of searches
1 km2 on aforgridneutrinos
with mean thatspacingmuons in showers
where the electromagnetic compThe IceCubetributed
neutrino
are generated
by
of
125
m
(Fig.
1).
In
the
center of
the array,three stations
been absorbed(low energies, outer region of sho
the universe’s most violent astrophysicalevents:explodingstars, has
gamma
ray
have been installed at intermediate positions. Together inclined showers).
bursts, and cataclysmic phenomena involving black holes and neutronstars [1].
with the neighbouring stations they form an in-fill array for For monitoring transient events via rate variations, th
The detector, roughly
one
cubic
kilometer
in
size,
is
locatednear
thegeographic
denser shower sampling. Each station comprises two cylin- of single hits in different tanks with various threshol
South Pole anddricalis buried
to ma apartdepth
ofeachabout
2.5
kma diameterin the Antarctic
ice [2].
tanks, 10
fromother,
withof histogrammed.
The detector is 1.86
illustratedin
Figure
1,
and
a
more
complete
descriptionisgiven
m and filled with 90 cm ice. The tanks are embedin Section 2. ded into the snow so that their top surface is level with thesurrounding
minimize it
temperature
variations
and in3 theShower
When a neutrino
enterssnow
the totelescope,occasionallyinteracts
ice and reconstruction
snow The
accumulation
by winddrift.
generates a muon.
neutrinocaused
direction
canbe However,inferred snow
from a reconstrucaccumulation(mainlyare
duealsoto irregularsnow bysurfaces)
can-raysFor
each triggered tank in an event, time and cha
tion of the muontrack. Muons
generatedcosmicinteracting
not becompletely
avoidedso thatthe snow height
has to raythesignal andare evaluated for further processing. Likein the atmosphere,
andseparationof thebackgroundof cosmic
muons
be monitored (see ref. [1]) and taken into account in simu- maximisation methods are used to reconstruct locatio
neutrino-induced muons is a necessary step for neutrino analysis. This
separalation and reconstruction (currently this is still a source of rection and size of the recorded showers. In general,tion is challenging,as the number
observed cosmic ray muons exceeds the
non-negligible
systematicofuncertainties).
times contain the direction information, and the charg
number of observed neutrino muons by over five orders of magnitude [3].
Each tank is equipped with two ‘Digital Optical Mod- tribution is connected to shower size and core location
ules’ (DOMs), each containing a 10�� photo multiplier tube standard analysis requires five or more triggered st(PMT) to record the Cherenkov light of charged particles leading to a reconstruction threshold of about 500 Te
4
that penetrate the tank. In addition, a DOM houses complex constant efficiency is reached at about 1 PeV, depe
electronic circuitry supplying signal digitisation, readout, on shower inclination. For small showers an effo
triggering, calibration, data transfer and various control launched to decrease the threshold to about 100 TeV
functions. The most important feature of the DOM elec- a modified reconstruction requiring only three station
tronics is the recording of the analog waveforms in 3.3 ns

155
156
157
158
159
160
161
162
163
164
165
166

167
168
169
170

The primary mechanism for separating the cosmic ray muons from the neutrino muons is reconstructing the muon track and determining whether the muon
was traveling downwards into the Earth or upwards out of the Earth. Because
neutrinos can penetrate through the Earth but cosmic ray muons cannot, it
follows that a muon traveling out of the Earth must have been generated by aneutrino. Thus, by selecting only the muons that are reconstructed as up-going,
the cosmic ray muons can, in principle, be removed from the data. Because thenumber of cosmic ray muons overwhelms the number of neutrino muons, highaccuracy is critical for preventing erroneous reconstruction of cosmic ray muonsas neutrino-induced.
Here, we examine two problems that arise in the separation of cosmic raymuons from neutrino muons in the IceCube detector:
1. Reconstruction, in which the track of a muon is reconstructed from theobserved light at different positions and times in the detector.
2. Coincident Event Detection, in which we detect the number of muons
inside the detector, and assign observed photons to a muon.

179

Sophisticated reconstruction techniques have been developed that computationally model in detail the muon’s Cherenkov cone, as well as the scatteringand absorption of photons through layers of Antarctic ice with varying opticalproperties [3–5]. Rather than further refining these techniques, the current work
focusses on improving the statistical techniques and optimizing data filtering in
the early online track reconstruction performed on the data in real time at theSouth Pole. Besides benefiting directly any analysis that uses the online reconstruction, such as the search for cosmogenic neutrinos, any later analysis will
benefit from improvements made at the early stages of the data collection.

180

1.1. Related Work

171
172
173
174
175
176
177
178

185

Track reconstruction and coincident event detection challenges are ubiquitous in particle physics [6–8], both in particle accelerators and cosmic particle
detectors. While the work described in this manuscript builds on the previous
technique developed for the IceCube detector [3], these techniques are general
purpose and potentially have applications in detectors beyond IceCube.

186

1.2. Outline

181
182
183
184

187
188
189
190
191
192

We begin by describing the IceCube detector and track reconstruction challenges in Section 2. In Section 3, we describe the reconstruction pipeline including the prior IceCube software, then we present improvements to the online
tracking algorithm and discuss the results. Section 4 describes improvementson coincident event detection and follows a parallel structure to Section 3. We
conclude in Section 5.

5

193

194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212

213
214
215
216
217
218

219
220
221

2. IceCube Detector and Track Reconstruction Challenges
The IceCube detector is composed of 5,160 optical detectors, each containing
a photomultiplier tube (PMT) and an onboard digitizer [9]. The PMTs are
spread over 86 vertical strings arranged in a hexagonal shape, with a total
instrumented volume of approximately one cubic kilometer. The PMTs on agiven string are separated vertically by 17 m, and the string-to-string separationis roughly 125 m.
At an abstract level, the IceCube detector operates by detecting muons
as they travel through the instrumented volume of ice. As the muon travels
through the detector, it radiates light [4], which is observed by the PMTs andquantized into discrete hits [10]. The detector uses several trigger criteria. The
most commonly used trigger selects time intervals where eight PMTs (with local
coincidences) are fired within 5 microseconds. When a trigger occurs, all data
within a 10-microsecond trigger window is saved, becoming an event. If thenumber of hits in an event is sufficiently large, the muon track reconstruction
algorithm is triggered.
There are several challenges for the reconstruction algorithms used in thedetector. Varying optical properties of the ice affect reconstruction accuracy,
the data may contain outlier hits due to uncorrelated noise, and there are finite
computational resources available to tracking code run on-site.
Modeling Difficulties. The details of the ice’s optical properties are nontrivial tomodel. Light propagating through the ice is affected by scattering and absorption. These effects cannot be analytically calculated, and the optical propertiesof the ice vary with depth [5]. In addition, the Cherenkov light originates both
directly from the muon and from particles showers initiated by stochastic energy
losses of the muon.
Noise. The noise inherent in the data is another challenge. Noise hits canarise, either from the thermal background of the photocathode or from photons
generated by radioactive decay inside the PMT [9].

225Computational Constraints. The reconstruction algorithms are also limited incomplexity by the computing resources available at the South Pole. The trackreconstruction algorithm has to process about 3,000 muons per second, so algorithms with excessive computational demands are discouraged.

226

3. Reconstruction Improvement

222
223
224

227
228
229

As shown in the following, augmenting the reconstruction algorithm withsome basic filters and classical data analysis techniques results in significant
improvement in the reconstruction algorithm’s accuracy.

6

Linefit
Reconstruction

Initial Data
y

y
x

SPE
Reconstruction
y
x

x
z

z

z

Figure 2: The reconstruction pipeline used to process data in the IceCube detector. Afterinitial data are collected, it is then processed by some basic noise filters, which remove clear
outliers. This cleaned data are processed by a basic reconstruction algorithm (solid line),
which is used as the seed for the more sophisticated reconstruction algorithm (dashed line).
The sophisticated reconstruction is then evaluated as a potential neutrino. The work presented
in this manuscript makes changes to the basic reconstruction step (indicated by the dashed
box).

230
231
232
233
234
235
236
237
238
239
240
241

3.1. Prior IceCube Software
The muon track reconstruction process (outlined in Figure 2) starts when thenumber of detected hits exceeds a preset threshold and initiates data collection.
After the initial data are collected, the event then passes through a series ofbasic filters to remove obvious outliers [11].
This is followed by a basic reconstruction algorithm, linefit [12], that disregards the Cherenkov cone and, instead, finds the track that minimizes thesum of the squares of the distances between the track and the hits. More formally, assume there are N hits; denote the position and time of the ith hit as~xi and ti , respectively. Let the reconstructed muon track have a velocity of ~v ,and let the reconstructed track pass through point ~x0 at time t0 . Then, linefit
reconstruction solves the least-squares optimization problem:
min

t0 ,~
x0 ,~
v
242

N
X

ρi (t0 , ~x0 , ~v )2 ,where
ρi (t0 , ~x0 , ~v ) = k~v (ti − t0 ) + ~x0 − ~xi k2 .

243
244
245
246
247
248
249
250
251

(1)

i=1

(2)

Linefit is an approximation primarily used to generate an initial track or seed
for a more sophisticated reconstruction.
The reconstruction algorithm for the sophisticated reconstruction is SinglePhoto-Electron-Fit (SPE fit) [3]. SPE fit uses the least-squares reconstruction,
the event data, and a parameterized probability distribution function of scattering in ice [3] to reconstruct the muon track. The SPE fit is the primaryreconstruction algorithm used in the initial data selection and filtering run atthe detector site, and the fit serves as a seed track to the more complex reconstructions used in off-site data analyses.
7

252
253
254
255
256
257
258
259
260
261

262
263
264
265
266
267
268
269

270
271
272
273

274
275
276
277
278
279
280
281
282
283
284
285
286

287
288
289
290
291
292

3.2. Algorithm Improvement
If angular deviations of the initial seed are large (>5-10 degrees), the simple
subsequent reconstruction, SPE, often does not converge to the global minimum,
and the efficiency is degraded. This can be resolved by more advanced but
time-consuming reconstruction algorithms or by improving the initial seed, as
described here.
As indicated in Equation 1, a least-squares fit models the muon as a single
point moving in a straight line, and hits are penalized quadratically in theirdistance from this line. Thus, there is an implicit assumption in this model:that all the hits will be near the muon. This assumption has several pitfalls:
1. It doesn’t account for the distinct Cherenkov emission profile from themuon.
2. It ignores the scattering effects of the ice medium. Some of the photons canscatter for over a microsecond, which means that when they are recorded
by a PMT, the muon will have traveled over 300 m away.
3. While the noise reduction steps remove most of the outlier noise, thenoise hits that survive can be far from the muon. Because these outliers
are given a quadratic weight, they exert a huge influence over the model.
The first two pitfalls occur because the model is incomplete and does notaccurately model the data, and the third demonstrates that the model is notrobust to noise. The solution to this is twofold: improve the model and increase
the noise robustness by replacing least squares with robust statistical techniques.
3.2.1. Improving the Model
While disregarding the Cherenkov profile is inherent to the simplified model
chosen for speed reasons, removing hits generated by photons that scattered
for a significant length of time will mitigate the effect of ignoring the photon
scattering in the ice. We found that a basic filter could identify these scatteredhits, and improve accuracy by almost a factor of two by removing them fromthe dataset.
More formally, for each hit hi , the algorithm looks at all neighboring hits
within a neighborhood of r, and if there exists a neighboring hit hj with a timestamp that is t earlier than hi , then hi is considered a scattered hit, and is
not used in the basic reconstruction algorithm. Optimal values of r and t were
found to be 156 m and 778 ns by tuning them on simulated muon data with an
E −2 power law spectrum.
3.2.2. Adding Robustness to NoiseAs described in Equation 1, the least squares model gives outliers quadratic
weight, whereas we would prefer that outliers had zero weight. There are robustmodels in classical statistics designed to marginalize outliers. We determinedthat replacing the least-squares model with a Huber fit [13] improves the reconstruction accuracy.

8

293

More formally, we replace Equation 1 with the optimization problem:
min

t0 ,~
x0 ,~
v

294

N
X

φ(ρi (t0 , ~x0 , ~v )),

(3)

i=1

where the Huber penalty function φ(ρ) is defined as 2
ρ
if ρ < µφ(ρ) ≡.
µ(2ρ − µ) if ρ ≥ µ

(4)

309

Here, ρi (t0 , ~x, ~v ) is defined in Equation 2 and µ is a constant calibrated to thedata (on simulated muon events with an E −2 power law spectrum, the optimalvalue of µ is 153 m).
The Huber penalty function has two regimes. In the near-hit regime (ρ < µ),hits are assumed to be strongly correlated with the muon’s track, and the Huber
penalty function behaves like least squares, giving these hits quadratic weight.
In the far-hit regime (ρ ≥ µ), hits are given linear weights, as they are more
likely to be noise.
In addition to its attractive robustness properties, the Huber fit’s weightassignment also has the added benefit that it inherently labels points as outliers(those with ρ ≥ µ). Thus, once the Huber fit is computed, we can go one stepfurther and simply remove the labeled outliers from the dataset. A better fit isthen obtained by computing the least-squares fit on the data with the outliers
removed. The entire algorithm has a mean runtime that is approximately six
times longer than Linefit’s mean runtime.

310

3.3. Results

295
296
297
298
299
300
301
302
303
304
305
306
307
308

311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326

The goal is to improve the accuracy of the reconstruction in order to better
separate neutrinos from cosmic rays. Thus, we present three measurements: (1)the accuracy change between linefit and the new algorithm; (2) the accuracychange when SPE is seeded with the new algorithm instead of linefit; and (3)the improvement in separation between neutrinos and cosmic rays.
To measure the improvement generated by the changes, we use the metricof median angular resolution θmed . The angular resolution of a reconstructionis the arc-distance between the reconstruction and the true track. The dataset
is drawn from simulated neutrino data and is designed to be similar to thatobserved by the detector.
We can improve the median angular resolution of the basic reconstruction
by 57.6%, as shown in Table 1. Seeding SPE with the improved basic reconstruction generates an improvement in the angular resolution of 12.9%. These
improvements in the reconstruction algorithm result in 10% fewer atmosphericmuons erroneously reconstructed as up-going, and 1% more muons correctly
reconstructed as up-going.

9

Table 1: Median angular resolution (degrees) for reconstruction improvements. The firstline is the accuracy of the prior least-squares model, and the subsequent lines are the accuracy measurements from cumulatively adding improvements into the basic reconstruction
algorithm.

Algorithm
Linefit Reconstruction (Least-Squares)
With Addition of Logical Filter
With Addition of Huber Regression
With Addition of Outlier Removal

θmed
9.917
5.205
4.672
4.211








Figure 3: In this example, an event that is clearly composed of two muons (actual tracks
shown as dashed lines) is treated as a single muon, and, thus, the reconstruction (sold line) is
inaccurate.

327

328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344

4. Coincident Event Improvements
In the second study, we look at the problem of determining when more than
one muon has entered the detector. In the most common case, a single muon
will pass though the detector and generate an event before exiting. These eventsare processed by the pipeline described in Figure 2. However, for roughly 9%of the events collected by the data collection algorithm, more than one muon
will be passing though the detector simultaneously, an occurrence known as acoincident event.
One of the primary sources of background noise in IceCube analyses is coincident background muons that have been erroneously reconstructed as neutrinos.
To see why this occurs, consider the coincident event shown in Figure 3. There
are two clear groups of hits; however, the reconstruction algorithm treats themas a single group, resulting in an erroneous reconstruction. In the ideal case,the reconstruction algorithm would identify coincident events and split them,as in Figure 4.
The challenge in this example is determining the number of muons in an
event. Our studies show that a simple spatial clustering algorithm can solve
this classification problem with less than 2% error.

10








Figure 4: Ideally, the detector would split coincident events before computing the reconstruction. Splitting the event results in more accurate reconstructions (reconstructions shown as
solid lines, true muon tracks shown as dashed lines). Note the difference in the reconstructions
compared with Figure 3.

345

4.1. Prior IceCube Software

348

Coincident events have been a concern in the IceCube analysis [14] for years,
and some software has been developed to handle coincident events. As a baselineof comparison, we use the TTrigger software, which is described in [15].

349

4.2. Algorithm Improvement

346
347

350
351
352
353

354
355
356
357
358
359

360
361
362
363

Here, we present a proximal clustering algorithm. The intuition in proximal
clustering is that points local in space and time are probably from the same
muon. The proximal clustering algorithm iterates through each pair of hits(i, j) and builds an adjacency matrix A as
1 if k∆x2 + ∆y 2 + ∆z 2 + (c∆t)2 k2 ≤ α,
Aij =
(5)
0 otherwise
where ∆x, ∆y, ∆z, and ∆t are the space and time differences between the pairof hits, and α is tuned to the data (in this application, the optimal value of
α is 450 m). The clustering can be recovered by extracting the connectedcomponents of the graph defined by A. A connected component of a graphis a subgraph such, that there exists a path between any two vertices of thissubgraph.
4.2.1. Improving the Model
When implemented naively, proximal clustering succeeded for the majorityof the events, but it failed if there was a gap in the muon track, which can occur
when the muon travels through dusty ice layers with short scattering length. If

11

364
365
366
367
368
369
370
371
372

there is a significantly large gap, the algorithm erroneously separates the hits
into two clusters.
To compensate, an additional heuristic is added, track connecting. After thedata segmentation is finished, track connecting determines if separate clusters
should be combined. It computes the mean position and time of each cluster,and connects a hypothetical muon track T between each pair of subspaces.
It checks if the speed s of the hypothetical track is within 25% of the speedof light c, and it checks that the mean distance between hits and T in bothclusters is less than 60 m. If T passes both checks, the clusters are combined.

385

4.2.2. Adding Robustness to Noise
Proximal clustering is susceptible to noise. Noise hits close to two disjoint
tracks will be considered adjacent to both tracks and, thus, can connect the two
tracks in the adjacency matrix.
One heuristic that worked well at mitigating this problem was to not use allof the hits in building the adjacency matrix. During data collection, some hits
are flagged as having a local coincidence condition, which indicates that boththey and a neighboring PMT reported a hit. These hits have a high probabilityof not being noise hits and, thus, exclusively using them to build the adjacency
matrix mitigates the problem of erroneously connecting two tracks.
After the proximal clustering algorithm has extracted the tracks from theadjacency matrix, the hits not used in the construction of the adjacency matrix
are simply assigned to the closest reconstructed track.

386

4.3. Results

373
374
375
376
377
378
379
380
381
382
383
384

387
388
389
390
391
392

393
394
395
396
397
398
399
400
401
402

There were two competing goals for coincident event detection algorithms:
the algorithm should be conservative enough that events containing single tracks
are not erroneously split, and aggressive enough that a useful fraction of coincident events are split correctly. Our algorithm is tuned to keep almost allof the single events correctly unsplit, while still correctly splitting 80% of thecoincident events.
4.3.1. Measurements
We modified the reconstruction pipeline shown in Figure 2, in between thenoise cleaning and the basic reconstruction, by adding a step for coincident event
detection, as shown in Figure 4. This step takes cleaned data and attempts toclassify the event as a single-track or multiple-track event.
We ran each algorithm on two datasets of simulated data. One dataset
comprised single-muon events, and the other dataset comprised multiple-muon
events. In each dataset, we measured the classification error E, which is thefraction of events that were misclassified. To get a global measurement, we
computed the total error Etot , defined as
Etot = wSingle ESingle + αwMultiple EMultiple .

12

(6)

Table 2: Error Rates for Classification Algorithms

Algorithm
TrivialTTrigger
Proximal clustering

ESingle %
0.0
11.5
0.2

EMultiple %
100.0
31.8
18.9

Etot %
41.5
23.7
8.0

418

For computing Etot , we use wSingle = 0.917 and wMultiple = 0.083, which isthe frequency in which single-muon and multiple-muon events appear in data
simulating the distribution of events that trigger the reconstruction algorithm.
We also include a factor of α in the weighting of the multiple-muon events. Thisfactor expresses that mischaracterizing a multiple-muon event as a single-muon
event degrades the quality of most higher-order analysis more than the reverse
mischaracterization. In our calculations, we use a value of α = 5.
We present the results for the coincident event problem by measuring how
well each algorithm performs at determining the number of subspaces in an
event.
There are two natural comparisons for the work: the prior software TTrigger,
as well as the trivial algorithm, which always classifies each event as a singletrack event. Clearly, the latter will always get the single-track events correct,
and always get the multiple-track events wrong. We provide a comparison ofthese techniques in Table 2. As shown, the new algorithm classifies the numberof muons in the detector 66% better than TTrigger.

419

5. Conclusions

403
404
405
406
407
408
409
410
411
412
413
414
415
416
417

429

We found that significant improvements can be achieved in the IceCube’s online track reconstruction by employing some classical data analysis algorithms.
Optimizing data filtering and refining the least-square model have led to significant improvements in the accuracy of the reconstruction direction. The newreconstruction software is fast enough to run on-site, and is now included in all
IceCube analyses.
We also looked at the problem of determining the number of muons in thedetector. We found that proximal clustering with some basic heuristics could
correctly determine whether an event contained a single muon or multiple muons
with less than 2% error, yielding a 66% improvement over the prior software.

430

References

420
421
422
423
424
425
426
427
428

431

432
433

[1] IceCube Collaboration, IceCube webpage, http://icecube.wisc.edu/.
[2] A. Achterberg et al., First year performance of the IceCube neutrino telescope, Astroparticle Physics 26 (3) (2006) 155–173.

13

434
435
436

437
438
439

440
441

442
443
444
445

446
447

448
449
450

451
452
453

454
455
456

457
458
459

460
461

462
463

464
465

466
467

[3] J.Ahrens et al., Muon track reconstruction and data selection techniques in
AMANDA, Nuclear Instruments and Methods in Physics Research Section
A 524 (2004) 169–194.
[4] M. G. Aartsen et al., Measurement of South Pole ice transparency with the
IceCube LED calibration system IceCube Collaboration, Nuclear Instruments and Methods in Physics Research Section A (2013) 73–89.
[5] M. Ackermann et al., Optical properties of deep glacial ice at the southpole, Journal of Geophysical Research 111 (D13) (2006) D13203.
[6] F. Hirsch, on behalf of the ATLAS collaboration, Tracking and vertexing
with the ATLAS detector at the LHC, Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment 650 (1) (2011) 218–223.
[7] R. S. Chivukulaa, M. Goldena, E. H. Simmons, Multi-jet physics at hadroncolliders, Nuclear Physics B 363 (1) (1991) 83–96.
[8] S. Ellis, J. Huston, K. Hatakeyama, P. Loch, M. Tönnesmann, Jets inhadron–hadron collisions, Progress in Particle and Nuclear Physics (60)(2008) 484–551.
[9] R. Abbasi et al., Calibration and characterization of the IceCube photomultiplier tube, Nuclear Instruments and Methods in Physics Research Section
A 618 (2010) 139–152.
[10] R. Abbasi et al., The icecube data acquisition system: Signal capture, digitization, and timestamping, Nuclear Instruments and Methods in Physics
Research Section A 601 (3) (2009) 294–316.
[11] M. Ackermann, Searches for signals from cosmic point-like sources of highenergy neutrinos in 5 years of AMANDA-II data, Ph.D. thesis, HumboldtUniversität zu Berlin (2006).
[12] V. Stenger, Track fitting for DUMAND-II Octagon Array, Tech. rep., University of Hawaii at Manoa (1990).
[13] S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University
Press, Pages 299, 2009.
[14] R. Abbasi et al., Measurement of the atmospheric neutrino energy spectrum
from 100 GeV to 400 TeV with IceCube, Physical Review D 83 (1).
[15] D. Chirkin, Measurement of the atmospheric neutrino energy spectrumwith IceCube, Proceedings of the 31st ICRC.

14